module eddy_diff 2,4
!--------------------------------------------------------------------------------- !
! !
! The University of Washington Moist Turbulence Scheme to compute eddy diffusion !
! coefficients associated with dry and moist turbulences in the whole !
! atmospheric layers. !
! !
! For detailed description of the code and its performances, see !
! !
! 1.'A new moist turbulence parametrization in the Community Atmosphere Model' !
! by Christopher S. Bretherton and Sungsu Park. J. Climate. 2009. 22. 3422-3448 !
! 2.'The University of Washington shallow convection and moist turbulence schemes !
! and their impact on climate simulations with the Community Atmosphere Model' !
! by Sungsu Park and Christopher S. Bretherton. J. Climate. 2009. 22. 3449-3469 !
! !
! For questions on the scheme and code, send an email to !
! Sungsu Park at sungsup@ucar.edu (tel: 303-497-1375) !
! Chris Bretherton at breth@washington.edu !
! !
! Developed by Chris Bretherton at the University of Washington, Seattle, WA. !
! Sungsu Park at the CGD/NCAR, Boulder, CO. !
! Last coded on May.2006, Dec.2009 by Sungsu Park. !
! !
!--------------------------------------------------------------------------------- !
use diffusion_solver
, only : vdiff_selector
use cam_history, only : outfld, addfld, phys_decomp
use cam_logfile, only : iulog
use ppgrid, only : pver
implicit none
private
save
public init_eddy_diff
public compute_eddy_diff
type(vdiff_selector) :: fieldlist_wet ! Logical switches for moist mixing ratio diffusion
type(vdiff_selector) :: fieldlist_dry ! Logical switches for dry mixing ratio diffusion
integer, parameter :: r8 = selected_real_kind(12) ! 8 byte real
! --------------------------------- !
! PBL Parameters used in the UW PBL !
! --------------------------------- !
character, parameter :: sftype = 'l' ! Method for calculating saturation fraction
character(len=4), parameter :: choice_evhc = 'maxi' ! 'orig', 'ramp', 'maxi' : recommended to be used with choice_radf
character(len=6), parameter :: choice_radf = 'maxi' ! 'orig', 'ramp', 'maxi' : recommended to be used with choice_evhc
character(len=6), parameter :: choice_SRCL = 'nonamb' ! 'origin', 'remove', 'nonamb'
character(len=6), parameter :: choice_tunl = 'rampcl' ! 'origin', 'rampsl'(Sungsu), 'rampcl'(Chris)
real(r8), parameter :: ctunl = 2._r8 ! Maximum asympt leng = ctunl*tunl when choice_tunl = 'rampsl(cl)' [ no unit ]
character(len=6), parameter :: choice_leng = 'origin' ! 'origin', 'takemn'
real(r8), parameter :: cleng = 3._r8 ! Order of 'leng' when choice_leng = 'origin' [ no unit ]
character(len=6), parameter :: choice_tkes = 'ibprod' ! 'ibprod' (include tkes in computing bprod), 'ebprod'(exclude)
! Parameters for 'sedimenttaion-entrainment feedback' for liquid stratus
! If .false., no sedimentation entrainment feedback ( i.e., use default evhc )
logical, parameter :: id_sedfact = .false.
real(r8), parameter :: ased = 9._r8 ! Valid only when id_sedfact = .true.
! --------------------------------------------------------------------------------------------------- !
! Parameters governing entrainment efficiency A = a1l(i)*evhc, evhc = 1 + a2l * a3l * L * ql / jt2slv !
! Here, 'ql' is cloud-top LWC and 'jt2slv' is the jump in 'slv' across !
! the cloud-top entrainment zone ( across two grid layers to consider full mixture ) !
! --------------------------------------------------------------------------------------------------- !
real(r8), parameter :: a1l = 0.10_r8 ! Dry entrainment efficiency for TKE closure
! a1l = 0.2*tunl*erat^-1.5, where erat = <e>/wstar^2 for dry CBL = 0.3.
real(r8), parameter :: a1i = 0.2_r8 ! Dry entrainment efficiency for wstar closure
real(r8), parameter :: ccrit = 0.5_r8 ! Minimum allowable sqrt(tke)/wstar. Used in solving cubic equation for 'ebrk'
real(r8), parameter :: wstar3factcrit = 0.5_r8 ! 1/wstar3factcrit is the maximally allowed enhancement of 'wstar3' due to entrainment.
real(r8), parameter :: a2l = 30._r8 ! Moist entrainment enhancement param (recommended range : 10~30 )
real(r8), parameter :: a3l = 0.8_r8 ! Approximation to a complicated thermodynamic parameters
real(r8), parameter :: jbumin = .001_r8 ! Minimum buoyancy jump at an entrainment jump, [m/s2]
real(r8), parameter :: evhcmax = 10._r8 ! Upper limit of evaporative enhancement factor
real(r8), parameter :: ustar_min = 0.01_r8 ! Minimum permitted value of ustar [ m/s ]
real(r8), parameter :: onet = 1._r8/3._r8 ! 1/3 power in wind gradient expression [ no unit ]
integer, parameter :: ncvmax = pver ! Max numbers of CLs (good to set to 'pver')
real(r8), parameter :: qmin = 1.e-5_r8 ! Minimum grid-mean LWC counted as clouds [kg/kg]
real(r8), parameter :: ntzero = 1.e-12_r8 ! Not zero (small positive number used in 's2')
real(r8), parameter :: b1 = 5.8_r8 ! TKE dissipation D = e^3/(b1*leng), e = b1*W.
real(r8) :: b123 ! b1**(2/3)
real(r8), parameter :: tunl = 0.085_r8 ! Asympt leng = tunl*(turb lay depth)
real(r8), parameter :: alph1 = 0.5562_r8 ! alph1~alph5 : Galperin instability function parameters
real(r8), parameter :: alph2 = -4.3640_r8 ! These coefficients are used to calculate
real(r8), parameter :: alph3 = -34.6764_r8 ! 'sh' and 'sm' from 'gh'.
real(r8), parameter :: alph4 = -6.1272_r8 !
real(r8), parameter :: alph5 = 0.6986_r8 !
real(r8), parameter :: ricrit = 0.19_r8 ! Critical Richardson number for turbulence. Can be any value >= 0.19.
real(r8), parameter :: ae = 1._r8 ! TKE transport efficiency [no unit]
real(r8), parameter :: rinc = -0.04_r8 ! Minimum W/<W> used for CL merging test
real(r8), parameter :: wpertmin = 1.e-6_r8 ! Minimum PBL eddy vertical velocity perturbation
real(r8), parameter :: wfac = 1._r8 ! Ratio of 'wpert' to sqrt(tke) for CL.
real(r8), parameter :: tfac = 1._r8 ! Ratio of 'tpert' to (w't')/wpert for CL. Same ratio also used for q
real(r8), parameter :: fak = 8.5_r8 ! Constant in surface temperature excess for stable STL. [ no unit ]
real(r8), parameter :: rcapmin = 0.1_r8 ! Minimum allowable e/<e> in a CL
real(r8), parameter :: rcapmax = 2.0_r8 ! Maximum allowable e/<e> in a CL
real(r8), parameter :: tkemax = 20._r8 ! TKE is capped at tkemax [m2/s2]
real(r8), parameter :: lambda = 0.5_r8 ! Under-relaxation factor ( 0 < lambda =< 1 )
logical, parameter :: use_kvf = .false. ! .true. (.false.) : initialize kvh/kvm = kvf ( 0. )
logical, parameter :: use_dw_surf = .true. ! Used in 'zisocl'. Default is 'true'
! If 'true', surface interfacial energy does not contribute to the CL mean
! stbility functions after finishing merging. For this case,
! 'dl2n2_surf' is only used for a merging test based on 'l2n2'
! If 'false',surface interfacial enery explicitly contribute to CL mean
! stability functions after finishing merging. For this case,
! 'dl2n2_surf' and 'dl2s2_surf' are directly used for calculating
! surface interfacial layer energetics
logical, parameter :: set_qrlzero = .false. ! .true. ( .false.) : turning-off ( on) radiative-turbulence interaction by setting qrl = 0.
! ------------------------------------- !
! PBL Parameters not used in the UW PBL !
! ------------------------------------- !
real(r8), parameter :: pblmaxp = 4.e4_r8 ! PBL max depth in pressure units.
real(r8), parameter :: zkmin = 0.01_r8 ! Minimum kneutral*f(ri).
real(r8), parameter :: betam = 15.0_r8 ! Constant in wind gradient expression.
real(r8), parameter :: betas = 5.0_r8 ! Constant in surface layer gradient expression.
real(r8), parameter :: betah = 15.0_r8 ! Constant in temperature gradient expression.
real(r8), parameter :: fakn = 7.2_r8 ! Constant in turbulent prandtl number.
real(r8), parameter :: ricr = 0.3_r8 ! Critical richardson number.
real(r8), parameter :: sffrac = 0.1_r8 ! Surface layer fraction of boundary layer
real(r8), parameter :: binm = betam*sffrac ! betam * sffrac
real(r8), parameter :: binh = betah*sffrac ! betah * sffrac
! ------------------------------------------------------- !
! PBL constants set using values from other parts of code !
! ------------------------------------------------------- !
real(r8) :: cpair ! Specific heat of dry air
real(r8) :: rair ! Gas const for dry air
real(r8) :: zvir ! rh2o/rair - 1
real(r8) :: latvap ! Latent heat of vaporization
real(r8) :: latice ! Latent heat of fusion
real(r8) :: latsub ! Latent heat of sublimation
real(r8) :: g ! Gravitational acceleration
real(r8) :: vk ! Von Karman's constant
real(r8) :: ccon ! fak * sffrac * vk
integer :: ntop_turb ! Top interface level to which turbulent vertical diffusion is applied ( = 1 )
integer :: nbot_turb ! Bottom interface level to which turbulent vertical diff is applied ( = pver )
real(r8), allocatable :: ml2(:) ! Mixing lengths squared. Not used in the UW PBL. Used for computing free air diffusivity.
CONTAINS
!============================================================================ !
! !
!============================================================================ !
subroutine init_eddy_diff( kind, pver, gravx, cpairx, rairx, zvirx, & 1,75
latvapx, laticex, ntop_eddy, nbot_eddy, hypm, vkx )
!---------------------------------------------------------------- !
! Purpose: !
! Initialize time independent constants/variables of PBL package. !
!---------------------------------------------------------------- !
use diffusion_solver, only: init_vdiff, vdiff_select
use cam_history, only: outfld, addfld, phys_decomp
implicit none
! --------- !
! Arguments !
! --------- !
integer, intent(in) :: kind ! Kind of reals being passed in
integer, intent(in) :: pver ! Number of vertical layers
integer, intent(in) :: ntop_eddy ! Top interface level to which eddy vertical diffusivity is applied ( = 1 )
integer, intent(in) :: nbot_eddy ! Bottom interface level to which eddy vertical diffusivity is applied ( = pver )
real(r8), intent(in) :: gravx ! Acceleration of gravity
real(r8), intent(in) :: cpairx ! Specific heat of dry air
real(r8), intent(in) :: rairx ! Gas constant for dry air
real(r8), intent(in) :: zvirx ! rh2o/rair - 1
real(r8), intent(in) :: latvapx ! Latent heat of vaporization
real(r8), intent(in) :: laticex ! Latent heat of fusion
real(r8), intent(in) :: hypm(pver) ! Reference pressures at midpoints
real(r8), intent(in) :: vkx ! Von Karman's constant
character(128) :: errstring ! Error status for init_vdiff
integer :: k ! Vertical loop index
if( kind .ne. r8 ) then
write(iulog,*) 'wrong KIND of reals passed to init_diffusvity -- exiting.'
stop 'init_eddy_diff'
endif
! --------------- !
! Basic constants !
! --------------- !
cpair = cpairx
rair = rairx
g = gravx
zvir = zvirx
latvap = latvapx
latice = laticex
latsub = latvap + latice
vk = vkx
ccon = fak*sffrac*vk
ntop_turb = ntop_eddy
nbot_turb = nbot_eddy
b123 = b1**(2._r8/3._r8)
! Set the square of the mixing lengths. Only for CAM3 HB PBL scheme.
! Not used for UW moist PBL. Used for free air eddy diffusivity.
allocate(ml2(pver+1))
ml2(1:ntop_turb) = 0._r8
do k = ntop_turb + 1, nbot_turb
ml2(k) = 30.0_r8**2
end do
ml2(nbot_turb+1:pver+1) = 0._r8
! Initialize diffusion solver module
call init_vdiff(r8, 1, rair, g, fieldlist_wet, fieldlist_dry, errstring)
! Select the fields which will be diffused
if(vdiff_select(fieldlist_wet,'s').ne.'') write(iulog,*) 'error: ', vdiff_select(fieldlist_wet,'s')
if(vdiff_select(fieldlist_wet,'q',1).ne.'') write(iulog,*) 'error: ', vdiff_select(fieldlist_wet,'q',1)
if(vdiff_select(fieldlist_wet,'u').ne.'') write(iulog,*) 'error: ', vdiff_select(fieldlist_wet,'u')
if(vdiff_select(fieldlist_wet,'v').ne.'') write(iulog,*) 'error: ', vdiff_select(fieldlist_wet,'v')
! ------------------------------------------------------------------- !
! Writing outputs for detailed analysis of UW moist turbulence scheme !
! ------------------------------------------------------------------- !
call addfld('UW_errorPBL', 'm2/s', 1, 'A', 'Error function of UW PBL', phys_decomp )
call addfld('UW_n2', 's-2', pver, 'A', 'Buoyancy Frequency, LI', phys_decomp )
call addfld('UW_s2', 's-2', pver, 'A', 'Shear Frequency, LI', phys_decomp )
call addfld('UW_ri', 'no', pver, 'A', 'Interface Richardson Number, I', phys_decomp )
call addfld('UW_sfuh', 'no', pver, 'A', 'Upper-Half Saturation Fraction, L', phys_decomp )
call addfld('UW_sflh', 'no', pver, 'A', 'Lower-Half Saturation Fraction, L', phys_decomp )
call addfld('UW_sfi', 'no', pver+1, 'A', 'Interface Saturation Fraction, I', phys_decomp )
call addfld('UW_cldn', 'no', pver, 'A', 'Cloud Fraction, L', phys_decomp )
call addfld('UW_qrl', 'g*W/m2', pver, 'A', 'LW cooling rate, L', phys_decomp )
call addfld('UW_ql', 'kg/kg', pver, 'A', 'ql(LWC), L', phys_decomp )
call addfld('UW_chu', 'g*kg/J', pver+1, 'A', 'Buoyancy Coefficient, chu, I', phys_decomp )
call addfld('UW_chs', 'g*kg/J', pver+1, 'A', 'Buoyancy Coefficient, chs, I', phys_decomp )
call addfld('UW_cmu', 'g/kg/kg', pver+1, 'A', 'Buoyancy Coefficient, cmu, I', phys_decomp )
call addfld('UW_cms', 'g/kg/kg', pver+1, 'A', 'Buoyancy Coefficient, cms, I', phys_decomp )
call addfld('UW_tke', 'm2/s2', pver+1, 'A', 'TKE, I', phys_decomp )
call addfld('UW_wcap', 'm2/s2', pver+1, 'A', 'Wcap, I', phys_decomp )
call addfld('UW_bprod', 'm2/s3', pver+1, 'A', 'Buoyancy production, I', phys_decomp )
call addfld('UW_sprod', 'm2/s3', pver+1, 'A', 'Shear production, I', phys_decomp )
call addfld('UW_kvh', 'm2/s', pver+1, 'A', 'Eddy diffusivity of heat, I', phys_decomp )
call addfld('UW_kvm', 'm2/s', pver+1, 'A', 'Eddy diffusivity of uv, I', phys_decomp )
call addfld('UW_pblh', 'm', 1, 'A', 'PBLH, 1', phys_decomp )
call addfld('UW_pblhp', 'Pa', 1, 'A', 'PBLH pressure, 1', phys_decomp )
call addfld('UW_tpert', 'K', 1, 'A', 'Convective T excess, 1', phys_decomp )
call addfld('UW_qpert', 'kg/kg', 1, 'A', 'Convective qt excess, I', phys_decomp )
call addfld('UW_wpert', 'm/s', 1, 'A', 'Convective W excess, I', phys_decomp )
call addfld('UW_ustar', 'm/s', 1, 'A', 'Surface Frictional Velocity, 1', phys_decomp )
call addfld('UW_tkes', 'm2/s2', 1, 'A', 'Surface TKE, 1', phys_decomp )
call addfld('UW_minpblh', 'm', 1, 'A', 'Minimum PBLH, 1', phys_decomp )
call addfld('UW_turbtype', 'no', pver+1, 'A', 'Interface Turbulence Type, I', phys_decomp )
call addfld('UW_kbase_o', 'no', ncvmax, 'A', 'Initial CL Base Exterbal Interface Index, CL', phys_decomp )
call addfld('UW_ktop_o', 'no', ncvmax, 'A', 'Initial Top Exterbal Interface Index, CL', phys_decomp )
call addfld('UW_ncvfin_o', '#', 1, 'A', 'Initial Total Number of CL regimes, CL', phys_decomp )
call addfld('UW_kbase_mg', 'no', ncvmax, 'A', 'kbase after merging, CL', phys_decomp )
call addfld('UW_ktop_mg', 'no', ncvmax, 'A', 'ktop after merging, CL', phys_decomp )
call addfld('UW_ncvfin_mg', '#', 1, 'A', 'ncvfin after merging, CL', phys_decomp )
call addfld('UW_kbase_f', 'no', ncvmax, 'A', 'Final kbase with SRCL, CL', phys_decomp )
call addfld('UW_ktop_f', 'no', ncvmax, 'A', 'Final ktop with SRCL, CL', phys_decomp )
call addfld('UW_ncvfin_f', '#', 1, 'A', 'Final ncvfin with SRCL, CL', phys_decomp )
call addfld('UW_wet', 'm/s', ncvmax, 'A', 'Entrainment rate at CL top, CL', phys_decomp )
call addfld('UW_web', 'm/s', ncvmax, 'A', 'Entrainment rate at CL base, CL', phys_decomp )
call addfld('UW_jtbu', 'm/s2', ncvmax, 'A', 'Buoyancy jump across CL top, CL', phys_decomp )
call addfld('UW_jbbu', 'm/s2', ncvmax, 'A', 'Buoyancy jump across CL base, CL', phys_decomp )
call addfld('UW_evhc', 'no', ncvmax, 'A', 'Evaporative enhancement factor, CL', phys_decomp )
call addfld('UW_jt2slv', 'J/kg', ncvmax, 'A', 'slv jump for evhc, CL', phys_decomp )
call addfld('UW_n2ht', 's-2', ncvmax, 'A', 'n2 at just below CL top interface, CL', phys_decomp )
call addfld('UW_n2hb', 's-2', ncvmax, 'A', 'n2 at just above CL base interface', phys_decomp )
call addfld('UW_lwp', 'kg/m2', ncvmax, 'A', 'LWP in the CL top layer, CL', phys_decomp )
call addfld('UW_optdepth', 'no', ncvmax, 'A', 'Optical depth of the CL top layer, CL', phys_decomp )
call addfld('UW_radfrac', 'no', ncvmax, 'A', 'Fraction of radiative cooling confined in the CL top', phys_decomp )
call addfld('UW_radf', 'm2/s3', ncvmax, 'A', 'Buoyancy production at the CL top by radf, I', phys_decomp )
call addfld('UW_wstar', 'm/s', ncvmax, 'A', 'Convective velocity, Wstar, CL', phys_decomp )
call addfld('UW_wstar3fact', 'no', ncvmax, 'A', 'Enhancement of wstar3 due to entrainment, CL', phys_decomp )
call addfld('UW_ebrk', 'm2/s2', ncvmax, 'A', 'CL-averaged TKE, CL', phys_decomp )
call addfld('UW_wbrk', 'm2/s2', ncvmax, 'A', 'CL-averaged W, CL', phys_decomp )
call addfld('UW_lbrk', 'm', ncvmax, 'A', 'CL internal thickness, CL', phys_decomp )
call addfld('UW_ricl', 'no', ncvmax, 'A', 'CL-averaged Ri, CL', phys_decomp )
call addfld('UW_ghcl', 'no', ncvmax, 'A', 'CL-averaged gh, CL', phys_decomp )
call addfld('UW_shcl', 'no', ncvmax, 'A', 'CL-averaged sh, CL', phys_decomp )
call addfld('UW_smcl', 'no', ncvmax, 'A', 'CL-averaged sm, CL', phys_decomp )
call addfld('UW_gh', 'no', pver+1, 'A', 'gh at all interfaces, I', phys_decomp )
call addfld('UW_sh', 'no', pver+1, 'A', 'sh at all interfaces, I', phys_decomp )
call addfld('UW_sm', 'no', pver+1, 'A', 'sm at all interfaces, I', phys_decomp )
call addfld('UW_ria', 'no', pver+1, 'A', 'ri at all interfaces, I', phys_decomp )
call addfld('UW_leng', 'm/s', pver+1, 'A', 'Turbulence length scale, I', phys_decomp )
return
end subroutine init_eddy_diff
!=============================================================================== !
! !
!=============================================================================== !
subroutine compute_eddy_diff( lchnk , & 1,73
pcols , pver , ncol , t , qv , ztodt , &
ql , qi , s , rpdel , cldn , qrl , wsedl , &
z , zi , pmid , pi , u , v , &
taux , tauy , shflx , qflx , wstarent , nturb , &
ustar , pblh , kvm_in , kvh_in , kvm_out , kvh_out , kvq , &
cgh , cgs , tpert , qpert , wpert , tke , bprod , &
sprod , sfi , qsat , kvinit , &
tauresx, tauresy, ksrftms , &
ipbl , kpblh , wstarPBL , turbtype, sm_aw )
!-------------------------------------------------------------------- !
! Purpose: Interface to compute eddy diffusivities. !
! Eddy diffusivities are calculated in a fully implicit way !
! through iteration process. !
! Author: Sungsu Park. August. 2006. !
! May. 2008. !
!-------------------------------------------------------------------- !
use diffusion_solver, only: compute_vdiff
use cam_history, only: outfld, addfld, phys_decomp
! use physics_types, only: physics_state
use phys_debug_util, only: phys_debug_col
use time_manager, only: is_first_step, get_nstep
implicit none
! type(physics_state) :: state ! Physics state variables
! --------------- !
! Input Variables !
! --------------- !
integer, intent(in) :: lchnk
integer, intent(in) :: pcols ! Number of atmospheric columns [ # ]
integer, intent(in) :: pver ! Number of atmospheric layers [ # ]
integer, intent(in) :: ncol ! Number of atmospheric columns [ # ]
integer, intent(in) :: nturb ! Number of iteration steps for calculating eddy diffusivity [ # ]
logical, intent(in) :: wstarent ! .true. means use the 'wstar' entrainment closure.
logical, intent(in) :: kvinit ! 'true' means time step = 1 : used for initializing kvh, kvm (uses kvf or zero)
real(r8), intent(in) :: ztodt ! Physics integration time step 2 delta-t [ s ]
real(r8), intent(in) :: t(pcols,pver) ! Temperature [K]
real(r8), intent(in) :: qv(pcols,pver) ! Water vapor specific humidity [ kg/kg ]
real(r8), intent(in) :: ql(pcols,pver) ! Liquid water specific humidity [ kg/kg ]
real(r8), intent(in) :: qi(pcols,pver) ! Ice specific humidity [ kg/kg ]
real(r8), intent(in) :: s(pcols,pver) ! Dry static energy [ J/kg ]
real(r8), intent(in) :: rpdel(pcols,pver) ! 1./pdel where 'pdel' is thickness of the layer [ Pa ]
real(r8), intent(in) :: cldn(pcols,pver) ! Stratiform cloud fraction [ fraction ]
real(r8), intent(in) :: qrl(pcols,pver) ! LW cooling rate
real(r8), intent(in) :: wsedl(pcols,pver) ! Sedimentation velocity of liquid stratus cloud droplet [ m/s ]
real(r8), intent(in) :: z(pcols,pver) ! Layer mid-point height above surface [ m ]
real(r8), intent(in) :: zi(pcols,pver+1) ! Interface height above surface [ m ]
real(r8), intent(in) :: pmid(pcols,pver) ! Layer mid-point pressure [ Pa ]
real(r8), intent(in) :: pi(pcols,pver+1) ! Interface pressure [ Pa ]
real(r8), intent(in) :: u(pcols,pver) ! Zonal velocity [ m/s ]
real(r8), intent(in) :: v(pcols,pver) ! Meridional velocity [ m/s ]
real(r8), intent(in) :: taux(pcols) ! Zonal wind stress at surface [ N/m2 ]
real(r8), intent(in) :: tauy(pcols) ! Meridional wind stress at surface [ N/m2 ]
real(r8), intent(in) :: shflx(pcols) ! Sensible heat flux at surface [ unit ? ]
real(r8), intent(in) :: qflx(pcols) ! Water vapor flux at surface [ unit ? ]
real(r8), intent(in) :: kvm_in(pcols,pver+1) ! kvm saved from last timestep [ m2/s ]
real(r8), intent(in) :: kvh_in(pcols,pver+1) ! kvh saved from last timestep [ m2/s ]
real(r8), intent(in) :: ksrftms(pcols) ! Surface drag coefficient of turbulent mountain stress [ unit ? ]
! ---------------- !
! Output Variables !
! ---------------- !
real(r8), intent(out) :: kvm_out(pcols,pver+1) ! Eddy diffusivity for momentum [ m2/s ]
real(r8), intent(out) :: kvh_out(pcols,pver+1) ! Eddy diffusivity for heat [ m2/s ]
real(r8), intent(out) :: kvq(pcols,pver+1) ! Eddy diffusivity for constituents, moisture and tracers [ m2/s ] (note not having '_out')
real(r8), intent(out) :: ustar(pcols) ! Surface friction velocity [ m/s ]
real(r8), intent(out) :: pblh(pcols) ! PBL top height [ m ]
real(r8), intent(out) :: cgh(pcols,pver+1) ! Counter-gradient term for heat [ J/kg/m ]
real(r8), intent(out) :: cgs(pcols,pver+1) ! Counter-gradient star [ cg/flux ]
real(r8), intent(out) :: tpert(pcols) ! Convective temperature excess [ K ]
real(r8), intent(out) :: qpert(pcols) ! Convective humidity excess [ kg/kg ]
real(r8), intent(out) :: wpert(pcols) ! Turbulent velocity excess [ m/s ]
real(r8), intent(out) :: tke(pcols,pver+1) ! Turbulent kinetic energy [ m2/s2 ]
real(r8), intent(out) :: bprod(pcols,pver+1) ! Buoyancy production [ m2/s3 ]
real(r8), intent(out) :: sprod(pcols,pver+1) ! Shear production [ m2/s3 ]
real(r8), intent(out) :: sfi(pcols,pver+1) ! Interfacial layer saturation fraction [ fraction ]
real(r8), intent(out) :: turbtype(pcols,pver+1) ! Turbulence type identifier at all interfaces [ no unit ]
real(r8), intent(out) :: sm_aw(pcols,pver+1) ! Normalized Galperin instability function for momentum [ no unit ]
! This is 1 when neutral condition (Ri=0), 4.964 for maximum unstable case, and 0 when Ri > Ricrit=0.19.
real(r8), intent(out) :: ipbl(pcols) ! If 1, PBL is CL, while if 0, PBL is STL.
real(r8), intent(out) :: kpblh(pcols) ! Layer index containing PBL top within or at the base interface
real(r8), intent(out) :: wstarPBL(pcols) ! Convective velocity within PBL [ m/s ]
! ---------------------- !
! Input-Output Variables !
! ---------------------- !
real(r8), intent(inout) :: tauresx(pcols) ! Residual stress to be added in vdiff to correct for turb
real(r8), intent(inout) :: tauresy(pcols) ! Stress mismatch between sfc and atm accumulated in prior timesteps
! --------------- !
! Local Variables !
! --------------- !
integer icol
integer i, k, iturb, status
integer, external :: qsat
character(128) :: errstring ! Error status for compute_vdiff
real(r8) :: tautotx(pcols) ! Total stress including tms
real(r8) :: tautoty(pcols) ! Total stress including tms
real(r8) :: kvf(pcols,pver+1) ! Free atmospheric eddy diffusivity [ m2/s ]
real(r8) :: kvm(pcols,pver+1) ! Eddy diffusivity for momentum [ m2/s ]
real(r8) :: kvh(pcols,pver+1) ! Eddy diffusivity for heat [ m2/s ]
real(r8) :: kvm_preo(pcols,pver+1) ! Eddy diffusivity for momentum [ m2/s ]
real(r8) :: kvh_preo(pcols,pver+1) ! Eddy diffusivity for heat [ m2/s ]
real(r8) :: kvm_pre(pcols,pver+1) ! Eddy diffusivity for momentum [ m2/s ]
real(r8) :: kvh_pre(pcols,pver+1) ! Eddy diffusivity for heat [ m2/s ]
real(r8) :: errorPBL(pcols) ! Error function showing whether PBL produced convergent solution or not. [ unit ? ]
real(r8) :: s2(pcols,pver) ! Shear squared, defined at interfaces except surface [ s-2 ]
real(r8) :: n2(pcols,pver) ! Buoyancy frequency, defined at interfaces except surface [ s-2 ]
real(r8) :: ri(pcols,pver) ! Richardson number, 'n2/s2', defined at interfaces except surface [ s-2 ]
real(r8) :: pblhp(pcols) ! PBL top pressure [ Pa ]
real(r8) :: minpblh(pcols) ! Minimum PBL height based on surface stress
real(r8) :: qt(pcols,pver) ! Total specific humidity [ kg/kg ]
real(r8) :: sfuh(pcols,pver) ! Saturation fraction in upper half-layer [ fraction ]
real(r8) :: sflh(pcols,pver) ! Saturation fraction in lower half-layer [ fraction ]
real(r8) :: sl(pcols,pver) ! Liquid water static energy [ J/kg ]
real(r8) :: slv(pcols,pver) ! Liquid water virtual static energy [ J/kg ]
real(r8) :: slslope(pcols,pver) ! Slope of 'sl' in each layer
real(r8) :: qtslope(pcols,pver) ! Slope of 'qt' in each layer
real(r8) :: rrho(pcols) ! Density at the lowest layer
real(r8) :: qvfd(pcols,pver) ! Specific humidity for diffusion [ kg/kg ]
real(r8) :: tfd(pcols,pver) ! Temperature for diffusion [ K ]
real(r8) :: slfd(pcols,pver) ! Liquid static energy [ J/kg ]
real(r8) :: qtfd(pcols,pver) ! Total specific humidity [ kg/kg ]
real(r8) :: qlfd(pcols,pver) ! Liquid water specific humidity for diffusion [ kg/kg ]
real(r8) :: ufd(pcols,pver) ! U-wind for diffusion [ m/s ]
real(r8) :: vfd(pcols,pver) ! V-wind for diffusion [ m/s ]
! Buoyancy coefficients : w'b' = ch * w'sl' + cm * w'qt'
real(r8) :: chu(pcols,pver+1) ! Heat buoyancy coef for dry states, defined at each interface, finally.
real(r8) :: chs(pcols,pver+1) ! Heat buoyancy coef for sat states, defined at each interface, finally.
real(r8) :: cmu(pcols,pver+1) ! Moisture buoyancy coef for dry states, defined at each interface, finally.
real(r8) :: cms(pcols,pver+1) ! Moisture buoyancy coef for sat states, defined at each interface, finally.
real(r8) :: jnk1d(pcols)
real(r8) :: jnk2d(pcols,pver+1)
real(r8) :: zero(pcols)
real(r8) :: zero2d(pcols,pver+1)
real(r8) :: es(1) ! Saturation vapor pressure
real(r8) :: qs(1) ! Saturation specific humidity
real(r8) :: gam(1) ! (L/cp)*dqs/dT
real(r8) :: ep2, templ, temps
! ------------------------------- !
! Variables for diagnostic output !
! ------------------------------- !
real(r8) :: tkes(pcols) ! TKE at surface interface [ m2/s2 ]
real(r8) :: kbase_o(pcols,ncvmax) ! Original external base interface index of CL from 'exacol'
real(r8) :: ktop_o(pcols,ncvmax) ! Original external top interface index of CL from 'exacol'
real(r8) :: ncvfin_o(pcols) ! Original number of CLs from 'exacol'
real(r8) :: kbase_mg(pcols,ncvmax) ! 'kbase' after extending-merging from 'zisocl'
real(r8) :: ktop_mg(pcols,ncvmax) ! 'ktop' after extending-merging from 'zisocl'
real(r8) :: ncvfin_mg(pcols) ! 'ncvfin' after extending-merging from 'zisocl'
real(r8) :: kbase_f(pcols,ncvmax) ! Final 'kbase' after extending-merging & including SRCL
real(r8) :: ktop_f(pcols,ncvmax) ! Final 'ktop' after extending-merging & including SRCL
real(r8) :: ncvfin_f(pcols) ! Final 'ncvfin' after extending-merging & including SRCL
real(r8) :: wet(pcols,ncvmax) ! Entrainment rate at the CL top [ m/s ]
real(r8) :: web(pcols,ncvmax) ! Entrainment rate at the CL base [ m/s ]. Set to zero if CL is based at surface.
real(r8) :: jtbu(pcols,ncvmax) ! Buoyancy jump across the CL top [ m/s2 ]
real(r8) :: jbbu(pcols,ncvmax) ! Buoyancy jump across the CL base [ m/s2 ]
real(r8) :: evhc(pcols,ncvmax) ! Evaporative enhancement factor at the CL top
real(r8) :: jt2slv(pcols,ncvmax) ! Jump of slv ( across two layers ) at CL top used only for evhc [ J/kg ]
real(r8) :: n2ht(pcols,ncvmax) ! n2 defined at the CL top interface but using sfuh(kt) instead of sfi(kt) [ s-2 ]
real(r8) :: n2hb(pcols,ncvmax) ! n2 defined at the CL base interface but using sflh(kb-1) instead of sfi(kb) [ s-2 ]
real(r8) :: lwp(pcols,ncvmax) ! LWP in the CL top layer [ kg/m2 ]
real(r8) :: opt_depth(pcols,ncvmax) ! Optical depth of the CL top layer
real(r8) :: radinvfrac(pcols,ncvmax) ! Fraction of radiative cooling confined in the top portion of CL top layer
real(r8) :: radf(pcols,ncvmax) ! Buoyancy production at the CL top due to LW radiative cooling [ m2/s3 ]
real(r8) :: wstar(pcols,ncvmax) ! Convective velocity in each CL [ m/s ]
real(r8) :: wstar3fact(pcols,ncvmax) ! Enhancement of 'wstar3' due to entrainment (inverse) [ no unit ]
real(r8) :: ebrk(pcols,ncvmax) ! Net mean TKE of CL including entrainment effect [ m2/s2 ]
real(r8) :: wbrk(pcols,ncvmax) ! Net mean normalized TKE (W) of CL, 'ebrk/b1' including entrainment effect [ m2/s2 ]
real(r8) :: lbrk(pcols,ncvmax) ! Energetic internal thickness of CL [m]
real(r8) :: ricl(pcols,ncvmax) ! CL internal mean Richardson number
real(r8) :: ghcl(pcols,ncvmax) ! Half of normalized buoyancy production of CL
real(r8) :: shcl(pcols,ncvmax) ! Galperin instability function of heat-moisture of CL
real(r8) :: smcl(pcols,ncvmax) ! Galperin instability function of mementum of CL
real(r8) :: ghi(pcols,pver+1) ! Half of normalized buoyancy production at all interfaces
real(r8) :: shi(pcols,pver+1) ! Galperin instability function of heat-moisture at all interfaces
real(r8) :: smi(pcols,pver+1) ! Galperin instability function of heat-moisture at all interfaces
real(r8) :: rii(pcols,pver+1) ! Interfacial Richardson number defined at all interfaces
real(r8) :: lengi(pcols,pver+1) ! Turbulence length scale at all interfaces [ m ]
real(r8) :: wcap(pcols,pver+1) ! Normalized TKE at all interfaces [ m2/s2 ]
! ---------- !
! Initialize !
! ---------- !
zero(:) = 0._r8
zero2d(:,:) = 0._r8
! ----------------------- !
! Main Computation Begins !
! ----------------------- !
ufd(:ncol,:) = u(:ncol,:)
vfd(:ncol,:) = v(:ncol,:)
tfd(:ncol,:) = t(:ncol,:)
qvfd(:ncol,:) = qv(:ncol,:)
qlfd(:ncol,:) = ql(:ncol,:)
do iturb = 1, nturb
! Compute total stress by including 'tms'.
! Here, in computing 'tms', we can use either iteratively changed 'ufd,vfd' or the
! initially given 'u,v' to the PBL scheme. Note that normal stress, 'taux, tauy'
! are not changed by iteration. In order to treat 'tms' in a fully implicit way,
! I am using updated wind, here.
tautotx(:ncol) = taux(:ncol) - ksrftms(:ncol) * ufd(:ncol,pver)
tautoty(:ncol) = tauy(:ncol) - ksrftms(:ncol) * vfd(:ncol,pver)
! Calculate (qt,sl,n2,s2,ri) from a given set of (t,qv,ql,qi,u,v)
call trbintd( &
pcols , pver , ncol , z , ufd , vfd , tfd , pmid , &
tautotx , tautoty , ustar , rrho , s2 , n2 , ri , zi , &
pi , cldn , qtfd , qvfd , qlfd , qi , sfi , sfuh , &
sflh , slfd , slv , slslope , qtslope , chs , chu , cms , &
cmu , minpblh , qsat )
! Save initial (i.e., before iterative diffusion) profile of (qt,sl) at each iteration.
! Only necessary for (qt,sl) not (u,v) because (qt,sl) are newly calculated variables.
if( iturb .eq. 1 ) then
qt(:ncol,:) = qtfd(:ncol,:)
sl(:ncol,:) = slfd(:ncol,:)
endif
! Get free atmosphere exchange coefficients. This 'kvf' is not used in UW moist PBL scheme
call austausch_atm( pcols, pver, ncol, ri, s2, kvf )
! Initialize kvh/kvm to send to caleddy, depending on model timestep and iteration number
! This is necessary for 'wstar-based' entrainment closure.
if( iturb .eq. 1 ) then
if( kvinit ) then
! First iteration of first model timestep : Use free tropospheric value or zero.
if( use_kvf ) then
kvh(:ncol,:) = kvf(:ncol,:)
kvm(:ncol,:) = kvf(:ncol,:)
else
kvh(:ncol,:) = 0._r8
kvm(:ncol,:) = 0._r8
endif
else
! First iteration on any model timestep except the first : Use value from previous timestep
kvh(:ncol,:) = kvh_in(:ncol,:)
kvm(:ncol,:) = kvm_in(:ncol,:)
endif
else
! Not the first iteration : Use from previous iteration
kvh(:ncol,:) = kvh_out(:ncol,:)
kvm(:ncol,:) = kvm_out(:ncol,:)
endif
! Calculate eddy diffusivity (kvh_out,kvm_out) and (tke,bprod,sprod) using
! a given (kvh,kvm) which are used only for initializing (bprod,sprod) at
! the first part of caleddy. (bprod,sprod) are fully updated at the end of
! caleddy after calculating (kvh_out,kvm_out)
call caleddy( pcols , pver , ncol , &
slfd , qtfd , qlfd , slv ,ufd , &
vfd , pi , z , zi , &
qflx , shflx , slslope , qtslope , &
chu , chs , cmu , cms ,sfuh , &
sflh , n2 , s2 , ri ,rrho , &
pblh , ustar , &
kvh , kvm , kvh_out , kvm_out , &
tpert , qpert , qrl , kvf , tke , &
wstarent , bprod , sprod , minpblh , wpert , &
tkes , turbtype , sm_aw , &
kbase_o , ktop_o , ncvfin_o , &
kbase_mg , ktop_mg , ncvfin_mg , &
kbase_f , ktop_f , ncvfin_f , &
wet , web , jtbu , jbbu , &
evhc , jt2slv , n2ht , n2hb , &
lwp , opt_depth , radinvfrac, radf , &
wstar , wstar3fact, &
ebrk , wbrk , lbrk , ricl , ghcl , &
shcl , smcl , ghi , shi , smi , &
rii , lengi , wcap , pblhp , cldn , &
ipbl , kpblh , wsedl )
! Calculate errorPBL to check whether PBL produced convergent solutions or not.
if( iturb .eq. nturb ) then
do i = 1, ncol
errorPBL(i) = 0._r8
do k = 1, pver
errorPBL(i) = errorPBL(i) + ( kvh(i,k) - kvh_out(i,k) )**2
end do
errorPBL(i) = sqrt(errorPBL(i)/pver)
end do
end if
! Eddy diffusivities which will be used for the initialization of (bprod,
! sprod) in 'caleddy' at the next iteration step.
if( iturb .gt. 1 .and. iturb .lt. nturb ) then
kvm_out(:ncol,:) = lambda * kvm_out(:ncol,:) + ( 1._r8 - lambda ) * kvm(:ncol,:)
kvh_out(:ncol,:) = lambda * kvh_out(:ncol,:) + ( 1._r8 - lambda ) * kvh(:ncol,:)
endif
! Set nonlocal terms to zero for flux diagnostics, since not used by caleddy.
cgh(:ncol,:) = 0._r8
cgs(:ncol,:) = 0._r8
if( iturb .lt. nturb ) then
! Each time we diffuse the original state
slfd(:ncol,:) = sl(:ncol,:)
qtfd(:ncol,:) = qt(:ncol,:)
ufd(:ncol,:) = u(:ncol,:)
vfd(:ncol,:) = v(:ncol,:)
! Diffuse initial profile of each time step using a given (kvh_out,kvm_out)
! In the below 'compute_vdiff', (slfd,qtfd,ufd,vfd) are 'inout' variables.
call compute_vdiff( lchnk , &
pcols , pver , 1 , ncol , pmid , &
pi , rpdel , t , ztodt , taux , &
tauy , shflx , qflx , ntop_turb , nbot_turb , &
kvh_out , kvm_out , kvh_out , cgs , cgh , &
zi , ksrftms , zero , fieldlist_wet, &
ufd , vfd , qtfd , slfd , &
jnk1d , jnk1d , jnk2d , jnk1d , errstring , &
tauresx , tauresy , 0 , .false. )
! Retrieve (tfd,qvfd,qlfd) from (slfd,qtfd) in order to
! use 'trbintd' at the next iteration.
do k = 1, pver
do i = 1, ncol
! ----------------------------------------------------- !
! Compute the condensate 'qlfd' in the updated profiles !
! ----------------------------------------------------- !
! Option.1 : Assume grid-mean condensate is homogeneously diffused by the moist turbulence scheme.
! This should bs used if 'pseudodiff = .false.' in vertical_diffusion.F90.
! Modification : Need to be check whether below is correct in the presence of ice, qi.
! I should understand why the variation of ice, qi is neglected during diffusion.
templ = ( slfd(i,k) - g*z(i,k) ) / cpair
status = qsat( templ, pmid(i,k), es(1), qs(1), gam(1), 1 )
ep2 = .622_r8
temps = templ + ( qtfd(i,k) - qs(1) ) / ( cpair / latvap + latvap * qs(1) / ( rair * templ**2 ) )
status = qsat( temps, pmid(i,k), es(1), qs(1), gam(1), 1 )
qlfd(i,k) = max( qtfd(i,k) - qi(i,k) - qs(1) ,0._r8 )
! Option.2 : Assume condensate is not diffused by the moist turbulence scheme.
! This should bs used if 'pseudodiff = .true.' in vertical_diffusion.F90.
! qlfd(i,k) = ql(i,k)
! ----------------------------- !
! Compute the other 'qvfd, tfd' !
! ----------------------------- !
qvfd(i,k) = max( 0._r8, qtfd(i,k) - qi(i,k) - qlfd(i,k) )
tfd(i,k) = ( slfd(i,k) + latvap * qlfd(i,k) + latsub * qi(i,k) - g*z(i,k)) / cpair
end do
end do
endif
! Debug
! icol = phys_debug_col(lchnk)
! if( icol > 0 .and. get_nstep() .ge. 1 ) then
! write(iulog,*) ' '
! write(iulog,*) 'eddy_diff debug at the end of iteration'
! write(iulog,*) 't, qv, ql, cld, u, v'
! do k = pver-3, pver
! write (iulog,*) k, tfd(icol,k), qvfd(icol,k), qlfd(icol,k), cldn(icol,k), ufd(icol,k), vfd(icol,k)
! end do
! endif
! Debug
end do ! End of 'iturb' iteration
kvq(:ncol,:) = kvh_out(:ncol,:)
! Compute 'wstar' within the PBL for use in the future convection scheme.
do i = 1, ncol
if( ipbl(i) .eq. 1._r8 ) then
wstarPBL(i) = max( 0._r8, wstar(i,1) )
else
wstarPBL(i) = 0._r8
endif
end do
! --------------------------------------------------------------- !
! Writing for detailed diagnostic analysis of UW moist PBL scheme !
! --------------------------------------------------------------- !
call outfld( 'UW_errorPBL', errorPBL, pcols, lchnk )
call outfld( 'UW_n2', n2, pcols, lchnk )
call outfld( 'UW_s2', s2, pcols, lchnk )
call outfld( 'UW_ri', ri, pcols, lchnk )
call outfld( 'UW_sfuh', sfuh, pcols, lchnk )
call outfld( 'UW_sflh', sflh, pcols, lchnk )
call outfld( 'UW_sfi', sfi, pcols, lchnk )
call outfld( 'UW_cldn', cldn, pcols, lchnk )
call outfld( 'UW_qrl', qrl, pcols, lchnk )
call outfld( 'UW_ql', qlfd, pcols, lchnk )
call outfld( 'UW_chu', chu, pcols, lchnk )
call outfld( 'UW_chs', chs, pcols, lchnk )
call outfld( 'UW_cmu', cmu, pcols, lchnk )
call outfld( 'UW_cms', cms, pcols, lchnk )
call outfld( 'UW_tke', tke, pcols, lchnk )
call outfld( 'UW_wcap', wcap, pcols, lchnk )
call outfld( 'UW_bprod', bprod, pcols, lchnk )
call outfld( 'UW_sprod', sprod, pcols, lchnk )
call outfld( 'UW_kvh', kvh_out, pcols, lchnk )
call outfld( 'UW_kvm', kvm_out, pcols, lchnk )
call outfld( 'UW_pblh', pblh, pcols, lchnk )
call outfld( 'UW_pblhp', pblhp, pcols, lchnk )
call outfld( 'UW_tpert', tpert, pcols, lchnk )
call outfld( 'UW_qpert', qpert, pcols, lchnk )
call outfld( 'UW_wpert', wpert, pcols, lchnk )
call outfld( 'UW_ustar', ustar, pcols, lchnk )
call outfld( 'UW_tkes', tkes, pcols, lchnk )
call outfld( 'UW_minpblh', minpblh, pcols, lchnk )
call outfld( 'UW_turbtype', turbtype, pcols, lchnk )
call outfld( 'UW_kbase_o', kbase_o, pcols, lchnk )
call outfld( 'UW_ktop_o', ktop_o, pcols, lchnk )
call outfld( 'UW_ncvfin_o', ncvfin_o, pcols, lchnk )
call outfld( 'UW_kbase_mg', kbase_mg, pcols, lchnk )
call outfld( 'UW_ktop_mg', ktop_mg, pcols, lchnk )
call outfld( 'UW_ncvfin_mg', ncvfin_mg, pcols, lchnk )
call outfld( 'UW_kbase_f', kbase_f, pcols, lchnk )
call outfld( 'UW_ktop_f', ktop_f, pcols, lchnk )
call outfld( 'UW_ncvfin_f', ncvfin_f, pcols, lchnk )
call outfld( 'UW_wet', wet, pcols, lchnk )
call outfld( 'UW_web', web, pcols, lchnk )
call outfld( 'UW_jtbu', jtbu, pcols, lchnk )
call outfld( 'UW_jbbu', jbbu, pcols, lchnk )
call outfld( 'UW_evhc', evhc, pcols, lchnk )
call outfld( 'UW_jt2slv', jt2slv, pcols, lchnk )
call outfld( 'UW_n2ht', n2ht, pcols, lchnk )
call outfld( 'UW_n2hb', n2hb, pcols, lchnk )
call outfld( 'UW_lwp', lwp, pcols, lchnk )
call outfld( 'UW_optdepth', opt_depth, pcols, lchnk )
call outfld( 'UW_radfrac', radinvfrac, pcols, lchnk )
call outfld( 'UW_radf', radf, pcols, lchnk )
call outfld( 'UW_wstar', wstar, pcols, lchnk )
call outfld( 'UW_wstar3fact', wstar3fact, pcols, lchnk )
call outfld( 'UW_ebrk', ebrk, pcols, lchnk )
call outfld( 'UW_wbrk', wbrk, pcols, lchnk )
call outfld( 'UW_lbrk', lbrk, pcols, lchnk )
call outfld( 'UW_ricl', ricl, pcols, lchnk )
call outfld( 'UW_ghcl', ghcl, pcols, lchnk )
call outfld( 'UW_shcl', shcl, pcols, lchnk )
call outfld( 'UW_smcl', smcl, pcols, lchnk )
call outfld( 'UW_gh', ghi, pcols, lchnk )
call outfld( 'UW_sh', shi, pcols, lchnk )
call outfld( 'UW_sm', smi, pcols, lchnk )
call outfld( 'UW_ria', rii, pcols, lchnk )
call outfld( 'UW_leng', lengi, pcols, lchnk )
return
end subroutine compute_eddy_diff
!=============================================================================== !
! !
!=============================================================================== !
subroutine sfdiag( pcols , pver , ncol , qt , ql , sl , & 1
pi , pm , zi , cld , sfi , sfuh , &
sflh , slslope , qtslope , qsat )
!----------------------------------------------------------------------- !
! !
! Purpose: Interface for calculating saturation fractions at upper and !
! lower-half layers, & interfaces for use by turbulence scheme !
! !
! Method : Various but 'l' should be chosen for consistency. !
! !
! Author : B. Stevens and C. Bretherton (August 2000) !
! Sungsu Park. August 2006. !
! May. 2008. !
! !
! S.Park : The computed saturation fractions are repeatedly !
! used to compute buoyancy coefficients in'trbintd' & 'caleddy'.!
!----------------------------------------------------------------------- !
implicit none
! --------------- !
! Input arguments !
! --------------- !
integer, external :: qsat
integer, intent(in) :: pcols ! Number of atmospheric columns
integer, intent(in) :: pver ! Number of atmospheric layers
integer, intent(in) :: ncol ! Number of atmospheric columns
real(r8), intent(in) :: sl(pcols,pver) ! Liquid water static energy [ J/kg ]
real(r8), intent(in) :: qt(pcols,pver) ! Total water specific humidity [ kg/kg ]
real(r8), intent(in) :: ql(pcols,pver) ! Liquid water specific humidity [ kg/kg ]
real(r8), intent(in) :: pi(pcols,pver+1) ! Interface pressures [ Pa ]
real(r8), intent(in) :: pm(pcols,pver) ! Layer mid-point pressures [ Pa ]
real(r8), intent(in) :: zi(pcols,pver+1) ! Interface heights [ m ]
real(r8), intent(in) :: cld(pcols,pver) ! Stratiform cloud fraction [ fraction ]
real(r8), intent(in) :: slslope(pcols,pver) ! Slope of 'sl' in each layer
real(r8), intent(in) :: qtslope(pcols,pver) ! Slope of 'qt' in each layer
! ---------------- !
! Output arguments !
! ---------------- !
real(r8), intent(out) :: sfi(pcols,pver+1) ! Interfacial layer saturation fraction [ fraction ]
real(r8), intent(out) :: sfuh(pcols,pver) ! Saturation fraction in upper half-layer [ fraction ]
real(r8), intent(out) :: sflh(pcols,pver) ! Saturation fraction in lower half-layer [ fraction ]
! --------------- !
! Local Variables !
! --------------- !
integer :: i ! Longitude index
integer :: k ! Vertical index
integer :: km1 ! k-1
integer :: status ! Status returned by function calls
real(r8) :: sltop, slbot ! sl at top/bot of grid layer
real(r8) :: qttop, qtbot ! qt at top/bot of grid layer
real(r8) :: tltop(1), tlbot(1) ! Liquid water temperature at top/bot of grid layer
real(r8) :: qxtop, qxbot ! Sat excess at top/bot of grid layer
real(r8) :: qxm ! Sat excess at midpoint
real(r8) :: es(1) ! Saturation vapor pressure
real(r8) :: qs(1) ! Saturation spec. humidity
real(r8) :: gam(1) ! (L/cp)*dqs/dT
real(r8) :: cldeff(pcols,pver) ! Effective Cloud Fraction [ fraction ]
! ----------------------- !
! Main Computation Begins !
! ----------------------- !
sfi(1:ncol,:) = 0._r8
sfuh(1:ncol,:) = 0._r8
sflh(1:ncol,:) = 0._r8
cldeff(1:ncol,:) = 0._r8
select case (sftype)
case ('d')
! ----------------------------------------------------------------------- !
! Simply use the given stratus fraction ('horizontal' cloud partitioning) !
! ----------------------------------------------------------------------- !
do k = ntop_turb + 1, nbot_turb
km1 = k - 1
do i = 1, ncol
sfuh(i,k) = cld(i,k)
sflh(i,k) = cld(i,k)
sfi(i,k) = 0.5_r8 * ( sflh(i,km1) + min( sflh(i,km1), sfuh(i,k) ) )
end do
end do
do i = 1, ncol
sfi(i,pver+1) = sflh(i,pver)
end do
case ('l')
! ------------------------------------------ !
! Use modified stratus fraction partitioning !
! ------------------------------------------ !
do k = ntop_turb + 1, nbot_turb
km1 = k - 1
do i = 1, ncol
cldeff(i,k) = cld(i,k)
sfuh(i,k) = cld(i,k)
sflh(i,k) = cld(i,k)
if( ql(i,k) .lt. qmin ) then
sfuh(i,k) = 0._r8
sflh(i,k) = 0._r8
end if
! Modification : The contribution of ice should be carefully considered.
if( choice_evhc .eq. 'ramp' .or. choice_radf .eq. 'ramp' ) then
cldeff(i,k) = cld(i,k) * min( ql(i,k) / qmin, 1._r8 )
sfuh(i,k) = cldeff(i,k)
sflh(i,k) = cldeff(i,k)
elseif( choice_evhc .eq. 'maxi' .or. choice_radf .eq. 'maxi' ) then
cldeff(i,k) = cld(i,k)
sfuh(i,k) = cldeff(i,k)
sflh(i,k) = cldeff(i,k)
endif
! At the stratus top, take the minimum interfacial saturation fraction
sfi(i,k) = 0.5_r8 * ( sflh(i,km1) + min( sfuh(i,k), sflh(i,km1) ) )
! Modification : Currently sfi at the top and surface interfaces are set to be zero.
! Also, sfuh and sflh in the top model layer is set to be zero.
! However, I may need to set
! do i = 1, ncol
! sfi(i,pver+1) = sflh(i,pver)
! end do
! for treating surface-based fog.
! OK. I added below block similar to the other cases.
end do
end do
do i = 1, ncol
sfi(i,pver+1) = sflh(i,pver)
end do
case ('u')
! ------------------------------------------------------------------------- !
! Use unsaturated buoyancy - since sfi, sfuh, sflh have already been zeroed !
! nothing more need be done for this case. !
! ------------------------------------------------------------------------- !
case ('z')
! ------------------------------------------------------------------------- !
! Calculate saturation fraction based on whether the air just above or just !
! below the interface is saturated, i.e. with vertical cloud partitioning. !
! The saturation fraction of the interfacial layer between mid-points k and !
! k+1 is computed by averaging the saturation fraction of the half-layers !
! above and below the interface, with a special provision for cloud tops !
! (more cloud in the half-layer below than in the half-layer above).In each !
! half-layer, vertical partitioning of cloud based on the slopes diagnosed !
! above is used. Loop down through the layers, computing the saturation !
! fraction in each half-layer (sfuh for upper half, sflh for lower half). !
! Once sfuh(i,k) is computed, use with sflh(i,k-1) to determine saturation !
! fraction sfi(i,k) for interfacial layer k-0.5. !
! This is 'not' chosen for full consistent treatment of stratus fraction in !
! all physics schemes. !
! ------------------------------------------------------------------------- !
do k = ntop_turb + 1, nbot_turb
km1 = k - 1
do i = 1, ncol
! Compute saturation excess at the mid-point of layer k
sltop = sl(i,k) + slslope(i,k) * ( pi(i,k) - pm(i,k) )
qttop = qt(i,k) + qtslope(i,k) * ( pi(i,k) - pm(i,k) )
tltop(1) = ( sltop - g * zi(i,k) ) / cpair
status = qsat( tltop(1), pi(i,k), es(1), qs(1), gam(1), 1 )
qxtop = qttop - qs(1)
slbot = sl(i,k) + slslope(i,k) * ( pi(i,k+1) - pm(i,k) )
qtbot = qt(i,k) + qtslope(i,k) * ( pi(i,k+1) - pm(i,k) )
tlbot(1) = ( slbot - g * zi(i,k+1) ) / cpair
status = qsat( tlbot(1), pi(i,k+1), es(1), qs(1), gam(1), 1 )
qxbot = qtbot - qs(1)
qxm = qxtop + ( qxbot - qxtop ) * ( pm(i,k) - pi(i,k) ) / ( pi(i,k+1) - pi(i,k) )
! Find the saturation fraction sfuh(i,k) of the upper half of layer k.
if( ( qxtop .lt. 0._r8 ) .and. ( qxm .lt. 0._r8 ) ) then
sfuh(i,k) = 0._r8
else if( ( qxtop .gt. 0._r8 ) .and. ( qxm .gt. 0._r8 ) ) then
sfuh(i,k) = 1._r8
else ! Either qxm < 0 and qxtop > 0 or vice versa
sfuh(i,k) = max( qxtop, qxm ) / abs( qxtop - qxm )
end if
! Combine with sflh(i) (still for layer k-1) to get interfac layer saturation fraction
sfi(i,k) = 0.5_r8 * ( sflh(i,k-1) + min( sflh(i,k-1), sfuh(i,k) ) )
! Update sflh to be for the lower half of layer k.
if( ( qxbot .lt. 0._r8 ) .and. ( qxm .lt. 0._r8 ) ) then
sflh(i,k) = 0._r8
else if( ( qxbot .gt. 0._r8 ) .and. ( qxm .gt. 0._r8 ) ) then
sflh(i,k) = 1._r8
else ! Either qxm < 0 and qxbot > 0 or vice versa
sflh(i,k) = max( qxbot, qxm ) / abs( qxbot - qxm )
end if
end do ! i
end do ! k
do i = 1, ncol
sfi(i,pver+1) = sflh(i,pver) ! Saturation fraction in the lowest half-layer.
end do
end select
return
end subroutine sfdiag
!=============================================================================== !
! !
!=============================================================================== !
subroutine trbintd( pcols , pver , ncol , & 2,2
z , u , v , &
t , pmid , taux , &
tauy , ustar , rrho , &
s2 , n2 , ri , &
zi , pi , cld , &
qt , qv , ql , qi , sfi , sfuh , &
sflh , sl , slv , slslope , qtslope , &
chs , chu , cms , cmu , minpblh , qsat )
!----------------------------------------------------------------------- !
! Purpose: Calculate buoyancy coefficients at all interfaces including !
! surface. Also, computes the profiles of ( sl,qt,n2,s2,ri ). !
! Note that (n2,s2,ri) are defined at each interfaces except !
! surface. !
! !
! Author: B. Stevens ( Extracted from pbldiff, August, 2000 ) !
! Sungsu Park ( August 2006, May. 2008 ) !
!----------------------------------------------------------------------- !
implicit none
! --------------- !
! Input arguments !
! --------------- !
integer, intent(in) :: pcols ! Number of atmospheric columns
integer, intent(in) :: pver ! Number of atmospheric layers
integer, intent(in) :: ncol ! Number of atmospheric columns
real(r8), intent(in) :: z(pcols,pver) ! Layer mid-point height above surface [ m ]
real(r8), intent(in) :: u(pcols,pver) ! Layer mid-point u [ m/s ]
real(r8), intent(in) :: v(pcols,pver) ! Layer mid-point v [ m/s ]
real(r8), intent(in) :: t(pcols,pver) ! Layer mid-point temperature [ K ]
real(r8), intent(in) :: pmid(pcols,pver) ! Layer mid-point pressure [ Pa ]
real(r8), intent(in) :: taux(pcols) ! Surface u stress [ N/m2 ]
real(r8), intent(in) :: tauy(pcols) ! Surface v stress [ N/m2 ]
real(r8), intent(in) :: zi(pcols,pver+1) ! Interface height [ m ]
real(r8), intent(in) :: pi(pcols,pver+1) ! Interface pressure [ Pa ]
real(r8), intent(in) :: cld(pcols,pver) ! Stratus fraction
real(r8), intent(in) :: qv(pcols,pver) ! Water vapor specific humidity [ kg/kg ]
real(r8), intent(in) :: ql(pcols,pver) ! Liquid water specific humidity [ kg/kg ]
real(r8), intent(in) :: qi(pcols,pver) ! Ice water specific humidity [ kg/kg ]
integer, external :: qsat
! ---------------- !
! Output arguments !
! ---------------- !
real(r8), intent(out) :: ustar(pcols) ! Surface friction velocity [ m/s ]
real(r8), intent(out) :: s2(pcols,pver) ! Interfacial ( except surface ) shear squared [ s-2 ]
real(r8), intent(out) :: n2(pcols,pver) ! Interfacial ( except surface ) buoyancy frequency [ s-2 ]
real(r8), intent(out) :: ri(pcols,pver) ! Interfacial ( except surface ) Richardson number, 'n2/s2'
real(r8), intent(out) :: qt(pcols,pver) ! Total specific humidity [ kg/kg ]
real(r8), intent(out) :: sfi(pcols,pver+1) ! Interfacial layer saturation fraction [ fraction ]
real(r8), intent(out) :: sfuh(pcols,pver) ! Saturation fraction in upper half-layer [ fraction ]
real(r8), intent(out) :: sflh(pcols,pver) ! Saturation fraction in lower half-layer [ fraction ]
real(r8), intent(out) :: sl(pcols,pver) ! Liquid water static energy [ J/kg ]
real(r8), intent(out) :: slv(pcols,pver) ! Liquid water virtual static energy [ J/kg ]
real(r8), intent(out) :: chu(pcols,pver+1) ! Heat buoyancy coef for dry states at all interfaces, finally. [ unit ? ]
real(r8), intent(out) :: chs(pcols,pver+1) ! heat buoyancy coef for sat states at all interfaces, finally. [ unit ? ]
real(r8), intent(out) :: cmu(pcols,pver+1) ! Moisture buoyancy coef for dry states at all interfaces, finally. [ unit ? ]
real(r8), intent(out) :: cms(pcols,pver+1) ! Moisture buoyancy coef for sat states at all interfaces, finally. [ unit ? ]
real(r8), intent(out) :: slslope(pcols,pver) ! Slope of 'sl' in each layer
real(r8), intent(out) :: qtslope(pcols,pver) ! Slope of 'qt' in each layer
real(r8), intent(out) :: rrho(pcols) ! 1./bottom level density [ m3/kg ]
real(r8), intent(out) :: minpblh(pcols) ! Minimum PBL height based on surface stress [ m ]
! --------------- !
! Local Variables !
! --------------- !
integer :: i ! Longitude index
integer :: k, km1 ! Level index
integer :: status ! Status returned by function calls
real(r8) :: qs(pcols,pver) ! Saturation specific humidity
real(r8) :: es(pcols,pver) ! Saturation vapor pressure
real(r8) :: gam(pcols,pver) ! (l/cp)*(d(qs)/dT)
real(r8) :: rdz ! 1 / (delta z) between midpoints
real(r8) :: dsldz ! 'delta sl / delta z' at interface
real(r8) :: dqtdz ! 'delta qt / delta z' at interface
real(r8) :: ch ! 'sfi' weighted ch at the interface
real(r8) :: cm ! 'sfi' weighted cm at the interface
real(r8) :: bfact ! Buoyancy factor in n2 calculations
real(r8) :: product ! Intermediate vars used to find slopes
real(r8) :: dsldp_a, dqtdp_a ! Slopes across interface above
real(r8) :: dsldp_b(pcols), dqtdp_b(pcols) ! Slopes across interface below
! ----------------------- !
! Main Computation Begins !
! ----------------------- !
! Compute ustar, and kinematic surface fluxes from surface energy fluxes
do i = 1, ncol
rrho(i) = rair * t(i,pver) / pmid(i,pver)
ustar(i) = max( sqrt( sqrt( taux(i)**2 + tauy(i)**2 ) * rrho(i) ), ustar_min )
minpblh(i) = 100.0_r8 * ustar(i) ! By construction, 'minpblh' is larger than 1 [m] when 'ustar_min = 0.01'.
end do
! Calculate conservative scalars (qt,sl,slv) and buoyancy coefficients at the layer mid-points.
! Note that 'ntop_turb = 1', 'nbot_turb = pver'
do k = ntop_turb, nbot_turb
status = qsat( t(1,k), pmid(1,k), es(1,k), qs(1,k), gam(1,k), ncol )
do i = 1, ncol
qt(i,k) = qv(i,k) + ql(i,k) + qi(i,k)
sl(i,k) = cpair * t(i,k) + g * z(i,k) - latvap * ql(i,k) - latsub * qi(i,k)
slv(i,k) = sl(i,k) * ( 1._r8 + zvir * qt(i,k) )
! Thermodynamic coefficients for buoyancy flux - in this loop these are
! calculated at mid-points; later, they will be averaged to interfaces,
! where they will ultimately be used. At the surface, the coefficients
! are taken from the lowest mid point.
bfact = g / ( t(i,k) * ( 1._r8 + zvir * qv(i,k) - ql(i,k) - qi(i,k) ) )
chu(i,k) = ( 1._r8 + zvir * qt(i,k) ) * bfact / cpair
chs(i,k) = ( ( 1._r8 + ( 1._r8 + zvir ) * gam(i,k) * cpair * t(i,k) / latvap ) / ( 1._r8 + gam(i,k) ) ) * bfact / cpair
cmu(i,k) = zvir * bfact * t(i,k)
cms(i,k) = latvap * chs(i,k) - bfact * t(i,k)
end do
end do
do i = 1, ncol
chu(i,pver+1) = chu(i,pver)
chs(i,pver+1) = chs(i,pver)
cmu(i,pver+1) = cmu(i,pver)
cms(i,pver+1) = cms(i,pver)
end do
! Compute slopes of conserved variables sl, qt within each layer k.
! 'a' indicates the 'above' gradient from layer k-1 to layer k and
! 'b' indicates the 'below' gradient from layer k to layer k+1.
! We take a smaller (in absolute value) of these gradients as the
! slope within layer k. If they have opposite signs, gradient in
! layer k is taken to be zero. I should re-consider whether this
! profile reconstruction is the best or not.
! This is similar to the profile reconstruction used in the UWShCu.
do i = 1, ncol
! Slopes at endpoints determined by extrapolation
slslope(i,pver) = ( sl(i,pver) - sl(i,pver-1) ) / ( pmid(i,pver) - pmid(i,pver-1) )
qtslope(i,pver) = ( qt(i,pver) - qt(i,pver-1) ) / ( pmid(i,pver) - pmid(i,pver-1) )
slslope(i,1) = ( sl(i,2) - sl(i,1) ) / ( pmid(i,2) - pmid(i,1) )
qtslope(i,1) = ( qt(i,2) - qt(i,1) ) / ( pmid(i,2) - pmid(i,1) )
dsldp_b(i) = slslope(i,1)
dqtdp_b(i) = qtslope(i,1)
end do
do k = 2, pver - 1
do i = 1, ncol
dsldp_a = dsldp_b(i)
dqtdp_a = dqtdp_b(i)
dsldp_b(i) = ( sl(i,k+1) - sl(i,k) ) / ( pmid(i,k+1) - pmid(i,k) )
dqtdp_b(i) = ( qt(i,k+1) - qt(i,k) ) / ( pmid(i,k+1) - pmid(i,k) )
product = dsldp_a * dsldp_b(i)
if( product .le. 0._r8 ) then
slslope(i,k) = 0._r8
else if( product .gt. 0._r8 .and. dsldp_a .lt. 0._r8 ) then
slslope(i,k) = max( dsldp_a, dsldp_b(i) )
else if( product .gt. 0._r8 .and. dsldp_a .gt. 0._r8 ) then
slslope(i,k) = min( dsldp_a, dsldp_b(i) )
end if
product = dqtdp_a*dqtdp_b(i)
if( product .le. 0._r8 ) then
qtslope(i,k) = 0._r8
else if( product .gt. 0._r8 .and. dqtdp_a .lt. 0._r8 ) then
qtslope(i,k) = max( dqtdp_a, dqtdp_b(i) )
else if( product .gt. 0._r8 .and. dqtdp_a .gt. 0._r8 ) then
qtslope(i,k) = min( dqtdp_a, dqtdp_b(i) )
end if
end do ! i
end do ! k
! Compute saturation fraction at the interfacial layers for use in buoyancy
! flux computation.
call sfdiag( pcols , pver , ncol , qt , ql , sl , &
pi , pmid , zi , cld , sfi , sfuh , &
sflh , slslope , qtslope , qsat )
! Calculate buoyancy coefficients at all interfaces (1:pver+1) and (n2,s2,ri)
! at all interfaces except surface. Note 'nbot_turb = pver', 'ntop_turb = 1'.
! With the previous definition of buoyancy coefficients at the surface, the
! resulting buoyancy coefficients at the top and surface interfaces becomes
! identical to the buoyancy coefficients at the top and bottom layers. Note
! that even though the dimension of (s2,n2,ri) is 'pver', they are defined
! at interfaces ( not at the layer mid-points ) except the surface.
do k = nbot_turb, ntop_turb + 1, -1
km1 = k - 1
do i = 1, ncol
rdz = 1._r8 / ( z(i,km1) - z(i,k) )
dsldz = ( sl(i,km1) - sl(i,k) ) * rdz
dqtdz = ( qt(i,km1) - qt(i,k) ) * rdz
chu(i,k) = ( chu(i,km1) + chu(i,k) ) * 0.5_r8
chs(i,k) = ( chs(i,km1) + chs(i,k) ) * 0.5_r8
cmu(i,k) = ( cmu(i,km1) + cmu(i,k) ) * 0.5_r8
cms(i,k) = ( cms(i,km1) + cms(i,k) ) * 0.5_r8
ch = chu(i,k) * ( 1._r8 - sfi(i,k) ) + chs(i,k) * sfi(i,k)
cm = cmu(i,k) * ( 1._r8 - sfi(i,k) ) + cms(i,k) * sfi(i,k)
n2(i,k) = ch * dsldz + cm * dqtdz
s2(i,k) = ( ( u(i,km1) - u(i,k) )**2 + ( v(i,km1) - v(i,k) )**2) * rdz**2
s2(i,k) = max( ntzero, s2(i,k) )
ri(i,k) = n2(i,k) / s2(i,k)
end do
end do
do i = 1, ncol
n2(i,1) = n2(i,2)
s2(i,1) = s2(i,2)
ri(i,1) = ri(i,2)
end do
return
end subroutine trbintd
!=============================================================================== !
! !
!=============================================================================== !
subroutine austausch_atm( pcols, pver, ncol, ri, s2, kvf ) 2
!---------------------------------------------------------------------- !
! !
! Purpose: Computes exchange coefficients for free turbulent flows. !
! This is not used in the UW moist turbulence scheme. !
! !
! Method: !
! !
! The free atmosphere diffusivities are based on standard mixing length !
! forms for the neutral diffusivity multiplied by functns of Richardson !
! number. K = l^2 * |dV/dz| * f(Ri). The same functions are used for !
! momentum, potential temperature, and constitutents. !
! !
! The stable Richardson num function (Ri>0) is taken from Holtslag and !
! Beljaars (1989), ECMWF proceedings. f = 1 / (1 + 10*Ri*(1 + 8*Ri)) !
! The unstable Richardson number function (Ri<0) is taken from CCM1. !
! f = sqrt(1 - 18*Ri) !
! !
! Author: B. Stevens (rewrite, August 2000) !
! !
!---------------------------------------------------------------------- !
implicit none
! --------------- !
! Input arguments !
! --------------- !
integer, intent(in) :: pcols ! Number of atmospheric columns
integer, intent(in) :: pver ! Number of atmospheric layers
integer, intent(in) :: ncol ! Number of atmospheric columns
real(r8), intent(in) :: s2(pcols,pver) ! Shear squared
real(r8), intent(in) :: ri(pcols,pver) ! Richardson no
! ---------------- !
! Output arguments !
! ---------------- !
real(r8), intent(out) :: kvf(pcols,pver+1) ! Eddy diffusivity for heat and tracers
! --------------- !
! Local Variables !
! --------------- !
real(r8) :: fofri ! f(ri)
real(r8) :: kvn ! Neutral Kv
integer :: i ! Longitude index
integer :: k ! Vertical index
! ----------------------- !
! Main Computation Begins !
! ----------------------- !
kvf(:ncol,:) = 0.0_r8
kvf(:ncol,pver+1) = 0.0_r8
kvf(:ncol,1:ntop_turb) = 0.0_r8
! Compute the free atmosphere vertical diffusion coefficients: kvh = kvq = kvm.
do k = ntop_turb + 1, nbot_turb
do i = 1, ncol
if( ri(i,k) < 0.0_r8 ) then
fofri = sqrt( max( 1._r8 - 18._r8 * ri(i,k), 0._r8 ) )
else
fofri = 1.0_r8 / ( 1.0_r8 + 10.0_r8 * ri(i,k) * ( 1.0_r8 + 8.0_r8 * ri(i,k) ) )
end if
kvn = ml2(k) * sqrt(s2(i,k))
kvf(i,k) = max( zkmin, kvn * fofri )
end do
end do
return
end subroutine austausch_atm
! ---------------------------------------------------------------------------- !
! !
! The University of Washington Moist Turbulence Scheme !
! !
! Authors : Chris Bretherton at the University of Washington, Seattle, WA !
! Sungsu Park at the CGD/NCAR, Boulder, CO !
! !
! ---------------------------------------------------------------------------- !
subroutine caleddy( pcols , pver , ncol , & 1,5
sl , qt , ql , slv , u , &
v , pi , z , zi , &
qflx , shflx , slslope , qtslope , &
chu , chs , cmu , cms , sfuh , &
sflh , n2 , s2 , ri , rrho , &
pblh , ustar , &
kvh_in , kvm_in , kvh , kvm , &
tpert , qpert , qrlin , kvf , tke , &
wstarent , bprod , sprod , minpblh , wpert , &
tkes , turbtype_f , sm_aw , &
kbase_o , ktop_o , ncvfin_o , &
kbase_mg , ktop_mg , ncvfin_mg , &
kbase_f , ktop_f , ncvfin_f , &
wet_CL , web_CL , jtbu_CL , jbbu_CL , &
evhc_CL , jt2slv_CL , n2ht_CL , n2hb_CL , lwp_CL , &
opt_depth_CL , radinvfrac_CL, radf_CL , wstar_CL , wstar3fact_CL, &
ebrk , wbrk , lbrk , ricl , ghcl , &
shcl , smcl , &
gh_a , sh_a , sm_a , ri_a , leng , &
wcap , pblhp , cld , ipbl , kpblh , &
wsedl )
!--------------------------------------------------------------------------------- !
! !
! Purpose : This is a driver routine to compute eddy diffusion coefficients !
! for heat (sl), momentum (u, v), moisture (qt), and other trace !
! constituents. This scheme uses first order closure for stable !
! turbulent layers (STL). For convective layers (CL), entrainment !
! closure is used at the CL external interfaces, which is coupled !
! to the diagnosis of a CL regime mean TKE from the instantaneous !
! thermodynamic and velocity profiles. The CLs are diagnosed by !
! extending original CL layers of moist static instability into !
! adjacent weakly stably stratified interfaces, stopping if the !
! stability is too strong. This allows a realistic depiction of !
! dry convective boundary layers with a downgradient approach. !
! !
! NOTE: This routine currently assumes ntop_turb = 1, nbot_turb = pver !
! ( turbulent diffusivities computed at all interior interfaces ) !
! and will require modification to handle a different ntop_turb. !
! !
! Authors: Sungsu Park and Chris Bretherton. 08/2006, 05/2008. !
! !
! For details, see !
! !
! 1. 'A new moist turbulence parametrization in the Community Atmosphere Model' !
! by Christopher S. Bretherton & Sungsu Park. J. Climate. 22. 3422-3448. 2009. !
! !
! 2. 'The University of Washington shallow convection and moist turbulence schemes !
! and their impact on climate simulations with the Community Atmosphere Model' !
! by Sungsu Park & Christopher S. Bretherton. J. Climate. 22. 3449-3469. 2009. !
! !
! For questions on the scheme and code, send an email to !
! sungsup@ucar.edu or breth@washington.edu !
! !
!--------------------------------------------------------------------------------- !
! ---------------- !
! Inputs variables !
! ---------------- !
implicit none
integer, intent(in) :: pcols ! Number of atmospheric columns
integer, intent(in) :: pver ! Number of atmospheric layers
integer, intent(in) :: ncol ! Number of atmospheric columns
real(r8), intent(in) :: u(pcols,pver) ! U wind [ m/s ]
real(r8), intent(in) :: v(pcols,pver) ! V wind [ m/s ]
real(r8), intent(in) :: sl(pcols,pver) ! Liquid water static energy, cp * T + g * z - Lv * ql - Ls * qi [ J/kg ]
real(r8), intent(in) :: slv(pcols,pver) ! Liquid water virtual static energy, sl * ( 1 + 0.608 * qt ) [ J/kg ]
real(r8), intent(in) :: qt(pcols,pver) ! Total speccific humidity qv + ql + qi [ kg/kg ]
real(r8), intent(in) :: ql(pcols,pver) ! Liquid water specific humidity [ kg/kg ]
real(r8), intent(in) :: pi(pcols,pver+1) ! Interface pressures [ Pa ]
real(r8), intent(in) :: z(pcols,pver) ! Layer midpoint height above surface [ m ]
real(r8), intent(in) :: zi(pcols,pver+1) ! Interface height above surface, i.e., zi(pver+1) = 0 all over the globe [ m ]
real(r8), intent(in) :: chu(pcols,pver+1) ! Buoyancy coeffi. unsaturated sl (heat) coef. at all interfaces. [ unit ? ]
real(r8), intent(in) :: chs(pcols,pver+1) ! Buoyancy coeffi. saturated sl (heat) coef. at all interfaces. [ unit ? ]
real(r8), intent(in) :: cmu(pcols,pver+1) ! Buoyancy coeffi. unsaturated qt (moisture) coef. at all interfaces [ unit ? ]
real(r8), intent(in) :: cms(pcols,pver+1) ! Buoyancy coeffi. saturated qt (moisture) coef. at all interfaces [ unit ? ]
real(r8), intent(in) :: sfuh(pcols,pver) ! Saturation fraction in upper half-layer [ fraction ]
real(r8), intent(in) :: sflh(pcols,pver) ! Saturation fraction in lower half-layer [ fraction ]
real(r8), intent(in) :: n2(pcols,pver) ! Interfacial (except surface) moist buoyancy frequency [ s-2 ]
real(r8), intent(in) :: s2(pcols,pver) ! Interfacial (except surface) shear frequency [ s-2 ]
real(r8), intent(in) :: ri(pcols,pver) ! Interfacial (except surface) Richardson number
real(r8), intent(in) :: qflx(pcols) ! Kinematic surface constituent ( water vapor ) flux [ kg/m2/s ]
real(r8), intent(in) :: shflx(pcols) ! Kinematic surface heat flux [ unit ? ]
real(r8), intent(in) :: slslope(pcols,pver) ! Slope of 'sl' in each layer [ J/kg/Pa ]
real(r8), intent(in) :: qtslope(pcols,pver) ! Slope of 'qt' in each layer [ kg/kg/Pa ]
real(r8), intent(in) :: qrlin(pcols,pver) ! Input grid-mean LW heating rate : [ K/s ] * cpair * dp = [ W/kg*Pa ]
real(r8), intent(in) :: wsedl(pcols,pver) ! Sedimentation velocity of liquid stratus cloud droplet [ m/s ]
real(r8), intent(in) :: ustar(pcols) ! Surface friction velocity [ m/s ]
real(r8), intent(in) :: rrho(pcols) ! 1./bottom mid-point density. Specific volume [ m3/kg ]
real(r8), intent(in) :: kvf(pcols,pver+1) ! Free atmosphere eddy diffusivity [ m2/s ]
logical, intent(in) :: wstarent ! Switch for choosing wstar3 entrainment parameterization
real(r8), intent(in) :: minpblh(pcols) ! Minimum PBL height based on surface stress [ m ]
real(r8), intent(in) :: kvh_in(pcols,pver+1) ! kvh saved from last timestep or last iterative step [ m2/s ]
real(r8), intent(in) :: kvm_in(pcols,pver+1) ! kvm saved from last timestep or last iterative step [ m2/s ]
real(r8), intent(in) :: cld(pcols,pver) ! Stratus Cloud Fraction [ fraction ]
! ---------------- !
! Output variables !
! ---------------- !
real(r8), intent(out) :: kvh(pcols,pver+1) ! Eddy diffusivity for heat, moisture, and tracers [ m2/s ]
real(r8), intent(out) :: kvm(pcols,pver+1) ! Eddy diffusivity for momentum [ m2/s ]
real(r8), intent(out) :: pblh(pcols) ! PBL top height [ m ]
real(r8), intent(out) :: pblhp(pcols) ! PBL top height pressure [ Pa ]
real(r8), intent(out) :: tpert(pcols) ! Convective temperature excess [ K ]
real(r8), intent(out) :: qpert(pcols) ! Convective humidity excess [ kg/kg ]
real(r8), intent(out) :: wpert(pcols) ! Turbulent velocity excess [ m/s ]
real(r8), intent(out) :: tke(pcols,pver+1) ! Turbulent kinetic energy [ m2/s2 ], 'tkes' at surface, pver+1.
real(r8), intent(out) :: bprod(pcols,pver+1) ! Buoyancy production [ m2/s3 ], 'bflxs' at surface, pver+1.
real(r8), intent(out) :: sprod(pcols,pver+1) ! Shear production [ m2/s3 ], (ustar(i)**3)/(vk*z(i,pver)) at surface, pver+1.
real(r8), intent(out) :: turbtype_f(pcols,pver+1) ! Turbulence type at each interface:
! 0. = Non turbulence interface
! 1. = Stable turbulence interface
! 2. = CL interior interface ( if bflxs > 0, surface is this )
! 3. = Bottom external interface of CL
! 4. = Top external interface of CL.
! 5. = Double entraining CL external interface
real(r8), intent(out) :: sm_aw(pcols,pver+1) ! Galperin instability function of momentum for use in the microphysics [ no unit ]
real(r8), intent(out) :: ipbl(pcols) ! If 1, PBL is CL, while if 0, PBL is STL.
real(r8), intent(out) :: kpblh(pcols) ! Layer index containing PBL within or at the base interface
! --------------------------- !
! Diagnostic output variables !
! --------------------------- !
real(r8) :: tkes(pcols) ! TKE at surface [ m2/s2 ]
real(r8) :: kbase_o(pcols,ncvmax) ! Original external base interface index of CL just after 'exacol'
real(r8) :: ktop_o(pcols,ncvmax) ! Original external top interface index of CL just after 'exacol'
real(r8) :: ncvfin_o(pcols) ! Original number of CLs just after 'exacol'
real(r8) :: kbase_mg(pcols,ncvmax) ! kbase just after extending-merging (after 'zisocl') but without SRCL
real(r8) :: ktop_mg(pcols,ncvmax) ! ktop just after extending-merging (after 'zisocl') but without SRCL
real(r8) :: ncvfin_mg(pcols) ! ncvfin just after extending-merging (after 'zisocl') but without SRCL
real(r8) :: kbase_f(pcols,ncvmax) ! Final kbase after adding SRCL
real(r8) :: ktop_f(pcols,ncvmax) ! Final ktop after adding SRCL
real(r8) :: ncvfin_f(pcols) ! Final ncvfin after adding SRCL
real(r8) :: wet_CL(pcols,ncvmax) ! Entrainment rate at the CL top [ m/s ]
real(r8) :: web_CL(pcols,ncvmax) ! Entrainment rate at the CL base [ m/s ]
real(r8) :: jtbu_CL(pcols,ncvmax) ! Buoyancy jump across the CL top [ m/s2 ]
real(r8) :: jbbu_CL(pcols,ncvmax) ! Buoyancy jump across the CL base [ m/s2 ]
real(r8) :: evhc_CL(pcols,ncvmax) ! Evaporative enhancement factor at the CL top
real(r8) :: jt2slv_CL(pcols,ncvmax) ! Jump of slv ( across two layers ) at CL top for use only in evhc [ J/kg ]
real(r8) :: n2ht_CL(pcols,ncvmax) ! n2 defined at the CL top interface but using sfuh(kt) instead of sfi(kt) [ s-2 ]
real(r8) :: n2hb_CL(pcols,ncvmax) ! n2 defined at the CL base interface but using sflh(kb-1) instead of sfi(kb) [ s-2 ]
real(r8) :: lwp_CL(pcols,ncvmax) ! LWP in the CL top layer [ kg/m2 ]
real(r8) :: opt_depth_CL(pcols,ncvmax) ! Optical depth of the CL top layer
real(r8) :: radinvfrac_CL(pcols,ncvmax) ! Fraction of LW radiative cooling confined in the top portion of CL
real(r8) :: radf_CL(pcols,ncvmax) ! Buoyancy production at the CL top due to radiative cooling [ m2/s3 ]
real(r8) :: wstar_CL(pcols,ncvmax) ! Convective velocity of CL including entrainment contribution finally [ m/s ]
real(r8) :: wstar3fact_CL(pcols,ncvmax) ! "wstar3fact" of CL. Entrainment enhancement of wstar3 (inverse)
real(r8) :: gh_a(pcols,pver+1) ! Half of normalized buoyancy production, -l2n2/2e. [ no unit ]
real(r8) :: sh_a(pcols,pver+1) ! Galperin instability function of heat-moisture at all interfaces [ no unit ]
real(r8) :: sm_a(pcols,pver+1) ! Galperin instability function of momentum at all interfaces [ no unit ]
real(r8) :: ri_a(pcols,pver+1) ! Interfacial Richardson number at all interfaces [ no unit ]
real(r8) :: ebrk(pcols,ncvmax) ! Net CL mean TKE [ m2/s2 ]
real(r8) :: wbrk(pcols,ncvmax) ! Net CL mean normalized TKE [ m2/s2 ]
real(r8) :: lbrk(pcols,ncvmax) ! Net energetic integral thickness of CL [ m ]
real(r8) :: ricl(pcols,ncvmax) ! Mean Richardson number of CL ( l2n2/l2s2 )
real(r8) :: ghcl(pcols,ncvmax) ! Half of normalized buoyancy production of CL
real(r8) :: shcl(pcols,ncvmax) ! Instability function of heat and moisture of CL
real(r8) :: smcl(pcols,ncvmax) ! Instability function of momentum of CL
real(r8) :: leng(pcols,pver+1) ! Turbulent length scale [ m ], 0 at the surface.
real(r8) :: wcap(pcols,pver+1) ! Normalized TKE [m2/s2], 'tkes/b1' at the surface and 'tke/b1' at
! the top/bottom entrainment interfaces of CL assuming no transport.
! ------------------------ !
! Local Internal Variables !
! ------------------------ !
logical :: belongcv(pcols,pver+1) ! True for interfaces in a CL (both interior and exterior are included)
logical :: belongst(pcols,pver+1) ! True for stable turbulent layer interfaces (STL)
logical :: in_CL ! True if interfaces k,k+1 both in same CL.
logical :: extend ! True when CL is extended in zisocl
logical :: extend_up ! True when CL is extended upward in zisocl
logical :: extend_dn ! True when CL is extended downward in zisocl
integer :: i ! Longitude index
integer :: k ! Vertical index
integer :: ks ! Vertical index
integer :: ncvfin(pcols) ! Total number of CL in column
integer :: ncvf ! Total number of CL in column prior to adding SRCL
integer :: ncv ! Index of current CL
integer :: ncvnew ! Index of added SRCL appended after regular CLs from 'zisocl'
integer :: ncvsurf ! If nonzero, CL index based on surface (usually 1, but can be > 1 when SRCL is based at sfc)
integer :: kbase(pcols,ncvmax) ! Vertical index of CL base interface
integer :: ktop(pcols,ncvmax) ! Vertical index of CL top interface
integer :: kb, kt ! kbase and ktop for current CL
integer :: ktblw ! ktop of the CL located at just below the current CL
integer :: turbtype(pcols,pver+1) ! Interface turbulence type :
! 0 = Non turbulence interface
! 1 = Stable turbulence interface
! 2 = CL interior interface ( if bflxs > 0, sfc is this )
! 3 = Bottom external interface of CL
! 4 = Top external interface of CL
! 5 = Double entraining CL external interface
integer :: ktopbl(pcols) ! PBL top height or interface index
real(r8) :: bflxs(pcols) ! Surface buoyancy flux [ m2/s3 ]
real(r8) :: rcap ! 'tke/ebrk' at all interfaces of CL. Set to 1 at the CL entrainment interfaces
real(r8) :: jtzm ! Interface layer thickness of CL top interface [ m ]
real(r8) :: jtsl ! Jump of s_l across CL top interface [ J/kg ]
real(r8) :: jtqt ! Jump of q_t across CL top interface [ kg/kg ]
real(r8) :: jtbu ! Jump of buoyancy across CL top interface [ m/s2 ]
real(r8) :: jtu ! Jump of u across CL top interface [ m/s ]
real(r8) :: jtv ! Jump of v across CL top interface [ m/s ]
real(r8) :: jt2slv ! Jump of slv ( across two layers ) at CL top for use only in evhc [ J/kg ]
real(r8) :: radf ! Buoyancy production at the CL top due to radiative cooling [ m2/s3 ]
real(r8) :: jbzm ! Interface layer thickness of CL base interface [ m ]
real(r8) :: jbsl ! Jump of s_l across CL base interface [ J/kg ]
real(r8) :: jbqt ! Jump of q_t across CL top interface [ kg/kg ]
real(r8) :: jbbu ! Jump of buoyancy across CL base interface [ m/s2 ]
real(r8) :: jbu ! Jump of u across CL base interface [ m/s ]
real(r8) :: jbv ! Jump of v across CL base interface [ m/s ]
real(r8) :: ch ! Buoyancy coefficients defined at the CL top and base interfaces using CL internal
real(r8) :: cm ! sfuh(kt) and sflh(kb-1) instead of sfi(kt) and sfi(kb), respectively. These are
! used for entrainment calculation at CL external interfaces and SRCL identification.
real(r8) :: n2ht ! n2 defined at the CL top interface but using sfuh(kt) instead of sfi(kt) [ s-2 ]
real(r8) :: n2hb ! n2 defined at the CL base interface but using sflh(kb-1) instead of sfi(kb) [ s-2 ]
real(r8) :: n2htSRCL ! n2 defined at the upper-half layer of SRCL. This is used only for identifying SRCL.
! n2htSRCL use SRCL internal slope sl and qt as well as sfuh(kt) instead of sfi(kt) [ s-2 ]
real(r8) :: gh ! Half of normalized buoyancy production ( -l2n2/2e ) [ no unit ]
real(r8) :: sh ! Galperin instability function for heat and moisture
real(r8) :: sm ! Galperin instability function for momentum
real(r8) :: lbulk ! Depth of turbulent layer, Master length scale (not energetic length)
real(r8) :: dzht ! Thickness of top half-layer [ m ]
real(r8) :: dzhb ! Thickness of bottom half-layer [ m ]
real(r8) :: rootp ! Sqrt(net CL-mean TKE including entrainment contribution) [ m/s ]
real(r8) :: evhc ! Evaporative enhancement factor: (1+E) with E = evap. cool. efficiency [ no unit ]
real(r8) :: kentr ! Effective entrainment diffusivity 'wet*dz', 'web*dz' [ m2/s ]
real(r8) :: lwp ! Liquid water path in the layer kt [ kg/m2 ]
real(r8) :: opt_depth ! Optical depth of the layer kt [ no unit ]
real(r8) :: radinvfrac ! Fraction of LW cooling in the layer kt concentrated at the CL top [ no unit ]
real(r8) :: wet ! CL top entrainment rate [ m/s ]
real(r8) :: web ! CL bot entrainment rate [ m/s ]. Set to zero if CL is based at surface.
real(r8) :: vyt ! n2ht/n2 at the CL top interface
real(r8) :: vyb ! n2hb/n2 at the CL base interface
real(r8) :: vut ! Inverse Ri (=s2/n2) at the CL top interface
real(r8) :: vub ! Inverse Ri (=s2/n2) at the CL base interface
real(r8) :: fact ! Factor relating TKE generation to entrainment [ no unit ]
real(r8) :: trma ! Intermediate variables used for solving quadratic ( for gh from ri )
real(r8) :: trmb ! and cubic equations ( for ebrk: the net CL mean TKE )
real(r8) :: trmc !
real(r8) :: trmp !
real(r8) :: trmq !
real(r8) :: qq !
real(r8) :: det !
real(r8) :: gg ! Intermediate variable used for calculating stability functions of
! SRCL or SBCL based at the surface with bflxs > 0.
real(r8) :: dzhb5 ! Half thickness of the bottom-most layer of current CL regime
real(r8) :: dzht5 ! Half thickness of the top-most layer of adjacent CL regime just below current CL
real(r8) :: qrlw(pcols,pver) ! Local grid-mean LW heating rate : [K/s] * cpair * dp = [ W/kg*Pa ]
real(r8) :: cldeff(pcols,pver) ! Effective stratus fraction
real(r8) :: qleff ! Used for computing evhc
real(r8) :: tunlramp ! Ramping tunl
real(r8) :: leng_imsi ! For Kv = max(Kv_STL, Kv_entrain)
real(r8) :: tke_imsi !
real(r8) :: kvh_imsi !
real(r8) :: kvm_imsi !
real(r8) :: alph4exs ! For extended stability function in the stable regime
real(r8) :: ghmin !
real(r8) :: sedfact ! For 'sedimentation-entrainment feedback'
! Local variables specific for 'wstar' entrainment closure
real(r8) :: cet ! Proportionality coefficient between wet and wstar3
real(r8) :: ceb ! Proportionality coefficient between web and wstar3
real(r8) :: wstar ! Convective velocity for CL [ m/s ]
real(r8) :: wstar3 ! Cubed convective velocity for CL [ m3/s3 ]
real(r8) :: wstar3fact ! 1/(relative change of wstar^3 by entrainment)
real(r8) :: rmin ! sqrt(p)
real(r8) :: fmin ! f(rmin), where f(r) = r^3 - 3*p*r - 2q
real(r8) :: rcrit ! ccrit*wstar
real(r8) :: fcrit ! f(rcrit)
logical noroot ! True if f(r) has no root r > rcrit
!-----------------------!
! Start of Main Program !
!-----------------------!
! Option: Turn-off LW radiative-turbulence interaction in PBL scheme
! by setting qrlw = 0. Logical parameter 'set_qrlzero' was
! defined in the first part of 'eddy_diff.F90' module.
if( set_qrlzero ) then
qrlw(:,:) = 0._r8
else
qrlw(:ncol,:pver) = qrlin(:ncol,:pver)
endif
! Define effective stratus fraction using the grid-mean ql.
! Modification : The contribution of ice should be carefully considered.
! This should be done in combination with the 'qrlw' and
! overlapping assumption of liquid and ice stratus.
do k = 1, pver
do i = 1, ncol
if( choice_evhc .eq. 'ramp' .or. choice_radf .eq. 'ramp' ) then
cldeff(i,k) = cld(i,k) * min( ql(i,k) / qmin, 1._r8 )
else
cldeff(i,k) = cld(i,k)
endif
end do
end do
! For an extended stability function in the stable regime, re-define
! alph4exe and ghmin. This is for future work.
if( ricrit .eq. 0.19_r8 ) then
alph4exs = alph4
ghmin = -3.5334_r8
elseif( ricrit .gt. 0.19_r8 ) then
alph4exs = -2._r8 * b1 * alph2 / ( alph3 - 2._r8 * b1 * alph5 ) / ricrit
ghmin = -1.e10_r8
else
write(iulog,*) 'Error : ricrit should be larger than 0.19 in UW PBL'
stop
endif
!
! Initialization of Diagnostic Output
!
do i = 1, ncol
wet_CL(i,:ncvmax) = 0._r8
web_CL(i,:ncvmax) = 0._r8
jtbu_CL(i,:ncvmax) = 0._r8
jbbu_CL(i,:ncvmax) = 0._r8
evhc_CL(i,:ncvmax) = 0._r8
jt2slv_CL(i,:ncvmax) = 0._r8
n2ht_CL(i,:ncvmax) = 0._r8
n2hb_CL(i,:ncvmax) = 0._r8
lwp_CL(i,:ncvmax) = 0._r8
opt_depth_CL(i,:ncvmax) = 0._r8
radinvfrac_CL(i,:ncvmax) = 0._r8
radf_CL(i,:ncvmax) = 0._r8
wstar_CL(i,:ncvmax) = 0._r8
wstar3fact_CL(i,:ncvmax) = 0._r8
ricl(i,:ncvmax) = 0._r8
ghcl(i,:ncvmax) = 0._r8
shcl(i,:ncvmax) = 0._r8
smcl(i,:ncvmax) = 0._r8
ebrk(i,:ncvmax) = 0._r8
wbrk(i,:ncvmax) = 0._r8
lbrk(i,:ncvmax) = 0._r8
gh_a(i,:pver+1) = 0._r8
sh_a(i,:pver+1) = 0._r8
sm_a(i,:pver+1) = 0._r8
ri_a(i,:pver+1) = 0._r8
sm_aw(i,:pver+1) = 0._r8
ipbl(i) = 0._r8
kpblh(i) = real(pver,r8)
end do
! kvh and kvm are stored over timesteps in 'vertical_diffusion.F90' and
! passed in as kvh_in and kvm_in. However, at the first timestep they
! need to be computed and these are done just before calling 'caleddy'.
! kvm and kvh are also stored over iterative time step in the first part
! of 'eddy_diff.F90'
do k = 1, pver + 1
do i = 1, ncol
! Initialize kvh and kvm to zero or kvf
if( use_kvf ) then
kvh(i,k) = kvf(i,k)
kvm(i,k) = kvf(i,k)
else
kvh(i,k) = 0._r8
kvm(i,k) = 0._r8
end if
! Zero diagnostic quantities for the new diffusion step.
wcap(i,k) = 0._r8
leng(i,k) = 0._r8
tke(i,k) = 0._r8
turbtype(i,k) = 0
end do
end do
! Initialize 'bprod' [ m2/s3 ] and 'sprod' [ m2/s3 ] at all interfaces.
! Note this initialization is a hybrid initialization since 'n2' [s-2] and 's2' [s-2]
! are calculated from the given current initial profile, while 'kvh_in' [m2/s] and
! 'kvm_in' [m2/s] are from the previous iteration or previous time step.
! This initially guessed 'bprod' and 'sprod' will be updated at the end of this
! 'caleddy' subroutine for diagnostic output.
! This computation of 'brpod,sprod' below is necessary for wstar-based entrainment closure.
do k = 2, pver
do i = 1, ncol
bprod(i,k) = -kvh_in(i,k) * n2(i,k)
sprod(i,k) = kvm_in(i,k) * s2(i,k)
end do
end do
! Set 'bprod' and 'sprod' at top and bottom interface.
! In calculating 'surface' (actually lowest half-layer) buoyancy flux,
! 'chu' at surface is defined to be the same as 'chu' at the mid-point
! of lowest model layer (pver) at the end of 'trbind'. The same is for
! the other buoyancy coefficients. 'sprod(i,pver+1)' is defined in a
! consistent way as the definition of 'tkes' in the original code.
! ( Important Option ) If I want to isolate surface buoyancy flux from
! the other parts of CL regimes energetically even though bflxs > 0,
! all I should do is to re-define 'bprod(i,pver+1)=0' in the below 'do'
! block. Additionally for merging test of extending SBCL based on 'l2n2'
! in 'zisocl', I should use 'l2n2 = - wint / sh' for similar treatment
! as previous code. All other parts of the code are fully consistently
! treated by these change only.
! My future general convection scheme will use bflxs(i).
do i = 1, ncol
bprod(i,1) = 0._r8 ! Top interface
sprod(i,1) = 0._r8 ! Top interface
ch = chu(i,pver+1) * ( 1._r8 - sflh(i,pver) ) + chs(i,pver+1) * sflh(i,pver)
cm = cmu(i,pver+1) * ( 1._r8 - sflh(i,pver) ) + cms(i,pver+1) * sflh(i,pver)
bflxs(i) = ch * shflx(i) * rrho(i) + cm * qflx(i) * rrho(i)
if( choice_tkes .eq. 'ibprod' ) then
bprod(i,pver+1) = bflxs(i)
else
bprod(i,pver+1) = 0._r8
endif
sprod(i,pver+1) = (ustar(i)**3)/(vk*z(i,pver))
end do
! Initially identify CL regimes in 'exacol'
! ktop : Interface index of the CL top external interface
! kbase : Interface index of the CL base external interface
! ncvfin: Number of total CLs
! Note that if surface buoyancy flux is positive ( bflxs = bprod(i,pver+1) > 0 ),
! surface interface is identified as an internal interface of CL. However, even
! though bflxs <= 0, if 'pver' interface is a CL internal interface (ri(pver)<0),
! surface interface is identified as an external interface of CL. If bflxs =< 0
! and ri(pver) >= 0, then surface interface is identified as a stable turbulent
! intereface (STL) as shown at the end of 'caleddy'. Even though a 'minpblh' is
! passed into 'exacol', it is not used in the 'exacol'.
call exacol( pcols, pver, ncol, ri, bflxs, minpblh, zi, ktop, kbase, ncvfin )
! Diagnostic output of CL interface indices before performing 'extending-merging'
! of CL regimes in 'zisocl'
do i = 1, ncol
do k = 1, ncvmax
kbase_o(i,k) = real(kbase(i,k),r8)
ktop_o(i,k) = real(ktop(i,k),r8)
ncvfin_o(i) = real(ncvfin(i),r8)
end do
end do
! ----------------------------------- !
! Perform calculation for each column !
! ----------------------------------- !
do i = 1, ncol
! Define Surface Interfacial Layer TKE, 'tkes'.
! In the current code, 'tkes' is used as representing TKE of surface interfacial
! layer (low half-layer of surface-based grid layer). In the code, when bflxs>0,
! surface interfacial layer is assumed to be energetically coupled to the other
! parts of the CL regime based at the surface. In this sense, it is conceptually
! more reasonable to include both 'bprod' and 'sprod' in the definition of 'tkes'.
! Since 'tkes' cannot be negative, it is lower bounded by small positive number.
! Note that inclusion of 'bprod' in the definition of 'tkes' may increase 'ebrk'
! and 'wstar3', and eventually, 'wet' at the CL top, especially when 'bflxs>0'.
! This might help to solve the problem of too shallow PBLH over the overcast Sc
! regime. If I want to exclude 'bprod(i,pver+1)' in calculating 'tkes' even when
! bflxs > 0, all I should to do is to set 'bprod(i,pver+1) = 0' in the above
! initialization 'do' loop (explained above), NOT changing the formulation of
! tkes(i) in the below block. This is because for consistent treatment in the
! other parts of the code also.
! tkes(i) = (b1*vk*z(i,pver)*sprod(i,pver+1))**(2._r8/3._r8)
tkes(i) = max(b1*vk*z(i,pver)*(bprod(i,pver+1)+sprod(i,pver+1)), 1.e-7_r8)**(2._r8/3._r8)
tkes(i) = min(tkes(i), tkemax)
tke(i,pver+1) = tkes(i)
wcap(i,pver+1) = tkes(i)/b1
! Extend and merge the initially identified CLs, relabel the CLs, and calculate
! CL internal mean energetics and stability functions in 'zisocl'.
! The CL nearest to the surface is CL(1) and the CL index, ncv, increases
! with height. The following outputs are from 'zisocl'. Here, the dimension
! of below outputs are (pcols,ncvmax) (except the 'ncvfin(pcols)' and
! 'belongcv(pcols,pver+1)) and 'ncv' goes from 1 to 'ncvfin'.
! For 'ncv = ncvfin+1, ncvmax', below output are already initialized to be zero.
! ncvfin : Total number of CLs
! kbase(ncv) : Base external interface index of CL
! ktop : Top external interface index of CL
! belongcv : True if the interface (either internal or external) is CL
! ricl : Mean Richardson number of internal CL
! ghcl : Normalized buoyancy production '-l2n2/2e' [no unit] of internal CL
! shcl : Galperin instability function of heat-moisture of internal CL
! smcl : Galperin instability function of momentum of internal CL
! lbrk, <l>int : Thickness of (energetically) internal CL (lint, [m])
! wbrk, <W>int : Mean normalized TKE of internal CL ([m2/s2])
! ebrk, <e>int : Mean TKE of internal CL (b1*wbrk,[m2/s2])
! The ncvsurf is an identifier saying which CL regime is based at the surface.
! If 'ncvsurf=1', then the first CL regime is based at the surface. If surface
! interface is not a part of CL (neither internal nor external), 'ncvsurf = 0'.
! After identifying and including SRCLs into the normal CL regimes (where newly
! identified SRCLs are simply appended to the normal CL regimes using regime
! indices of 'ncvfin+1','ncvfin+2' (as will be shown in the below SRCL part),..
! where 'ncvfin' is the final CL regime index produced after extending-merging
! in 'zisocl' but before adding SRCLs), if any newly identified SRCL (e.g.,
! 'ncvfin+1') is based at surface, then 'ncvsurf = ncvfin+1'. Thus 'ncvsurf' can
! be 0, 1, or >1. 'ncvsurf' can be a useful diagnostic output.
ncvsurf = 0
if( ncvfin(i) .gt. 0 ) then
call zisocl( pcols , pver , i , &
z , zi , n2 , s2 , &
bprod , sprod , bflxs , tkes , &
ncvfin , kbase , ktop , belongcv, &
ricl , ghcl , shcl , smcl , &
lbrk , wbrk , ebrk , &
extend , extend_up, extend_dn )
if( kbase(i,1) .eq. pver + 1 ) ncvsurf = 1
else
belongcv(i,:) = .false.
endif
! Diagnostic output after finishing extending-merging process in 'zisocl'
! Since we are adding SRCL additionally, we need to print out these here.
do k = 1, ncvmax
kbase_mg(i,k) = real(kbase(i,k))
ktop_mg(i,k) = real(ktop(i,k))
ncvfin_mg(i) = real(ncvfin(i))
end do
! ----------------------- !
! Identification of SRCLs !
! ----------------------- !
! Modification : This cannot identify the 'cirrus' layer due to the condition of
! ql(i,k) .gt. qmin. This should be modified in future to identify
! a single thin cirrus layer.
! Instead of ql, we may use cldn in future, including ice
! contribution.
! ------------------------------------------------------------------------------ !
! Find single-layer radiatively-driven cloud-topped convective layers (SRCLs). !
! SRCLs extend through a single model layer k, with entrainment at the top and !
! bottom interfaces, unless bottom interface is the surface. !
! The conditions for an SRCL is identified are: !
! !
! 1. Cloud in the layer, k : ql(i,k) .gt. qmin = 1.e-5 [ kg/kg ] !
! 2. No cloud in the above layer (else assuming that some fraction of the LW !
! flux divergence in layer k is concentrated at just below top interface !
! of layer k is invalid). Then, this condition might be sensitive to the !
! vertical resolution of grid. !
! 3. LW radiative cooling (SW heating is assumed uniformly distributed through !
! layer k, so not relevant to buoyancy production) in the layer k. However, !
! SW production might also contribute, which may be considered in a future. !
! 4. Internal stratification 'n2ht' of upper-half layer should be unstable. !
! The 'n2ht' is pure internal stratification of upper half layer, obtained !
! using internal slopes of sl, qt in layer k (in contrast to conventional !
! interfacial slope) and saturation fraction in the upper-half layer, !
! sfuh(k) (in contrast to sfi(k)). !
! 5. Top and bottom interfaces not both in the same existing convective layer. !
! If SRCL is within the previouisly identified CL regimes, we don't define !
! a new SRCL. !
! 6. k >= ntop_turb + 1 = 2 !
! 7. Ri at the top interface > ricrit = 0.19 (otherwise turbulent mixing will !
! broadly distribute the cloud top in the vertical, preventing localized !
! radiative destabilization at the top interface). !
! !
! Note if 'k = pver', it identifies a surface-based single fog layer, possibly, !
! warm advection fog. Note also the CL regime index of SRCLs itself increases !
! with height similar to the regular CLs indices identified from 'zisocl'. !
! ------------------------------------------------------------------------------ !
ncv = 1
ncvf = ncvfin(i)
if( choice_SRCL .eq. 'remove' ) goto 222
do k = nbot_turb, ntop_turb + 1, -1 ! 'k = pver, 2, -1' is a layer index.
if( ql(i,k) .gt. qmin .and. ql(i,k-1) .lt. qmin .and. qrlw(i,k) .lt. 0._r8 &
.and. ri(i,k) .ge. ricrit ) then
! In order to avoid any confliction with the treatment of ambiguous layer,
! I need to impose an additional constraint that ambiguous layer cannot be
! SRCL. So, I added constraint that 'k+1' interface (base interface of k
! layer) should not be a part of previously identified CL. Since 'belongcv'
! is even true for external entrainment interfaces, below constraint is
! fully sufficient.
if( choice_SRCL .eq. 'nonamb' .and. belongcv(i,k+1) ) then
go to 220
endif
ch = ( 1._r8 - sfuh(i,k) ) * chu(i,k) + sfuh(i,k) * chs(i,k)
cm = ( 1._r8 - sfuh(i,k) ) * cmu(i,k) + sfuh(i,k) * cms(i,k)
n2htSRCL = ch * slslope(i,k) + cm * qtslope(i,k)
if( n2htSRCL .le. 0._r8 ) then
! Test if bottom and top interfaces are part of the pre-existing CL.
! If not, find appropriate index for the new SRCL. Note that this
! calculation makes use of 'ncv set' obtained from 'zisocl'. The
! 'in_CL' is a parameter testing whether the new SRCL is already
! within the pre-existing CLs (.true.) or not (.false.).
in_CL = .false.
do while ( ncv .le. ncvf )
if( ktop(i,ncv) .le. k ) then
if( kbase(i,ncv) .gt. k ) then
in_CL = .true.
endif
exit ! Exit from 'do while' loop if SRCL is within the CLs.
else
ncv = ncv + 1 ! Go up one CL
end if
end do ! ncv
if( .not. in_CL ) then ! SRCL is not within the pre-existing CLs.
! Identify a new SRCL and add it to the pre-existing CL regime group.
ncvfin(i) = ncvfin(i) + 1
ncvnew = ncvfin(i)
ktop(i,ncvnew) = k
kbase(i,ncvnew) = k+1
belongcv(i,k) = .true.
belongcv(i,k+1) = .true.
! Calculate internal energy of SRCL. There is no internal energy if
! SRCL is elevated from the surface. Also, we simply assume neutral
! stability function. Note that this assumption of neutral stability
! does not influence numerical calculation- stability functions here
! are just for diagnostic output. In general SRCLs other than a SRCL
! based at surface with bflxs <= 0, there is no other way but to use
! neutral stability function. However, in case of SRCL based at the
! surface, we can explicitly calculate non-zero stability functions
! in a consistent way. Even though stability functions of SRCL are
! just diagnostic outputs not influencing numerical calculations, it
! would be informative to write out correct reasonable values rather
! than simply assuming neutral stability. I am doing this right now.
! Similar calculations were done for the SBCL and when surface inter
! facial layer was merged by overlying CL in 'ziscol'.
if( k .lt. pver ) then
wbrk(i,ncvnew) = 0._r8
ebrk(i,ncvnew) = 0._r8
lbrk(i,ncvnew) = 0._r8
ghcl(i,ncvnew) = 0._r8
shcl(i,ncvnew) = 0._r8
smcl(i,ncvnew) = 0._r8
ricl(i,ncvnew) = 0._r8
else ! Surface-based fog
if( bflxs(i) .gt. 0._r8 ) then ! Incorporate surface TKE into CL interior energy
! It is likely that this case cannot exist since
! if surface buoyancy flux is positive, it would
! have been identified as SBCL in 'zisocl' ahead.
ebrk(i,ncvnew) = tkes(i)
lbrk(i,ncvnew) = z(i,pver)
wbrk(i,ncvnew) = tkes(i) / b1
write(iulog,*) 'Major mistake in SRCL: bflxs > 0 for surface-based SRCL'
write(iulog,*) 'bflxs = ', bflxs(i)
write(iulog,*) 'ncvfin_o = ', ncvfin_o(i)
write(iulog,*) 'ncvfin_mg = ', ncvfin_mg(i)
do ks = 1, ncvmax
write(iulog,*) 'ncv =', ks, ' ', kbase_o(i,ks), ktop_o(i,ks), kbase_mg(i,ks), ktop_mg(i,ks)
end do
stop
else ! Don't incorporate surface interfacial TKE into CL interior energy
ebrk(i,ncvnew) = 0._r8
lbrk(i,ncvnew) = 0._r8
wbrk(i,ncvnew) = 0._r8
endif
! Calculate stability functions (ghcl, shcl, smcl, ricl) explicitly
! using an reverse procedure starting from tkes(i). Note that it is
! possible to calculate stability functions even when bflxs < 0.
! Previous code just assumed neutral stability functions. Note that
! since alph5 = 0.7 > 0, alph3 = -35 < 0, the denominator of gh is
! always positive if bflxs > 0. However, if bflxs < 0, denominator
! can be zero. For this case, we provide a possible maximum negative
! value (the most stable state) to gh. Note also tkes(i) is always a
! positive value by a limiter. Also, sprod(i,pver+1) > 0 by limiter.
gg = 0.5_r8 * vk * z(i,pver) * bprod(i,pver+1) / ( tkes(i)**(3._r8/2._r8) )
if( abs(alph5-gg*alph3) .le. 1.e-7_r8 ) then
! gh = -0.28_r8
! gh = -3.5334_r8
gh = ghmin
else
gh = gg / ( alph5 - gg * alph3 )
end if
! gh = min(max(gh,-0.28_r8),0.0233_r8)
! gh = min(max(gh,-3.5334_r8),0.0233_r8)
gh = min(max(gh,ghmin),0.0233_r8)
ghcl(i,ncvnew) = gh
shcl(i,ncvnew) = max(0._r8,alph5/(1._r8+alph3*gh))
smcl(i,ncvnew) = max(0._r8,(alph1 + alph2*gh)/(1._r8+alph3*gh)/(1._r8+alph4exs*gh))
ricl(i,ncvnew) = -(smcl(i,ncvnew)/shcl(i,ncvnew))*(bprod(i,pver+1)/sprod(i,pver+1))
! 'ncvsurf' is CL regime index based at the surface. If there is no
! such regime, then 'ncvsurf = 0'.
ncvsurf = ncvnew
end if
end if
end if
end if
220 continue
end do ! End of 'k' loop where 'k' is a grid layer index running from 'pver' to 2
222 continue
! -------------------------------------------------------------------------- !
! Up to this point, we identified all kinds of CL regimes : !
! 1. A SBCL. By construction, 'bflxs > 0' for SBCL. !
! 2. Surface-based CL with multiple layers and 'bflxs =< 0' !
! 3. Surface-based CL with multiple layers and 'bflxs > 0' !
! 4. Regular elevated CL with two entraining interfaces !
! 5. SRCLs. If SRCL is based at surface, it will be bflxs < 0. !
! '1-4' were identified from 'zisocl' while '5' were identified separately !
! after performing 'zisocl'. CL regime index of '1-4' increases with height !
! ( e.g., CL = 1 is the CL regime nearest to the surface ) while CL regime !
! index of SRCL is simply appended after the final index of CL regimes from !
! 'zisocl'. However, CL regime indices of SRCLs itself increases with height !
! when there are multiple SRCLs, similar to the regular CLs from 'zisocl'. !
! -------------------------------------------------------------------------- !
! Diagnostic output of final CL regimes indices
do k = 1, ncvmax
kbase_f(i,k) = real(kbase(i,k))
ktop_f(i,k) = real(ktop(i,k))
ncvfin_f(i) = real(ncvfin(i))
end do
! ---------------------------------------- !
! Perform do loop for individual CL regime !
! ---------------------------------------- ! -------------------------------- !
! For individual CLs, compute !
! 1. Entrainment rates at the CL top and (if any) base interfaces using !
! appropriate entrainment closure (current code use 'wstar' closure). !
! 2. Net CL mean (i.e., including entrainment contribution) TKE (ebrk) !
! and normalized TKE (wbrk). !
! 3. TKE (tke) and normalized TKE (wcap) profiles at all CL interfaces. !
! 4. ( kvm, kvh ) profiles at all CL interfaces. !
! 5. ( bprod, sprod ) profiles at all CL interfaces. !
! Also calculate !
! 1. PBL height as the top external interface of surface-based CL, if any. !
! 2. Characteristic excesses of convective 'updraft velocity (wpert)', !
! 'temperature (tpert)', and 'moisture (qpert)' in the surface-based CL, !
! if any, for use in the separate convection scheme. !
! If there is no surface-based CL, 'PBL height' and 'convective excesses' are !
! calculated later from surface-based STL (Stable Turbulent Layer) properties.!
! --------------------------------------------------------------------------- !
ktblw = 0
do ncv = 1, ncvfin(i)
kt = ktop(i,ncv)
kb = kbase(i,ncv)
! Check whether surface interface is energetically interior or not.
if( kb .eq. (pver+1) .and. bflxs(i) .le. 0._r8 ) then
lbulk = zi(i,kt) - z(i,pver)
else
lbulk = zi(i,kt) - zi(i,kb)
end if
! Calculate 'turbulent length scale (leng)' and 'normalized TKE (wcap)'
! at all CL interfaces except the surface. Note that below 'wcap' at
! external interfaces are not correct. However, it does not influence
! numerical calculation and correct normalized TKE at the entraining
! interfaces will be re-calculated at the end of this 'do ncv' loop.
do k = min(kb,pver), kt, -1
if( choice_tunl .eq. 'rampcl' ) then
! In order to treat the case of 'ricl(i,ncv) >> 0' of surface-based SRCL
! with 'bflxs(i) < 0._r8', I changed ricl(i,ncv) -> min(0._r8,ricl(i,ncv))
! in the below exponential. This is necessary to prevent the model crash
! by too large values (e.g., 700) of ricl(i,ncv)
tunlramp = ctunl*tunl*(1._r8-(1._r8-1._r8/ctunl)*exp(min(0._r8,ricl(i,ncv))))
tunlramp = min(max(tunlramp,tunl),ctunl*tunl)
elseif( choice_tunl .eq. 'rampsl' ) then
tunlramp = ctunl*tunl
! tunlramp = 0.765_r8
else
tunlramp = tunl
endif
if( choice_leng .eq. 'origin' ) then
leng(i,k) = ( (vk*zi(i,k))**(-cleng) + (tunlramp*lbulk)**(-cleng) )**(-1._r8/cleng)
! leng(i,k) = vk*zi(i,k) / (1._r8+vk*zi(i,k)/(tunlramp*lbulk))
else
leng(i,k) = min( vk*zi(i,k), tunlramp*lbulk )
endif
wcap(i,k) = (leng(i,k)**2) * (-shcl(i,ncv)*n2(i,k)+smcl(i,ncv)*s2(i,k))
end do ! k
! Calculate basic cross-interface variables ( jump condition ) across the
! base external interface of CL.
if( kb .lt. pver+1 ) then
jbzm = z(i,kb-1) - z(i,kb) ! Interfacial layer thickness [m]
jbsl = sl(i,kb-1) - sl(i,kb) ! Interfacial jump of 'sl' [J/kg]
jbqt = qt(i,kb-1) - qt(i,kb) ! Interfacial jump of 'qt' [kg/kg]
jbbu = n2(i,kb) * jbzm ! Interfacial buoyancy jump [m/s2] considering saturation ( > 0 )
jbbu = max(jbbu,jbumin) ! Set minimum buoyancy jump, jbumin = 1.e-3
jbu = u(i,kb-1) - u(i,kb) ! Interfacial jump of 'u' [m/s]
jbv = v(i,kb-1) - v(i,kb) ! Interfacial jump of 'v' [m/s]
ch = (1._r8 -sflh(i,kb-1))*chu(i,kb) + sflh(i,kb-1)*chs(i,kb) ! Buoyancy coefficient just above the base interface
cm = (1._r8 -sflh(i,kb-1))*cmu(i,kb) + sflh(i,kb-1)*cms(i,kb) ! Buoyancy coefficient just above the base interface
n2hb = (ch*jbsl + cm*jbqt)/jbzm ! Buoyancy frequency [s-2] just above the base interface
vyb = n2hb*jbzm/jbbu ! Ratio of 'n2hb/n2' at 'kb' interface
vub = min(1._r8,(jbu**2+jbv**2)/(jbbu*jbzm) ) ! Ratio of 's2/n2 = 1/Ri' at 'kb' interface
else
! Below setting is necessary for consistent treatment when 'kb' is at the surface.
jbbu = 0._r8
n2hb = 0._r8
vyb = 0._r8
vub = 0._r8
web = 0._r8
end if
! Calculate basic cross-interface variables ( jump condition ) across the
! top external interface of CL. The meanings of variables are similar to
! the ones at the base interface.
jtzm = z(i,kt-1) - z(i,kt)
jtsl = sl(i,kt-1) - sl(i,kt)
jtqt = qt(i,kt-1) - qt(i,kt)
jtbu = n2(i,kt)*jtzm ! Note : 'jtbu' is guaranteed positive by definition of CL top.
jtbu = max(jtbu,jbumin) ! But threshold it anyway to be sure.
jtu = u(i,kt-1) - u(i,kt)
jtv = v(i,kt-1) - v(i,kt)
ch = (1._r8 -sfuh(i,kt))*chu(i,kt) + sfuh(i,kt)*chs(i,kt)
cm = (1._r8 -sfuh(i,kt))*cmu(i,kt) + sfuh(i,kt)*cms(i,kt)
n2ht = (ch*jtsl + cm*jtqt)/jtzm
vyt = n2ht*jtzm/jtbu
vut = min(1._r8,(jtu**2+jtv**2)/(jtbu*jtzm))
! Evaporative enhancement factor of entrainment rate at the CL top interface, evhc.
! We take the full inversion strength to be 'jt2slv = slv(i,kt-2)-slv(i,kt)'
! where 'kt-1' is in the ambiguous layer. However, for a cloud-topped CL overlain
! by another CL, it is possible that 'slv(i,kt-2) < slv(i,kt)'. To avoid negative
! or excessive evhc, we lower-bound jt2slv and upper-bound evhc. Note 'jtslv' is
! used only for calculating 'evhc' : when calculating entrainment rate, we will
! use normal interfacial buoyancy jump across CL top interface.
evhc = 1._r8
jt2slv = 0._r8
! Modification : I should check whether below 'jbumin' produces reasonable limiting value.
! In addition, our current formulation does not consider ice contribution.
if( choice_evhc .eq. 'orig' ) then
if( ql(i,kt) .gt. qmin .and. ql(i,kt-1) .lt. qmin ) then
jt2slv = slv(i,max(kt-2,1)) - slv(i,kt)
jt2slv = max( jt2slv, jbumin*slv(i,kt-1)/g )
evhc = 1._r8 + a2l * a3l * latvap * ql(i,kt) / jt2slv
evhc = min( evhc, evhcmax )
end if
elseif( choice_evhc .eq. 'ramp' ) then
jt2slv = slv(i,max(kt-2,1)) - slv(i,kt)
jt2slv = max( jt2slv, jbumin*slv(i,kt-1)/g )
evhc = 1._r8 + max(cldeff(i,kt)-cldeff(i,kt-1),0._r8) * a2l * a3l * latvap * ql(i,kt) / jt2slv
evhc = min( evhc, evhcmax )
elseif( choice_evhc .eq. 'maxi' ) then
qleff = max( ql(i,kt-1), ql(i,kt) )
jt2slv = slv(i,max(kt-2,1)) - slv(i,kt)
jt2slv = max( jt2slv, jbumin*slv(i,kt-1)/g )
evhc = 1._r8 + a2l * a3l * latvap * qleff / jt2slv
evhc = min( evhc, evhcmax )
endif
! Calculate cloud-top radiative cooling contribution to buoyancy production.
! Here, 'radf' [m2/s3] is additional buoyancy flux at the CL top interface
! associated with cloud-top LW cooling being mainly concentrated near the CL
! top interface ( just below CL top interface ). Contribution of SW heating
! within the cloud is not included in this radiative buoyancy production
! since SW heating is more broadly distributed throughout the CL top layer.
lwp = 0._r8
opt_depth = 0._r8
radinvfrac = 0._r8
radf = 0._r8
if( choice_radf .eq. 'orig' ) then
if( ql(i,kt) .gt. qmin .and. ql(i,kt-1) .lt. qmin ) then
lwp = ql(i,kt) * ( pi(i,kt+1) - pi(i,kt) ) / g
opt_depth = 156._r8 * lwp ! Estimated LW optical depth in the CL top layer
! Approximate LW cooling fraction concentrated at the inversion by using
! polynomial approx to exact formula 1-2/opt_depth+2/(exp(opt_depth)-1))
radinvfrac = opt_depth * ( 4._r8 + opt_depth ) / ( 6._r8 * ( 4._r8 + opt_depth ) + opt_depth**2 )
radf = qrlw(i,kt) / ( pi(i,kt) - pi(i,kt+1) ) ! Cp*radiative cooling = [ W/kg ]
radf = max( radinvfrac * radf * ( zi(i,kt) - zi(i,kt+1) ), 0._r8 ) * chs(i,kt)
! We can disable cloud LW cooling contribution to turbulence by uncommenting:
! radf = 0._r8
end if
elseif( choice_radf .eq. 'ramp' ) then
lwp = ql(i,kt) * ( pi(i,kt+1) - pi(i,kt) ) / g
opt_depth = 156._r8 * lwp ! Estimated LW optical depth in the CL top layer
radinvfrac = opt_depth * ( 4._r8 + opt_depth ) / ( 6._r8 * ( 4._r8 + opt_depth ) + opt_depth**2 )
radinvfrac = max(cldeff(i,kt)-cldeff(i,kt-1),0._r8) * radinvfrac
radf = qrlw(i,kt) / ( pi(i,kt) - pi(i,kt+1) ) ! Cp*radiative cooling [W/kg]
radf = max( radinvfrac * radf * ( zi(i,kt) - zi(i,kt+1) ), 0._r8 ) * chs(i,kt)
elseif( choice_radf .eq. 'maxi' ) then
! Radiative flux divergence both in 'kt' and 'kt-1' layers are included
! 1. From 'kt' layer
lwp = ql(i,kt) * ( pi(i,kt+1) - pi(i,kt) ) / g
opt_depth = 156._r8 * lwp ! Estimated LW optical depth in the CL top layer
radinvfrac = opt_depth * ( 4._r8 + opt_depth ) / ( 6._r8 * ( 4._r8 + opt_depth ) + opt_depth**2 )
radf = max( radinvfrac * qrlw(i,kt) / ( pi(i,kt) - pi(i,kt+1) ) * ( zi(i,kt) - zi(i,kt+1) ), 0._r8 )
! 2. From 'kt-1' layer and add the contribution from 'kt' layer
lwp = ql(i,kt-1) * ( pi(i,kt) - pi(i,kt-1) ) / g
opt_depth = 156._r8 * lwp ! Estimated LW optical depth in the CL top layer
radinvfrac = opt_depth * ( 4._r8 + opt_depth ) / ( 6._r8 * ( 4._r8 + opt_depth) + opt_depth**2 )
radf = radf + max( radinvfrac * qrlw(i,kt-1) / ( pi(i,kt-1) - pi(i,kt) ) * ( zi(i,kt-1) - zi(i,kt) ), 0._r8 )
radf = max( radf, 0._r8 ) * chs(i,kt)
endif
! ------------------------------------------------------------------- !
! Calculate 'wstar3' by summing buoyancy productions within CL from !
! 1. Interior buoyancy production ( bprod: fcn of TKE ) !
! 2. Cloud-top radiative cooling !
! 3. Surface buoyancy flux contribution only when bflxs > 0. !
! Note that master length scale, lbulk, has already been !
! corrctly defined at the first part of this 'do ncv' loop !
! considering the sign of bflxs. !
! This 'wstar3' is used for calculation of entrainment rate. !
! Note that this 'wstar3' formula does not include shear production !
! and the effect of drizzle, which should be included later. !
! Q : Strictly speaking, in calculating interior buoyancy production, !
! the use of 'bprod' is not correct, since 'bprod' is not correct !
! value but initially guessed value. More reasonably, we should !
! use '-leng(i,k)*sqrt(b1*wcap(i,k))*shcl(i,ncv)*n2(i,k)' instead !
! of 'bprod(i,k)', although this is still an approximation since !
! tke(i,k) is not exactly 'b1*wcap(i,k)' due to a transport term.!
! However since iterative calculation will be performed after all,!
! below might also be OK. But I should test this alternative. !
! ------------------------------------------------------------------- !
dzht = zi(i,kt) - z(i,kt) ! Thickness of CL top half-layer
dzhb = z(i,kb-1) - zi(i,kb) ! Thickness of CL bot half-layer
wstar3 = radf * dzht
do k = kt + 1, kb - 1 ! If 'kt = kb - 1', this loop will not be performed.
wstar3 = wstar3 + bprod(i,k) * ( z(i,k-1) - z(i,k) )
! Below is an alternative which may speed up convergence.
! However, for interfaces merged into original CL, it can
! be 'wcap(i,k)<0' since 'n2(i,k)>0'. Thus, I should use
! the above original one.
! wstar3 = wstar3 - leng(i,k)*sqrt(b1*wcap(i,k))*shcl(i,ncv)*n2(i,k)* &
! (z(i,k-1) - z(i,k))
end do
if( kb .eq. (pver+1) .and. bflxs(i) .gt. 0._r8 ) then
wstar3 = wstar3 + bflxs(i) * dzhb
! wstar3 = wstar3 + bprod(i,pver+1) * dzhb
end if
wstar3 = max( 2.5_r8 * wstar3, 0._r8 )
! -------------------------------------------------------------- !
! Below single block is for 'sedimentation-entrainment feedback' !
! -------------------------------------------------------------- !
if( id_sedfact ) then
! wsed = 7.8e5_r8*(ql(i,kt)/ncliq(i,kt))**(2._r8/3._r8)
sedfact = exp(-ased*wsedl(i,kt)/(wstar3**(1._r8/3._r8)+1.e-6))
if( choice_evhc .eq. 'orig' ) then
if (ql(i,kt).gt.qmin .and. ql(i,kt-1).lt.qmin) then
jt2slv = slv(i,max(kt-2,1)) - slv(i,kt)
jt2slv = max(jt2slv, jbumin*slv(i,kt-1)/g)
evhc = 1._r8+sedfact*a2l*a3l*latvap*ql(i,kt) / jt2slv
evhc = min(evhc,evhcmax)
end if
elseif( choice_evhc .eq. 'ramp' ) then
jt2slv = slv(i,max(kt-2,1)) - slv(i,kt)
jt2slv = max(jt2slv, jbumin*slv(i,kt-1)/g)
evhc = 1._r8+max(cldeff(i,kt)-cldeff(i,kt-1),0._r8)*sedfact*a2l*a3l*latvap*ql(i,kt) / jt2slv
evhc = min(evhc,evhcmax)
elseif( choice_evhc .eq. 'maxi' ) then
qleff = max(ql(i,kt-1),ql(i,kt))
jt2slv = slv(i,max(kt-2,1)) - slv(i,kt)
jt2slv = max(jt2slv, jbumin*slv(i,kt-1)/g)
evhc = 1._r8+sedfact*a2l*a3l*latvap*qleff / jt2slv
evhc = min(evhc,evhcmax)
endif
endif
! -------------------------------------------------------------------------- !
! Now diagnose CL top and bottom entrainment rates (and the contribution of !
! top/bottom entrainments to wstar3) using entrainment closures of the form !
! !
! wet = cet*wstar3, web = ceb*wstar3 !
! !
! where cet and ceb depend on the entrainment interface jumps, ql, etc. !
! No entrainment is diagnosed unless the wstar3 > 0. Note '1/wstar3fact' is !
! a factor indicating the enhancement of wstar3 due to entrainment process. !
! Q : Below setting of 'wstar3fact = max(..,0.5)'might prevent the possible !
! case when buoyancy consumption by entrainment is stronger than cloud !
! top radiative cooling production. Is that OK ? No. According to bulk !
! modeling study, entrainment buoyancy consumption was always a certain !
! fraction of other net productions, rather than a separate sum. Thus, !
! below max limit of wstar3fact is correct. 'wstar3fact = max(.,0.5)' !
! prevents unreasonable enhancement of CL entrainment rate by cloud-top !
! entrainment instability, CTEI. !
! Q : Use of the same dry entrainment coefficient, 'a1i' both at the CL top !
! and base interfaces may result in too small 'wstar3' and 'ebrk' below, !
! as was seen in my generalized bulk modeling study. This should be re- !
! considered later !
! -------------------------------------------------------------------------- !
if( wstar3 .gt. 0._r8 ) then
cet = a1i * evhc / ( jtbu * lbulk )
if( kb .eq. pver + 1 ) then
wstar3fact = max( 1._r8 + 2.5_r8 * cet * n2ht * jtzm * dzht, wstar3factcrit )
else
ceb = a1i / ( jbbu * lbulk )
wstar3fact = max( 1._r8 + 2.5_r8 * cet * n2ht * jtzm * dzht &
+ 2.5_r8 * ceb * n2hb * jbzm * dzhb, wstar3factcrit )
end if
wstar3 = wstar3 / wstar3fact
else ! wstar3 == 0
wstar3fact = 0._r8 ! This is just for dianostic output
cet = 0._r8
ceb = 0._r8
end if
! ---------------------------------------------------------------------------- !
! Calculate net CL mean TKE including entrainment contribution by solving a !
! canonical cubic equation. The solution of cubic equ. is 'rootp**2 = ebrk' !
! where 'ebrk' originally (before solving cubic eq.) was interior CL mean TKE, !
! but after solving cubic equation, it is replaced by net CL mean TKE in the !
! same variable 'ebrk'. !
! ---------------------------------------------------------------------------- !
! Solve cubic equation (canonical form for analytic solution) !
! r^3 - 3*trmp*r - 2*trmq = 0, r = sqrt<e> !
! to estimate <e> for CL, derived from layer-mean TKE balance: !
! !
! <e>^(3/2)/(b_1*<l>) \approx <B + S> (*) !
! <B+S> = (<B+S>_int * l_int + <B+S>_et * dzt + <B+S>_eb * dzb)/lbulk !
! <B+S>_int = <e>^(1/2)/(b_1*<l>)*<e>_int !
! <B+S>_et = (-vyt+vut)*wet*jtbu + radf !
! <B+S>_eb = (-vyb+vub)*web*jbbu !
! !
! where: !
! <> denotes a vertical avg (over the whole CL unless indicated) !
! l_int (called lbrk below) is aggregate thickness of interior CL layers !
! dzt = zi(i,kt)-z(i,kt) is thickness of top entrainment layer !
! dzb = z(i,kb-1)-zi(i,kb) is thickness of bot entrainment layer !
! <e>_int (called ebrk below) is the CL-mean TKE if only interior !
! interfaces contributed. !
! wet, web are top. bottom entrainment rates !
! !
! For a single-level radiatively-driven convective layer, there are no !
! interior interfaces so 'ebrk' = 'lbrk' = 0. If the CL goes to the !
! surface, 'vyb' and 'vub' are set to zero before and 'ebrk' and 'lbrk' !
! have already incorporated the surface interfacial layer contribution, !
! so the same formulas still apply. !
! !
! In the original formulation based on TKE, !
! wet*jtbu = a1l*evhc*<e>^3/2/leng(i,kt) !
! web*jbbu = a1l*<e>^3/2/leng(i,kt) !
! !
! In the wstar formulation !
! wet*jtbu = a1i*evhc*wstar3/lbulk !
! web*jbbu = a1i*wstar3/lbulk, !
! ---------------------------------------------------------------------------- !
fact = ( evhc * ( -vyt + vut ) * dzht + ( -vyb + vub ) * dzhb * leng(i,kb) / leng(i,kt) ) / lbulk
if( wstarent ) then
! (Option 1) 'wstar' entrainment formulation
! Here trmq can have either sign, and will usually be nonzero even for non-
! cloud topped CLs. If trmq > 0, there will be two positive roots r; we take
! the larger one. Why ? If necessary, we limit entrainment and wstar to prevent
! a solution with r < ccrit*wstar ( Why ? ) where we take ccrit = 0.5.
trma = 1._r8
trmp = ebrk(i,ncv) * ( lbrk(i,ncv) / lbulk ) / 3._r8 + ntzero
trmq = 0.5_r8 * b1 * ( leng(i,kt) / lbulk ) * ( radf * dzht + a1i * fact * wstar3 )
! Check if there is an acceptable root with r > rcrit = ccrit*wstar.
! To do this, first find local minimum fmin of the cubic f(r) at sqrt(p),
! and value fcrit = f(rcrit).
rmin = sqrt(trmp)
fmin = rmin * ( rmin * rmin - 3._r8 * trmp ) - 2._r8 * trmq
wstar = wstar3**onet
rcrit = ccrit * wstar
fcrit = rcrit * ( rcrit * rcrit - 3._r8 * trmp ) - 2._r8 * trmq
! No acceptable root exists (noroot = .true.) if either:
! 1) rmin < rcrit (in which case cubic is monotone increasing for r > rcrit)
! and f(rcrit) > 0.
! or 2) rmin > rcrit (in which case min of f(r) in r > rcrit is at rmin)
! and f(rmin) > 0.
! In this case, we reduce entrainment and wstar3 such that r/wstar = ccrit;
! this changes the coefficients of the cubic. It might be informative to
! check when and how many 'noroot' cases occur, since when 'noroot', we
! will impose arbitrary limit on 'wstar3, wet, web, and ebrk' using ccrit.
noroot = ( ( rmin .lt. rcrit ) .and. ( fcrit .gt. 0._r8 ) ) &
.or. ( ( rmin .ge. rcrit ) .and. ( fmin .gt. 0._r8 ) )
if( noroot ) then ! Solve cubic for r
trma = 1._r8 - b1 * ( leng(i,kt) / lbulk ) * a1i * fact / ccrit**3
trma = max( trma, 0.5_r8 ) ! Limit entrainment enhancement of ebrk
trmp = trmp / trma
trmq = 0.5_r8 * b1 * ( leng(i,kt) / lbulk ) * radf * dzht / trma
end if ! noroot
! Solve the cubic equation
qq = trmq**2 - trmp**3
if( qq .ge. 0._r8 ) then
rootp = ( trmq + sqrt(qq) )**(1._r8/3._r8) + ( max( trmq - sqrt(qq), 0._r8 ) )**(1._r8/3._r8)
else
rootp = 2._r8 * sqrt(trmp) * cos( acos( trmq / sqrt(trmp**3) ) / 3._r8 )
end if
! Adjust 'wstar3' only if there is 'noroot'.
! And calculate entrainment rates at the top and base interfaces.
if( noroot ) wstar3 = ( rootp / ccrit )**3 ! Adjust wstar3
wet = cet * wstar3 ! Find entrainment rates
if( kb .lt. pver + 1 ) web = ceb * wstar3 ! When 'kb.eq.pver+1', it was set to web=0.
else !
! (Option.2) wstarentr = .false. Use original entrainment formulation.
! trmp > 0 if there are interior interfaces in CL, trmp = 0 otherwise.
! trmq > 0 if there is cloudtop radiative cooling, trmq = 0 otherwise.
trma = 1._r8 - b1 * a1l * fact
trma = max( trma, 0.5_r8 ) ! Prevents runaway entrainment instability
trmp = ebrk(i,ncv) * ( lbrk(i,ncv) / lbulk ) / ( 3._r8 * trma )
trmq = 0.5_r8 * b1 * ( leng(i,kt) / lbulk ) * radf * dzht / trma
qq = trmq**2 - trmp**3
if( qq .ge. 0._r8 ) then
rootp = ( trmq + sqrt(qq) )**(1._r8/3._r8) + ( max( trmq - sqrt(qq), 0._r8 ) )**(1._r8/3._r8)
else ! Also part of case 3
rootp = 2._r8 * sqrt(trmp) * cos( acos( trmq / sqrt(trmp**3) ) / 3._r8 )
end if ! qq
! Find entrainment rates and limit them by free-entrainment values a1l*sqrt(e)
wet = a1l * rootp * min( evhc * rootp**2 / ( leng(i,kt) * jtbu ), 1._r8 )
if( kb .lt. pver + 1 ) web = a1l * rootp * min( evhc * rootp**2 / ( leng(i,kb) * jbbu ), 1._r8 )
end if ! wstarentr
! ---------------------------------------------------- !
! Finally, get the net CL mean TKE and normalized TKE !
! ---------------------------------------------------- !
ebrk(i,ncv) = rootp**2
ebrk(i,ncv) = min(ebrk(i,ncv),tkemax) ! Limit CL-avg TKE used for entrainment
wbrk(i,ncv) = ebrk(i,ncv)/b1
! The only way ebrk = 0 is for SRCL which are actually radiatively cooled
! at top interface. In this case, we remove 'convective' label from the
! interfaces around this layer. This case should now be impossible, so
! we flag it. Q: I can't understand why this case is impossible now. Maybe,
! due to various limiting procedures used in solving cubic equation ?
! In case of SRCL, 'ebrk' should be positive due to cloud top LW radiative
! cooling contribution, although 'ebrk(internal)' of SRCL before including
! entrainment contribution (which include LW cooling contribution also) is
! zero.
if( ebrk(i,ncv) .le. 0._r8 ) then
write(iulog,*) 'CALEDDY: Warning, CL with zero TKE, i, kt, kb ', i, kt, kb
belongcv(i,kt) = .false.
belongcv(i,kb) = .false.
end if
! ----------------------------------------------------------------------- !
! Calculate complete TKE profiles at all CL interfaces, capped by tkemax. !
! We approximate TKE = <e> at entrainment interfaces. However when CL is !
! based at surface, correct 'tkes' will be inserted to tke(i,pver+1). !
! Note that this approximation at CL external interfaces do not influence !
! numerical calculation since 'e' at external interfaces are not used in !
! actual numerical calculation afterward. In addition in order to extract !
! correct TKE averaged over the PBL in the cumulus scheme,it is necessary !
! to set e = <e> at the top entrainment interface. Since net CL mean TKE !
! 'ebrk' obtained by solving cubic equation already includes tkes ( tkes !
! is included when bflxs > 0 but not when bflxs <= 0 into internal ebrk ),!
! 'tkes' should be written to tke(i,pver+1) !
! ----------------------------------------------------------------------- !
! 1. At internal interfaces
do k = kb - 1, kt + 1, -1
rcap = ( b1 * ae + wcap(i,k) / wbrk(i,ncv) ) / ( b1 * ae + 1._r8 )
rcap = min( max(rcap,rcapmin), rcapmax )
tke(i,k) = ebrk(i,ncv) * rcap
tke(i,k) = min( tke(i,k), tkemax )
kvh(i,k) = leng(i,k) * sqrt(tke(i,k)) * shcl(i,ncv)
kvm(i,k) = leng(i,k) * sqrt(tke(i,k)) * smcl(i,ncv)
bprod(i,k) = -kvh(i,k) * n2(i,k)
sprod(i,k) = kvm(i,k) * s2(i,k)
turbtype(i,k) = 2 ! CL interior interfaces.
sm_aw(i,k) = smcl(i,ncv)/alph1 ! Diagnostic output for microphysics
end do
! 2. At CL top entrainment interface
kentr = wet * jtzm
kvh(i,kt) = kentr
kvm(i,kt) = kentr
bprod(i,kt) = -kentr * n2ht + radf ! I must use 'n2ht' not 'n2'
sprod(i,kt) = kentr * s2(i,kt)
turbtype(i,kt) = 4 ! CL top entrainment interface
trmp = -b1 * ae / ( 1._r8 + b1 * ae )
trmq = -(bprod(i,kt)+sprod(i,kt))*b1*leng(i,kt)/(1._r8+b1*ae)/(ebrk(i,ncv)**(3._r8/2._r8))
rcap = compute_cubic(0._r8,trmp,trmq)**2._r8
rcap = min( max(rcap,rcapmin), rcapmax )
tke(i,kt) = ebrk(i,ncv) * rcap
tke(i,kt) = min( tke(i,kt), tkemax )
sm_aw(i,kt) = smcl(i,ncv) / alph1 ! Diagnostic output for microphysics
! 3. At CL base entrainment interface and double entraining interfaces
! When current CL base is also the top interface of CL regime below,
! simply add the two contributions for calculating eddy diffusivity
! and buoyancy/shear production. Below code correctly works because
! we (CL regime index) always go from surface upward.
if( kb .lt. pver + 1 ) then
kentr = web * jbzm
if( kb .ne. ktblw ) then
kvh(i,kb) = kentr
kvm(i,kb) = kentr
bprod(i,kb) = -kvh(i,kb)*n2hb ! I must use 'n2hb' not 'n2'
sprod(i,kb) = kvm(i,kb)*s2(i,kb)
turbtype(i,kb) = 3 ! CL base entrainment interface
trmp = -b1*ae/(1._r8+b1*ae)
trmq = -(bprod(i,kb)+sprod(i,kb))*b1*leng(i,kb)/(1._r8+b1*ae)/(ebrk(i,ncv)**(3._r8/2._r8))
rcap = compute_cubic(0._r8,trmp,trmq)**2._r8
rcap = min( max(rcap,rcapmin), rcapmax )
tke(i,kb) = ebrk(i,ncv) * rcap
tke(i,kb) = min( tke(i,kb),tkemax )
else
kvh(i,kb) = kvh(i,kb) + kentr
kvm(i,kb) = kvm(i,kb) + kentr
! dzhb5 : Half thickness of the lowest layer of current CL regime
! dzht5 : Half thickness of the highest layer of adjacent CL regime just below current CL.
dzhb5 = z(i,kb-1) - zi(i,kb)
dzht5 = zi(i,kb) - z(i,kb)
bprod(i,kb) = ( dzht5*bprod(i,kb) - dzhb5*kentr*n2hb ) / ( dzhb5 + dzht5 )
sprod(i,kb) = ( dzht5*sprod(i,kb) + dzhb5*kentr*s2(i,kb) ) / ( dzhb5 + dzht5 )
trmp = -b1*ae/(1._r8+b1*ae)
trmq = -kentr*(s2(i,kb)-n2hb)*b1*leng(i,kb)/(1._r8+b1*ae)/(ebrk(i,ncv)**(3._r8/2._r8))
rcap = compute_cubic(0._r8,trmp,trmq)**2._r8
rcap = min( max(rcap,rcapmin), rcapmax )
tke_imsi = ebrk(i,ncv) * rcap
tke_imsi = min( tke_imsi, tkemax )
tke(i,kb) = ( dzht5*tke(i,kb) + dzhb5*tke_imsi ) / ( dzhb5 + dzht5 )
tke(i,kb) = min(tke(i,kb),tkemax)
turbtype(i,kb) = 5 ! CL double entraining interface
end if
else
! If CL base interface is surface, compute similarly using wcap(i,kb)=tkes/b1
! Even when bflx < 0, use the same formula in order to impose consistency of
! tke(i,kb) at bflx = 0._r8
rcap = (b1*ae + wcap(i,kb)/wbrk(i,ncv))/(b1*ae + 1._r8)
rcap = min( max(rcap,rcapmin), rcapmax )
tke(i,kb) = ebrk(i,ncv) * rcap
tke(i,kb) = min( tke(i,kb),tkemax )
end if
! For double entraining interface, simply use smcl(i,ncv) of the overlying CL.
! Below 'sm_aw' is a diagnostic output for use in the microphysics.
! When 'kb' is surface, 'sm' will be over-written later below.
sm_aw(i,kb) = smcl(i,ncv)/alph1
! Calculate wcap at all interfaces of CL. Put a minimum threshold on TKE
! to prevent possible division by zero. 'wcap' at CL internal interfaces
! are already calculated in the first part of 'do ncv' loop correctly.
! When 'kb.eq.pver+1', below formula produces the identical result to the
! 'tkes(i)/b1' if leng(i,kb) is set to vk*z(i,pver). Note wcap(i,pver+1)
! is already defined as 'tkes(i)/b1' at the first part of caleddy.
wcap(i,kt) = (bprod(i,kt)+sprod(i,kt))*leng(i,kt)/sqrt(max(tke(i,kt),1.e-6_r8))
if( kb .lt. pver + 1 ) then
wcap(i,kb) = (bprod(i,kb)+sprod(i,kb))*leng(i,kb)/sqrt(max(tke(i,kb),1.e-6_r8))
end if
! Save the index of upper external interface of current CL-regime in order to
! handle the case when this interface is also the lower external interface of
! CL-regime located just above.
ktblw = kt
! Diagnostic Output
wet_CL(i,ncv) = wet
web_CL(i,ncv) = web
jtbu_CL(i,ncv) = jtbu
jbbu_CL(i,ncv) = jbbu
evhc_CL(i,ncv) = evhc
jt2slv_CL(i,ncv) = jt2slv
n2ht_CL(i,ncv) = n2ht
n2hb_CL(i,ncv) = n2hb
lwp_CL(i,ncv) = lwp
opt_depth_CL(i,ncv) = opt_depth
radinvfrac_CL(i,ncv) = radinvfrac
radf_CL(i,ncv) = radf
wstar_CL(i,ncv) = wstar
wstar3fact_CL(i,ncv) = wstar3fact
end do ! ncv
! Calculate PBL height and characteristic cumulus excess for use in the
! cumulus convection shceme. Also define turbulence type at the surface
! when the lowest CL is based at the surface. These are just diagnostic
! outputs, not influencing numerical calculation of current PBL scheme.
! If the lowest CL is based at the surface, define the PBL depth as the
! CL top interface. The same rule is applied for all CLs including SRCL.
if( ncvsurf .gt. 0 ) then
ktopbl(i) = ktop(i,ncvsurf)
pblh(i) = zi(i, ktopbl(i))
pblhp(i) = pi(i, ktopbl(i))
wpert(i) = max(wfac*sqrt(ebrk(i,ncvsurf)),wpertmin)
tpert(i) = max(abs(shflx(i)*rrho(i)/cpair)*tfac/wpert(i),0._r8)
qpert(i) = max(abs(qflx(i)*rrho(i))*tfac/wpert(i),0._r8)
if( bflxs(i) .gt. 0._r8 ) then
turbtype(i,pver+1) = 2 ! CL interior interface
else
turbtype(i,pver+1) = 3 ! CL external base interface
endif
ipbl(i) = 1._r8
kpblh(i) = ktopbl(i) - 1._r8
end if ! End of the calculationf of te properties of surface-based CL.
! -------------------------------------------- !
! Treatment of Stable Turbulent Regime ( STL ) !
! -------------------------------------------- !
! Identify top and bottom most (internal) interfaces of STL except surface.
! Also, calculate 'turbulent length scale (leng)' at each STL interfaces.
belongst(i,1) = .false. ! k = 1 (top interface) is assumed non-turbulent
do k = 2, pver ! k is an interface index
belongst(i,k) = ( ri(i,k) .lt. ricrit ) .and. ( .not. belongcv(i,k) )
if( belongst(i,k) .and. ( .not. belongst(i,k-1) ) ) then
kt = k ! Top interface index of STL
elseif( .not. belongst(i,k) .and. belongst(i,k-1) ) then
kb = k - 1 ! Base interface index of STL
lbulk = z(i,kt-1) - z(i,kb)
do ks = kt, kb
if( choice_tunl .eq. 'rampcl' ) then
tunlramp = tunl
elseif( choice_tunl .eq. 'rampsl' ) then
tunlramp = max( 1.e-3_r8, ctunl * tunl * exp(-log(ctunl)*ri(i,ks)/ricrit) )
! tunlramp = 0.065_r8 + 0.7_r8 * exp(-20._r8*ri(i,ks))
else
tunlramp = tunl
endif
if( choice_leng .eq. 'origin' ) then
leng(i,ks) = ( (vk*zi(i,ks))**(-cleng) + (tunlramp*lbulk)**(-cleng) )**(-1._r8/cleng)
! leng(i,ks) = vk*zi(i,ks) / (1._r8+vk*zi(i,ks)/(tunlramp*lbulk))
else
leng(i,ks) = min( vk*zi(i,ks), tunlramp*lbulk )
endif
end do
end if
end do ! k
! Now look whether STL extends to ground. If STL extends to surface,
! re-define master length scale,'lbulk' including surface interfacial
! layer thickness, and re-calculate turbulent length scale, 'leng' at
! all STL interfaces again. Note that surface interface is assumed to
! always be STL if it is not CL.
belongst(i,pver+1) = .not. belongcv(i,pver+1)
if( belongst(i,pver+1) ) then ! kb = pver+1 (surface STL)
turbtype(i,pver+1) = 1 ! Surface is STL interface
if( belongst(i,pver) ) then ! STL includes interior
! 'kt' already defined above as the top interface of STL
lbulk = z(i,kt-1)
else ! STL with no interior turbulence
kt = pver+1
lbulk = z(i,kt-1)
end if
! PBL height : Layer mid-point just above the highest STL interface
! Note in contrast to the surface based CL regime where PBL height
! was defined at the top external interface, PBL height of surface
! based STL is defined as the layer mid-point.
ktopbl(i) = kt - 1
pblh(i) = z(i,ktopbl(i))
pblhp(i) = 0.5_r8 * ( pi(i,ktopbl(i)) + pi(i,ktopbl(i)+1) )
! Re-calculate turbulent length scale including surface interfacial
! layer contribution to lbulk.
do ks = kt, pver
if( choice_tunl .eq. 'rampcl' ) then
tunlramp = tunl
elseif( choice_tunl .eq. 'rampsl' ) then
tunlramp = max(1.e-3_r8,ctunl*tunl*exp(-log(ctunl)*ri(i,ks)/ricrit))
! tunlramp = 0.065_r8 + 0.7_r8 * exp(-20._r8*ri(i,ks))
else
tunlramp = tunl
endif
if( choice_leng .eq. 'origin' ) then
leng(i,ks) = ( (vk*zi(i,ks))**(-cleng) + (tunlramp*lbulk)**(-cleng) )**(-1._r8/cleng)
! leng(i,ks) = vk*zi(i,ks) / (1._r8+vk*zi(i,ks)/(tunlramp*lbulk))
else
leng(i,ks) = min( vk*zi(i,ks), tunlramp*lbulk )
endif
end do ! ks
! Characteristic cumulus excess of surface-based STL.
! We may be able to use ustar for wpert.
wpert(i) = 0._r8
tpert(i) = max(shflx(i)*rrho(i)/cpair*fak/ustar(i),0._r8) ! CCM stable-layer forms
qpert(i) = max(qflx(i)*rrho(i)*fak/ustar(i),0._r8)
ipbl(i) = 0._r8
kpblh(i) = ktopbl(i)
end if
! Calculate stability functions and energetics at the STL interfaces
! except the surface. Note that tke(i,pver+1) and wcap(i,pver+1) are
! already calculated in the first part of 'caleddy', kvm(i,pver+1) &
! kvh(i,pver+1) were already initialized to be zero, bprod(i,pver+1)
! & sprod(i,pver+1) were direcly calculated from the bflxs and ustar.
! Note transport term is assumed to be negligible at STL interfaces.
do k = 2, pver
if( belongst(i,k) ) then
turbtype(i,k) = 1 ! STL interfaces
trma = alph3*alph4exs*ri(i,k) + 2._r8*b1*(alph2-alph4exs*alph5*ri(i,k))
trmb = (alph3+alph4exs)*ri(i,k) + 2._r8*b1*(-alph5*ri(i,k)+alph1)
trmc = ri(i,k)
det = max(trmb*trmb-4._r8*trma*trmc,0._r8)
! Sanity Check
if( det .lt. 0._r8 ) then
write(iulog,*) 'The det < 0. for the STL in UW eddy_diff'
stop
end if
gh = (-trmb + sqrt(det))/(2._r8*trma)
! gh = min(max(gh,-0.28_r8),0.0233_r8)
! gh = min(max(gh,-3.5334_r8),0.0233_r8)
gh = min(max(gh,ghmin),0.0233_r8)
sh = max(0._r8,alph5/(1._r8+alph3*gh))
sm = max(0._r8,(alph1 + alph2*gh)/(1._r8+alph3*gh)/(1._r8+alph4exs*gh))
tke(i,k) = b1*(leng(i,k)**2)*(-sh*n2(i,k)+sm*s2(i,k))
tke(i,k) = min(tke(i,k),tkemax)
wcap(i,k) = tke(i,k)/b1
kvh(i,k) = leng(i,k) * sqrt(tke(i,k)) * sh
kvm(i,k) = leng(i,k) * sqrt(tke(i,k)) * sm
bprod(i,k) = -kvh(i,k) * n2(i,k)
sprod(i,k) = kvm(i,k) * s2(i,k)
sm_aw(i,k) = sm/alph1 ! This is diagnostic output for use in the microphysics
end if
end do ! k
! --------------------------------------------------- !
! End of treatment of Stable Turbulent Regime ( STL ) !
! --------------------------------------------------- !
! --------------------------------------------------------------- !
! Re-computation of eddy diffusivity at the entrainment interface !
! assuming that it is purely STL (0<Ri<0.19). Note even Ri>0.19, !
! turbulent can exist at the entrainment interface since 'Sh,Sm' !
! do not necessarily go to zero even when Ri>0.19. Since Ri can !
! be fairly larger than 0.19 at the entrainment interface, I !
! should set minimum value of 'tke' to be 0. in order to prevent !
! sqrt(tke) from being imaginary. !
! --------------------------------------------------------------- !
! goto 888
do k = 2, pver
if( ( turbtype(i,k) .eq. 3 ) .or. ( turbtype(i,k) .eq. 4 ) .or. &
( turbtype(i,k) .eq. 5 ) ) then
trma = alph3*alph4exs*ri(i,k) + 2._r8*b1*(alph2-alph4exs*alph5*ri(i,k))
trmb = (alph3+alph4exs)*ri(i,k) + 2._r8*b1*(-alph5*ri(i,k)+alph1)
trmc = ri(i,k)
det = max(trmb*trmb-4._r8*trma*trmc,0._r8)
gh = (-trmb + sqrt(det))/(2._r8*trma)
! gh = min(max(gh,-0.28_r8),0.0233_r8)
! gh = min(max(gh,-3.5334_r8),0.0233_r8)
gh = min(max(gh,ghmin),0.0233_r8)
sh = max(0._r8,alph5/(1._r8+alph3*gh))
sm = max(0._r8,(alph1 + alph2*gh)/(1._r8+alph3*gh)/(1._r8+alph4exs*gh))
lbulk = z(i,k-1) - z(i,k)
if( choice_tunl .eq. 'rampcl' ) then
tunlramp = tunl
elseif( choice_tunl .eq. 'rampsl' ) then
tunlramp = max(1.e-3_r8,ctunl*tunl*exp(-log(ctunl)*ri(i,k)/ricrit))
! tunlramp = 0.065_r8 + 0.7_r8*exp(-20._r8*ri(i,k))
else
tunlramp = tunl
endif
if( choice_leng .eq. 'origin' ) then
leng_imsi = ( (vk*zi(i,k))**(-cleng) + (tunlramp*lbulk)**(-cleng) )**(-1._r8/cleng)
! leng_imsi = vk*zi(i,k) / (1._r8+vk*zi(i,k)/(tunlramp*lbulk))
else
leng_imsi = min( vk*zi(i,k), tunlramp*lbulk )
endif
tke_imsi = b1*(leng_imsi**2)*(-sh*n2(i,k)+sm*s2(i,k))
tke_imsi = min(max(tke_imsi,0._r8),tkemax)
kvh_imsi = leng_imsi * sqrt(tke_imsi) * sh
kvm_imsi = leng_imsi * sqrt(tke_imsi) * sm
if( kvh(i,k) .lt. kvh_imsi ) then
kvh(i,k) = kvh_imsi
kvm(i,k) = kvm_imsi
leng(i,k) = leng_imsi
tke(i,k) = tke_imsi
wcap(i,k) = tke_imsi / b1
bprod(i,k) = -kvh_imsi * n2(i,k)
sprod(i,k) = kvm_imsi * s2(i,k)
sm_aw(i,k) = sm/alph1 ! This is diagnostic output for use in the microphysics
turbtype(i,k) = 1 ! This was added on Dec.10.2009 for use in microphysics.
endif
end if
end do
! 888 continue
! ------------------------------------------------------------------ !
! End of recomputation of eddy diffusivity at entrainment interfaces !
! ------------------------------------------------------------------ !
! As an option, we can impose a certain minimum back-ground diffusivity.
! do k = 1, pver+1
! kvh(i,k) = max(0.01_r8,kvh(i,k))
! kvm(i,k) = max(0.01_r8,kvm(i,k))
! enddo
! --------------------------------------------------------------------- !
! Diagnostic Output !
! Just for diagnostic purpose, calculate stability functions at each !
! interface including surface. Instead of assuming neutral stability, !
! explicitly calculate stability functions using an reverse procedure !
! starting from tkes(i) similar to the case of SRCL and SBCL in zisocl. !
! Note that it is possible to calculate stability functions even when !
! bflxs < 0. Note that this inverse method allows us to define Ri even !
! at the surface. Note also tkes(i) and sprod(i,pver+1) are always !
! positive values by limiters (e.g., ustar_min = 0.01). !
! Dec.12.2006 : Also just for diagnostic output, re-set !
! 'bprod(i,pver+1)= bflxs(i)' here. Note that this setting does not !
! influence numerical calculation at all - it is just for diagnostic !
! output. !
! --------------------------------------------------------------------- !
bprod(i,pver+1) = bflxs(i)
gg = 0.5_r8*vk*z(i,pver)*bprod(i,pver+1)/(tkes(i)**(3._r8/2._r8))
if( abs(alph5-gg*alph3) .le. 1.e-7_r8 ) then
! gh = -0.28_r8
if( bprod(i,pver+1) .gt. 0._r8 ) then
gh = -3.5334_r8
else
gh = ghmin
endif
else
gh = gg/(alph5-gg*alph3)
end if
! gh = min(max(gh,-0.28_r8),0.0233_r8)
if( bprod(i,pver+1) .gt. 0._r8 ) then
gh = min(max(gh,-3.5334_r8),0.0233_r8)
else
gh = min(max(gh,ghmin),0.0233_r8)
endif
gh_a(i,pver+1) = gh
sh_a(i,pver+1) = max(0._r8,alph5/(1._r8+alph3*gh))
if( bprod(i,pver+1) .gt. 0._r8 ) then
sm_a(i,pver+1) = max(0._r8,(alph1+alph2*gh)/(1._r8+alph3*gh)/(1._r8+alph4*gh))
else
sm_a(i,pver+1) = max(0._r8,(alph1+alph2*gh)/(1._r8+alph3*gh)/(1._r8+alph4exs*gh))
endif
sm_aw(i,pver+1) = sm_a(i,pver+1)/alph1
ri_a(i,pver+1) = -(sm_a(i,pver+1)/sh_a(i,pver+1))*(bprod(i,pver+1)/sprod(i,pver+1))
do k = 1, pver
if( ri(i,k) .lt. 0._r8 ) then
trma = alph3*alph4*ri(i,k) + 2._r8*b1*(alph2-alph4*alph5*ri(i,k))
trmb = (alph3+alph4)*ri(i,k) + 2._r8*b1*(-alph5*ri(i,k)+alph1)
trmc = ri(i,k)
det = max(trmb*trmb-4._r8*trma*trmc,0._r8)
gh = (-trmb + sqrt(det))/(2._r8*trma)
gh = min(max(gh,-3.5334_r8),0.0233_r8)
gh_a(i,k) = gh
sh_a(i,k) = max(0._r8,alph5/(1._r8+alph3*gh))
sm_a(i,k) = max(0._r8,(alph1+alph2*gh)/(1._r8+alph3*gh)/(1._r8+alph4*gh))
ri_a(i,k) = ri(i,k)
else
if( ri(i,k) .gt. ricrit ) then
gh_a(i,k) = ghmin
sh_a(i,k) = 0._r8
sm_a(i,k) = 0._r8
ri_a(i,k) = ri(i,k)
else
trma = alph3*alph4exs*ri(i,k) + 2._r8*b1*(alph2-alph4exs*alph5*ri(i,k))
trmb = (alph3+alph4exs)*ri(i,k) + 2._r8*b1*(-alph5*ri(i,k)+alph1)
trmc = ri(i,k)
det = max(trmb*trmb-4._r8*trma*trmc,0._r8)
gh = (-trmb + sqrt(det))/(2._r8*trma)
gh = min(max(gh,ghmin),0.0233_r8)
gh_a(i,k) = gh
sh_a(i,k) = max(0._r8,alph5/(1._r8+alph3*gh))
sm_a(i,k) = max(0._r8,(alph1+alph2*gh)/(1._r8+alph3*gh)/(1._r8+alph4exs*gh))
ri_a(i,k) = ri(i,k)
endif
endif
end do
do k = 1, pver + 1
turbtype_f(i,k) = real(turbtype(i,k))
end do
end do ! End of column index loop, i
return
end subroutine caleddy
!============================================================================== !
! !
!============================================================================== !
subroutine exacol( pcols, pver, ncol, ri, bflxs, minpblh, zi, ktop, kbase, ncvfin ) 1
! ---------------------------------------------------------------------------- !
! Object : Find unstable CL regimes and determine the indices !
! kbase, ktop which delimit these unstable layers : !
! ri(kbase) > 0 and ri(ktop) > 0, but ri(k) < 0 for ktop < k < kbase. !
! Author : Chris Bretherton 08/2000, !
! Sungsu Park 08/2006, 11/2008 !
!----------------------------------------------------------------------------- !
implicit none
! --------------- !
! Input variables !
! --------------- !
integer, intent(in) :: pcols ! Number of atmospheric columns
integer, intent(in) :: pver ! Number of atmospheric vertical layers
integer, intent(in) :: ncol ! Number of atmospheric columns
real(r8), intent(in) :: ri(pcols,pver) ! Moist gradient Richardson no.
real(r8), intent(in) :: bflxs(pcols) ! Buoyancy flux at surface
real(r8), intent(in) :: minpblh(pcols) ! Minimum PBL height based on surface stress
real(r8), intent(in) :: zi(pcols,pver+1) ! Interface heights
! ---------------- !
! Output variables !
! ---------------- !
integer, intent(out) :: kbase(pcols,ncvmax) ! External interface index of CL base
integer, intent(out) :: ktop(pcols,ncvmax) ! External interface index of CL top
integer, intent(out) :: ncvfin(pcols) ! Total number of CLs
! --------------- !
! Local variables !
! --------------- !
integer :: i
integer :: k
integer :: ncv
real(r8) :: rimaxentr
real(r8) :: riex(pver+1) ! Column Ri profile extended to surface
! ----------------------- !
! Main Computation Begins !
! ----------------------- !
do i = 1, ncol
ncvfin(i) = 0
do ncv = 1, ncvmax
ktop(i,ncv) = 0
kbase(i,ncv) = 0
end do
end do
! ------------------------------------------------------ !
! Find CL regimes starting from the surface going upward !
! ------------------------------------------------------ !
rimaxentr = 0._r8
do i = 1, ncol
riex(2:pver) = ri(i,2:pver)
! Below allows consistent treatment of surface and other interfaces.
! Simply, if surface buoyancy flux is positive, Ri of surface is set to be negative.
riex(pver+1) = rimaxentr - bflxs(i)
ncv = 0
k = pver + 1 ! Work upward from surface interface
do while ( k .gt. ntop_turb + 1 )
! Below means that if 'bflxs > 0' (do not contain '=' sign), surface
! interface is energetically interior surface.
if( riex(k) .lt. rimaxentr ) then
! Identify a new CL
ncv = ncv + 1
! First define 'kbase' as the first interface below the lower-most unstable interface
! Thus, Richardson number at 'kbase' is positive.
kbase(i,ncv) = min(k+1,pver+1)
! Decrement k until top unstable level
do while( riex(k) .lt. rimaxentr .and. k .gt. ntop_turb + 1 )
k = k - 1
end do
! ktop is the first interface above upper-most unstable interface
! Thus, Richardson number at 'ktop' is positive.
ktop(i,ncv) = k
else
! Search upward for a CL.
k = k - 1
end if
end do ! End of CL regime finding for each atmospheric column
ncvfin(i) = ncv
end do ! End of atmospheric column do loop
return
end subroutine exacol
!============================================================================== !
! !
!============================================================================== !
subroutine zisocl( pcols , pver , long , & 1
z , zi , n2 , s2 , &
bprod , sprod , bflxs, tkes , &
ncvfin , kbase , ktop , belongcv, &
ricl , ghcl , shcl , smcl , &
lbrk , wbrk , ebrk , extend , extend_up, extend_dn )
!------------------------------------------------------------------------ !
! Object : This 'zisocl' vertically extends original CLs identified from !
! 'exacol' using a merging test based on either 'wint' or 'l2n2' !
! and identify new CL regimes. Similar to the case of 'exacol', !
! CL regime index increases with height. After identifying new !
! CL regimes ( kbase, ktop, ncvfin ),calculate CL internal mean !
! energetics (lbrk : energetic thickness integral, wbrk, ebrk ) !
! and stability functions (ricl, ghcl, shcl, smcl) by including !
! surface interfacial layer contribution when bflxs > 0. Note !
! that there are two options in the treatment of the energetics !
! of surface interfacial layer (use_dw_surf= 'true' or 'false') !
! Author : Sungsu Park 08/2006, 11/2008 !
!------------------------------------------------------------------------ !
implicit none
! --------------- !
! Input variables !
! --------------- !
integer, intent(in) :: long ! Longitude of the column
integer, intent(in) :: pcols ! Number of atmospheric columns
integer, intent(in) :: pver ! Number of atmospheric vertical layers
real(r8), intent(in) :: z(pcols, pver) ! Layer mid-point height [ m ]
real(r8), intent(in) :: zi(pcols, pver+1) ! Interface height [ m ]
real(r8), intent(in) :: n2(pcols, pver) ! Buoyancy frequency at interfaces except surface [ s-2 ]
real(r8), intent(in) :: s2(pcols, pver) ! Shear frequency at interfaces except surface [ s-2 ]
real(r8), intent(in) :: bprod(pcols,pver+1) ! Buoyancy production [ m2/s3 ]. bprod(i,pver+1) = bflxs
real(r8), intent(in) :: sprod(pcols,pver+1) ! Shear production [ m2/s3 ]. sprod(i,pver+1) = usta**3/(vk*z(i,pver))
real(r8), intent(in) :: bflxs(pcols) ! Surface buoyancy flux [ m2/s3 ]. bprod(i,pver+1) = bflxs
real(r8), intent(in) :: tkes(pcols) ! TKE at the surface [ s2/s2 ]
! ---------------------- !
! Input/output variables !
! ---------------------- !
integer, intent(inout) :: kbase(pcols,ncvmax) ! Base external interface index of CL
integer, intent(inout) :: ktop(pcols,ncvmax) ! Top external interface index of CL
integer, intent(inout) :: ncvfin(pcols) ! Total number of CLs
! ---------------- !
! Output variables !
! ---------------- !
logical, intent(out) :: belongcv(pcols,pver+1) ! True if interface is in a CL ( either internal or external )
real(r8), intent(out) :: ricl(pcols,ncvmax) ! Mean Richardson number of internal CL
real(r8), intent(out) :: ghcl(pcols,ncvmax) ! Half of normalized buoyancy production of internal CL
real(r8), intent(out) :: shcl(pcols,ncvmax) ! Galperin instability function of heat-moisture of internal CL
real(r8), intent(out) :: smcl(pcols,ncvmax) ! Galperin instability function of momentum of internal CL
real(r8), intent(out) :: lbrk(pcols,ncvmax) ! Thickness of (energetically) internal CL ( lint, [m] )
real(r8), intent(out) :: wbrk(pcols,ncvmax) ! Mean normalized TKE of internal CL [ m2/s2 ]
real(r8), intent(out) :: ebrk(pcols,ncvmax) ! Mean TKE of internal CL ( b1*wbrk, [m2/s2] )
! ------------------ !
! Internal variables !
! ------------------ !
logical :: extend ! True when CL is extended in zisocl
logical :: extend_up ! True when CL is extended upward in zisocl
logical :: extend_dn ! True when CL is extended downward in zisocl
logical :: bottom ! True when CL base is at surface ( kb = pver + 1 )
integer :: i ! Local index for the longitude
integer :: ncv ! CL Index increasing with height
integer :: incv
integer :: k
integer :: kb ! Local index for kbase
integer :: kt ! Local index for ktop
integer :: ncvinit ! Value of ncv at routine entrance
integer :: cntu ! Number of merged CLs during upward extension of individual CL
integer :: cntd ! Number of merged CLs during downward extension of individual CL
integer :: kbinc ! Index for incorporating underlying CL
integer :: ktinc ! Index for incorporating overlying CL
real(r8) :: wint ! Normalized TKE of internal CL
real(r8) :: dwinc ! Normalized TKE of CL external interfaces
real(r8) :: dw_surf ! Normalized TKE of surface interfacial layer
real(r8) :: dzinc
real(r8) :: gh
real(r8) :: sh
real(r8) :: sm
real(r8) :: gh_surf ! Half of normalized buoyancy production in surface interfacial layer
real(r8) :: sh_surf ! Galperin instability function in surface interfacial layer
real(r8) :: sm_surf ! Galperin instability function in surface interfacial layer
real(r8) :: l2n2 ! Vertical integral of 'l^2N^2' over CL. Include thickness product
real(r8) :: l2s2 ! Vertical integral of 'l^2S^2' over CL. Include thickness product
real(r8) :: dl2n2 ! Vertical integration of 'l^2*N^2' of CL external interfaces
real(r8) :: dl2s2 ! Vertical integration of 'l^2*S^2' of CL external interfaces
real(r8) :: dl2n2_surf ! 'dl2n2' defined in the surface interfacial layer
real(r8) :: dl2s2_surf ! 'dl2s2' defined in the surface interfacial layer
real(r8) :: lint ! Thickness of (energetically) internal CL
real(r8) :: dlint ! Interfacial layer thickness of CL external interfaces
real(r8) :: dlint_surf ! Surface interfacial layer thickness
real(r8) :: lbulk ! Master Length Scale : Whole CL thickness from top to base external interface
real(r8) :: lz ! Turbulent length scale
real(r8) :: ricll ! Mean Richardson number of internal CL
real(r8) :: trma
real(r8) :: trmb
real(r8) :: trmc
real(r8) :: det
real(r8) :: zbot ! Height of CL base
real(r8) :: l2rat ! Square of ratio of actual to initial CL (not used)
real(r8) :: gg ! Intermediate variable used for calculating stability functions of SBCL
real(r8) :: tunlramp ! Ramping tunl
! ----------------------- !
! Main Computation Begins !
! ----------------------- !
i = long
! Initialize main output variables
do k = 1, ncvmax
ricl(i,k) = 0._r8
ghcl(i,k) = 0._r8
shcl(i,k) = 0._r8
smcl(i,k) = 0._r8
lbrk(i,k) = 0._r8
wbrk(i,k) = 0._r8
ebrk(i,k) = 0._r8
end do
extend = .false.
extend_up = .false.
extend_dn = .false.
! ----------------------------------------------------------- !
! Loop over each CL to see if any of them need to be extended !
! ----------------------------------------------------------- !
ncv = 1
do while( ncv .le. ncvfin(i) )
ncvinit = ncv
cntu = 0
cntd = 0
kb = kbase(i,ncv)
kt = ktop(i,ncv)
! ---------------------------------------------------------------------------- !
! Calculation of CL interior energetics including surface before extension !
! ---------------------------------------------------------------------------- !
! Note that the contribution of interior interfaces (not surface) to 'wint' is !
! accounted by using '-sh*l2n2 + sm*l2s2' while the contribution of surface is !
! accounted by using 'dwsurf = tkes/b1' when bflxs > 0. This approach is fully !
! reasonable. Another possible alternative, which seems to be also consistent !
! is to calculate 'dl2n2_surf' and 'dl2s2_surf' of surface interfacial layer !
! separately, and this contribution is explicitly added by initializing 'l2n2' !
! 'l2s2' not by zero, but by 'dl2n2_surf' and 'ds2n2_surf' below. At the same !
! time, 'dwsurf' should be excluded in 'wint' calculation below. The only diff.!
! between two approaches is that in case of the latter approach, contributions !
! of surface interfacial layer to the CL mean stability function (ri,gh,sh,sm) !
! are explicitly included while the first approach is not. In this sense, the !
! second approach seems to be more conceptually consistent, but currently, I !
! (Sungsu) will keep the first default approach. There is a switch !
! 'use_dw_surf' at the first part of eddy_diff.F90 chosing one of !
! these two options. !
! ---------------------------------------------------------------------------- !
! ------------------------------------------------------ !
! Step 0: Calculate surface interfacial layer energetics !
! ------------------------------------------------------ !
lbulk = zi(i,kt) - zi(i,kb)
dlint_surf = 0._r8
dl2n2_surf = 0._r8
dl2s2_surf = 0._r8
dw_surf = 0._r8
if( kb .eq. pver+1 ) then
if( bflxs(i) .gt. 0._r8 ) then
! Calculate stability functions of surface interfacial layer
! from the given 'bprod(i,pver+1)' and 'sprod(i,pver+1)' using
! inverse approach. Since alph5>0 and alph3<0, denominator of
! gg is always positive if bprod(i,pver+1)>0.
gg = 0.5_r8*vk*z(i,pver)*bprod(i,pver+1)/(tkes(i)**(3._r8/2._r8))
gh = gg/(alph5-gg*alph3)
! gh = min(max(gh,-0.28_r8),0.0233_r8)
gh = min(max(gh,-3.5334_r8),0.0233_r8)
sh = alph5/(1._r8+alph3*gh)
sm = (alph1 + alph2*gh)/(1._r8+alph3*gh)/(1._r8+alph4*gh)
ricll = min(-(sm/sh)*(bprod(i,pver+1)/sprod(i,pver+1)),ricrit)
! Calculate surface interfacial layer contribution to CL internal
! energetics. By construction, 'dw_surf = -dl2n2_surf + ds2n2_surf'
! is exactly satisfied, which corresponds to assuming turbulent
! length scale of surface interfacial layer = vk * z(i,pver). Note
! 'dl2n2_surf','dl2s2_surf','dw_surf' include thickness product.
dlint_surf = z(i,pver)
dl2n2_surf = -vk*(z(i,pver)**2)*bprod(i,pver+1)/(sh*sqrt(tkes(i)))
dl2s2_surf = vk*(z(i,pver)**2)*sprod(i,pver+1)/(sm*sqrt(tkes(i)))
dw_surf = (tkes(i)/b1)*z(i,pver)
else
! Note that this case can happen when surface is an external
! interface of CL.
lbulk = zi(i,kt) - z(i,pver)
end if
end if
! ------------------------------------------------------ !
! Step 1: Include surface interfacial layer contribution !
! ------------------------------------------------------ !
lint = dlint_surf
l2n2 = dl2n2_surf
l2s2 = dl2s2_surf
wint = dw_surf
if( use_dw_surf ) then
l2n2 = 0._r8
l2s2 = 0._r8
else
wint = 0._r8
end if
! --------------------------------------------------------------------------------- !
! Step 2. Include the contribution of 'pure internal interfaces' other than surface !
! --------------------------------------------------------------------------------- !
if( kt .lt. kb - 1 ) then ! The case of non-SBCL.
do k = kb - 1, kt + 1, -1
if( choice_tunl .eq. 'rampcl' ) then
! Modification : I simply used the average tunlramp between the two limits.
tunlramp = 0.5_r8*(1._r8+ctunl)*tunl
elseif( choice_tunl .eq. 'rampsl' ) then
tunlramp = ctunl*tunl
! tunlramp = 0.765_r8
else
tunlramp = tunl
endif
if( choice_leng .eq. 'origin' ) then
lz = ( (vk*zi(i,k))**(-cleng) + (tunlramp*lbulk)**(-cleng) )**(-1._r8/cleng)
! lz = vk*zi(i,k) / (1._r8+vk*zi(i,k)/(tunlramp*lbulk))
else
lz = min( vk*zi(i,k), tunlramp*lbulk )
endif
dzinc = z(i,k-1) - z(i,k)
l2n2 = l2n2 + lz*lz*n2(i,k)*dzinc
l2s2 = l2s2 + lz*lz*s2(i,k)*dzinc
lint = lint + dzinc
end do
! Calculate initial CL stability functions (gh,sh,sm) and net
! internal energy of CL including surface contribution if any.
! Modification : It seems that below cannot be applied when ricrit > 0.19.
! May need future generalization.
ricll = min(l2n2/max(l2s2,ntzero),ricrit) ! Mean Ri of internal CL
trma = alph3*alph4*ricll+2._r8*b1*(alph2-alph4*alph5*ricll)
trmb = ricll*(alph3+alph4)+2._r8*b1*(-alph5*ricll+alph1)
trmc = ricll
det = max(trmb*trmb-4._r8*trma*trmc,0._r8)
gh = (-trmb + sqrt(det))/2._r8/trma
! gh = min(max(gh,-0.28_r8),0.0233_r8)
gh = min(max(gh,-3.5334_r8),0.0233_r8)
sh = alph5/(1._r8+alph3*gh)
sm = (alph1 + alph2*gh)/(1._r8+alph3*gh)/(1._r8+alph4*gh)
wint = wint - sh*l2n2 + sm*l2s2
else ! The case of SBCL
! If there is no pure internal interface, use only surface interfacial
! values. However, re-set surface interfacial values such that it can
! be used in the merging tests (either based on 'wint' or 'l2n2') and
! in such that surface interfacial energy is not double-counted.
! Note that regardless of the choise of 'use_dw_surf', below should be
! kept as it is below, for consistent merging test of extending SBCL.
lint = dlint_surf
l2n2 = dl2n2_surf
l2s2 = dl2s2_surf
wint = dw_surf
! Aug.29.2006 : Only for the purpose of merging test of extending SRCL
! based on 'l2n2', re-define 'l2n2' of surface interfacial layer using
! 'wint'. This part is designed for similar treatment of merging as in
! the original 'eddy_diff.F90' code, where 'l2n2' of SBCL was defined
! as 'l2n2 = - wint / sh'. Note that below block is used only when (1)
! surface buoyancy production 'bprod(i,pver+1)' is NOT included in the
! calculation of surface TKE in the initialization of 'bprod(i,pver+1)'
! in the main subroutine ( even though bflxs > 0 ), and (2) to force
! current scheme be similar to the previous scheme in the treatment of
! extending-merging test of SBCL based on 'l2n2'. Otherwise below line
! must be commented out. Note at this stage, correct non-zero value of
! 'sh' has been already computed.
if( choice_tkes .eq. 'ebprod' ) then
l2n2 = - wint / sh
endif
endif
! Set consistent upper limits on 'l2n2' and 'l2s2'. Below limits are
! reasonable since l2n2 of CL interior interface is always negative.
l2n2 = -min(-l2n2, tkemax*lint/(b1*sh))
l2s2 = min( l2s2, tkemax*lint/(b1*sm))
! Note that at this stage, ( gh, sh, sm ) are the values of surface
! interfacial layer if there is no pure internal interface, while if
! there is pure internal interface, ( gh, sh, sm ) are the values of
! pure CL interfaces or the values that include both the CL internal
! interfaces and surface interfaces, depending on the 'use_dw_surf'.
! ----------------------------------------------------------------------- !
! Perform vertical extension-merging process !
! ----------------------------------------------------------------------- !
! During the merging process, we assumed ( lbulk, sh, sm ) of CL external !
! interfaces are the same as the ones of the original merging CL. This is !
! an inevitable approximation since we don't know ( sh, sm ) of external !
! interfaces at this stage. Note that current default merging test is !
! purely based on buoyancy production without including shear production, !
! since we used 'l2n2' instead of 'wint' as a merging parameter. However, !
! merging test based on 'wint' maybe conceptually more attractable. !
! Downward CL merging process is identical to the upward merging process, !
! but when the base of extended CL reaches to the surface, surface inter !
! facial layer contribution to the energetic of extended CL must be done !
! carefully depending on the sign of surface buoyancy flux. The contribu !
! tion of surface interfacial layer energetic is included to the internal !
! energetics of merging CL only when bflxs > 0. !
! ----------------------------------------------------------------------- !
! ---------------------------- !
! Step 1. Extend the CL upward !
! ---------------------------- !
extend = .false. ! This will become .true. if CL top or base is extended
! Calculate contribution of potentially incorporable CL top interface
if( choice_tunl .eq. 'rampcl' ) then
tunlramp = 0.5_r8*(1._r8+ctunl)*tunl
elseif( choice_tunl .eq. 'rampsl' ) then
tunlramp = ctunl*tunl
! tunlramp = 0.765_r8
else
tunlramp = tunl
endif
if( choice_leng .eq. 'origin' ) then
lz = ( (vk*zi(i,kt))**(-cleng) + (tunlramp*lbulk)**(-cleng) )**(-1._r8/cleng)
! lz = vk*zi(i,kt) / (1._r8+vk*zi(i,kt)/(tunlramp*lbulk))
else
lz = min( vk*zi(i,kt), tunlramp*lbulk )
endif
dzinc = z(i,kt-1)-z(i,kt)
dl2n2 = lz*lz*n2(i,kt)*dzinc
dl2s2 = lz*lz*s2(i,kt)*dzinc
dwinc = -sh*dl2n2 + sm*dl2s2
! ------------ !
! Merging Test !
! ------------ !
! do while ( dwinc .gt. ( rinc*dzinc*wint/(lint+(1._r8-rinc)*dzinc)) ) ! Merging test based on wint
! do while ( -dl2n2 .gt. (-rinc*dzinc*l2n2/(lint+(1._r8-rinc)*dzinc)) ) ! Merging test based on l2n2
do while ( -dl2n2 .gt. (-rinc*l2n2/(1._r8-rinc)) ) ! Integral merging test
! Add contribution of top external interface to interior energy.
! Note even when we chose 'use_dw_surf='true.', the contribution
! of surface interfacial layer to 'l2n2' and 'l2s2' are included
! here. However it is not double counting of surface interfacial
! energy : surface interfacial layer energy is counted in 'wint'
! formula and 'l2n2' is just used for performing merging test in
! this 'do while' loop.
lint = lint + dzinc
l2n2 = l2n2 + dl2n2
l2n2 = -min(-l2n2, tkemax*lint/(b1*sh))
l2s2 = l2s2 + dl2s2
wint = wint + dwinc
! Extend top external interface of CL upward after merging
kt = kt - 1
extend = .true.
extend_up = .true.
if( kt .eq. ntop_turb ) then
write(iulog,*) 'zisocl: Error: Tried to extend CL to the model top'
stop
end if
! If the top external interface of extending CL is the same as the
! top interior interface of the overlying CL, overlying CL will be
! automatically merged. Then,reduce total number of CL regime by 1.
! and increase 'cntu'(number of merged CLs during upward extension)
! by 1.
ktinc = kbase(i,ncv+cntu+1) - 1 ! Lowest interior interface of overlying CL
if( kt .eq. ktinc ) then
do k = kbase(i,ncv+cntu+1) - 1, ktop(i,ncv+cntu+1) + 1, -1
if( choice_tunl .eq. 'rampcl' ) then
tunlramp = 0.5_r8*(1._r8+ctunl)*tunl
elseif( choice_tunl .eq. 'rampsl' ) then
tunlramp = ctunl*tunl
! tunlramp = 0.765_r8
else
tunlramp = tunl
endif
if( choice_leng .eq. 'origin' ) then
lz = ( (vk*zi(i,k))**(-cleng) + (tunlramp*lbulk)**(-cleng) )**(-1._r8/cleng)
! lz = vk*zi(i,k) / (1._r8+vk*zi(i,k)/(tunlramp*lbulk))
else
lz = min( vk*zi(i,k), tunlramp*lbulk )
endif
dzinc = z(i,k-1)-z(i,k)
dl2n2 = lz*lz*n2(i,k)*dzinc
dl2s2 = lz*lz*s2(i,k)*dzinc
dwinc = -sh*dl2n2 + sm*dl2s2
lint = lint + dzinc
l2n2 = l2n2 + dl2n2
l2n2 = -min(-l2n2, tkemax*lint/(b1*sh))
l2s2 = l2s2 + dl2s2
wint = wint + dwinc
end do
kt = ktop(i,ncv+cntu+1)
ncvfin(i) = ncvfin(i) - 1
cntu = cntu + 1
end if
! Again, calculate the contribution of potentially incorporatable CL
! top external interface of CL regime.
if( choice_tunl .eq. 'rampcl' ) then
tunlramp = 0.5_r8*(1._r8+ctunl)*tunl
elseif( choice_tunl .eq. 'rampsl' ) then
tunlramp = ctunl*tunl
! tunlramp = 0.765_r8
else
tunlramp = tunl
endif
if( choice_leng .eq. 'origin' ) then
lz = ( (vk*zi(i,kt))**(-cleng) + (tunlramp*lbulk)**(-cleng) )**(-1._r8/cleng)
! lz = vk*zi(i,kt) / (1._r8+vk*zi(i,kt)/(tunlramp*lbulk))
else
lz = min( vk*zi(i,kt), tunlramp*lbulk )
endif
dzinc = z(i,kt-1)-z(i,kt)
dl2n2 = lz*lz*n2(i,kt)*dzinc
dl2s2 = lz*lz*s2(i,kt)*dzinc
dwinc = -sh*dl2n2 + sm*dl2s2
end do ! End of upward merging test 'do while' loop
! Update CL interface indices appropriately if any CL was merged.
! Note that below only updated the interface index of merged CL,
! not the original merging CL. Updates of 'kbase' and 'ktop' of
! the original merging CL will be done after finishing downward
! extension also later.
if( cntu .gt. 0 ) then
do incv = 1, ncvfin(i) - ncv
kbase(i,ncv+incv) = kbase(i,ncv+cntu+incv)
ktop(i,ncv+incv) = ktop(i,ncv+cntu+incv)
end do
end if
! ------------------------------ !
! Step 2. Extend the CL downward !
! ------------------------------ !
if( kb .ne. pver + 1 ) then
! Calculate contribution of potentially incorporable CL base interface
if( choice_tunl .eq. 'rampcl' ) then
tunlramp = 0.5_r8*(1._r8+ctunl)*tunl
elseif( choice_tunl .eq. 'rampsl' ) then
tunlramp = ctunl*tunl
! tunlramp = 0.765_r8
else
tunlramp = tunl
endif
if( choice_leng .eq. 'origin' ) then
lz = ( (vk*zi(i,kb))**(-cleng) + (tunlramp*lbulk)**(-cleng) )**(-1._r8/cleng)
! lz = vk*zi(i,kb) / (1._r8+vk*zi(i,kb)/(tunlramp*lbulk))
else
lz = min( vk*zi(i,kb), tunlramp*lbulk )
endif
dzinc = z(i,kb-1)-z(i,kb)
dl2n2 = lz*lz*n2(i,kb)*dzinc
dl2s2 = lz*lz*s2(i,kb)*dzinc
dwinc = -sh*dl2n2 + sm*dl2s2
! ------------ !
! Merging test !
! ------------ !
! In the below merging tests, I must keep '.and.(kb.ne.pver+1)',
! since 'kb' is continuously updated within the 'do while' loop
! whenever CL base is merged.
! do while( ( dwinc .gt. ( rinc*dzinc*wint/(lint+(1._r8-rinc)*dzinc)) ) & ! Merging test based on wint
! do while( ( -dl2n2 .gt. (-rinc*dzinc*l2n2/(lint+(1._r8-rinc)*dzinc)) ) & ! Merging test based on l2n2
! .and.(kb.ne.pver+1))
do while( ( -dl2n2 .gt. (-rinc*l2n2/(1._r8-rinc)) ) & ! Integral merging test
.and.(kb.ne.pver+1))
! Add contributions from interfacial layer kb to CL interior
lint = lint + dzinc
l2n2 = l2n2 + dl2n2
l2n2 = -min(-l2n2, tkemax*lint/(b1*sh))
l2s2 = l2s2 + dl2s2
wint = wint + dwinc
! Extend the base external interface of CL downward after merging
kb = kb + 1
extend = .true.
extend_dn = .true.
! If the base external interface of extending CL is the same as the
! base interior interface of the underlying CL, underlying CL will
! be automatically merged. Then, reduce total number of CL by 1.
! For a consistent treatment with 'upward' extension, I should use
! 'kbinc = kbase(i,ncv-1) - 1' instead of 'ktop(i,ncv-1) + 1' below.
! However, it seems that these two methods produce the same results.
! Note also that in contrast to upward merging, the decrease of ncv
! should be performed here.
! Note that below formula correctly works even when upperlying CL
! regime incorporates below SBCL.
kbinc = 0
if( ncv .gt. 1 ) kbinc = ktop(i,ncv-1) + 1
if( kb .eq. kbinc ) then
do k = ktop(i,ncv-1) + 1, kbase(i,ncv-1) - 1
if( choice_tunl .eq. 'rampcl' ) then
tunlramp = 0.5_r8*(1._r8+ctunl)*tunl
elseif( choice_tunl .eq. 'rampsl' ) then
tunlramp = ctunl*tunl
! tunlramp = 0.765_r8
else
tunlramp = tunl
endif
if( choice_leng .eq. 'origin' ) then
lz = ( (vk*zi(i,k))**(-cleng) + (tunlramp*lbulk)**(-cleng) )**(-1._r8/cleng)
! lz = vk*zi(i,k) / (1._r8+vk*zi(i,k)/(tunlramp*lbulk))
else
lz = min( vk*zi(i,k), tunlramp*lbulk )
endif
dzinc = z(i,k-1)-z(i,k)
dl2n2 = lz*lz*n2(i,k)*dzinc
dl2s2 = lz*lz*s2(i,k)*dzinc
dwinc = -sh*dl2n2 + sm*dl2s2
lint = lint + dzinc
l2n2 = l2n2 + dl2n2
l2n2 = -min(-l2n2, tkemax*lint/(b1*sh))
l2s2 = l2s2 + dl2s2
wint = wint + dwinc
end do
! We are incorporating interior of CL ncv-1, so merge
! this CL into the current CL.
kb = kbase(i,ncv-1)
ncv = ncv - 1
ncvfin(i) = ncvfin(i) -1
cntd = cntd + 1
end if
! Calculate the contribution of potentially incorporatable CL
! base external interface. Calculate separately when the base
! of extended CL is surface and non-surface.
if( kb .eq. pver + 1 ) then
if( bflxs(i) .gt. 0._r8 ) then
! Calculate stability functions of surface interfacial layer
gg = 0.5_r8*vk*z(i,pver)*bprod(i,pver+1)/(tkes(i)**(3._r8/2._r8))
gh_surf = gg/(alph5-gg*alph3)
! gh_surf = min(max(gh_surf,-0.28_r8),0.0233_r8)
gh_surf = min(max(gh_surf,-3.5334_r8),0.0233_r8)
sh_surf = alph5/(1._r8+alph3*gh_surf)
sm_surf = (alph1 + alph2*gh_surf)/(1._r8+alph3*gh_surf)/(1._r8+alph4*gh_surf)
! Calculate surface interfacial layer contribution. By construction,
! it exactly becomes 'dw_surf = -dl2n2_surf + ds2n2_surf'
dlint_surf = z(i,pver)
dl2n2_surf = -vk*(z(i,pver)**2._r8)*bprod(i,pver+1)/(sh_surf*sqrt(tkes(i)))
dl2s2_surf = vk*(z(i,pver)**2._r8)*sprod(i,pver+1)/(sm_surf*sqrt(tkes(i)))
dw_surf = (tkes(i)/b1)*z(i,pver)
else
dlint_surf = 0._r8
dl2n2_surf = 0._r8
dl2s2_surf = 0._r8
dw_surf = 0._r8
end if
! If (kb.eq.pver+1), updating of CL internal energetics should be
! performed here inside of 'do while' loop, since 'do while' loop
! contains the constraint of '.and.(kb.ne.pver+1)',so updating of
! CL internal energetics cannot be performed within this do while
! loop when kb.eq.pver+1. Even though I updated all 'l2n2','l2s2',
! 'wint' below, only the updated 'wint' is used in the following
! numerical calculation.
lint = lint + dlint_surf
l2n2 = l2n2 + dl2n2_surf
l2n2 = -min(-l2n2, tkemax*lint/(b1*sh))
l2s2 = l2s2 + dl2s2_surf
wint = wint + dw_surf
else
if( choice_tunl .eq. 'rampcl' ) then
tunlramp = 0.5_r8*(1._r8+ctunl)*tunl
elseif( choice_tunl .eq. 'rampsl' ) then
tunlramp = ctunl*tunl
! tunlramp = 0.765_r8
else
tunlramp = tunl
endif
if( choice_leng .eq. 'origin' ) then
lz = ( (vk*zi(i,kb))**(-cleng) + (tunlramp*lbulk)**(-cleng) )**(-1._r8/cleng)
! lz = vk*zi(i,kb) / (1._r8+vk*zi(i,kb)/(tunlramp*lbulk))
else
lz = min( vk*zi(i,kb), tunlramp*lbulk )
endif
dzinc = z(i,kb-1)-z(i,kb)
dl2n2 = lz*lz*n2(i,kb)*dzinc
dl2s2 = lz*lz*s2(i,kb)*dzinc
dwinc = -sh*dl2n2 + sm*dl2s2
end if
end do ! End of merging test 'do while' loop
if( (kb.eq.pver+1) .and. (ncv.ne.1) ) then
write(iulog,*) 'Major mistake zisocl: the CL based at surface is not indexed 1'
stop
end if
end if ! Done with bottom extension of CL
! Update CL interface indices appropriately if any CL was merged.
! Note that below only updated the interface index of merged CL,
! not the original merging CL. Updates of 'kbase' and 'ktop' of
! the original merging CL will be done later below. I should
! check in detail if below index updating is correct or not.
if( cntd .gt. 0 ) then
do incv = 1, ncvfin(i) - ncv
kbase(i,ncv+incv) = kbase(i,ncvinit+incv)
ktop(i,ncv+incv) = ktop(i,ncvinit+incv)
end do
end if
! Sanity check for positive wint.
if( wint .lt. 0.01_r8 ) then
wint = 0.01_r8
end if
! -------------------------------------------------------------------------- !
! Finally update CL mean internal energetics including surface contribution !
! after finishing all the CL extension-merging process. As mentioned above, !
! there are two possible ways in the treatment of surface interfacial layer, !
! either through 'dw_surf' or 'dl2n2_surf and dl2s2_surf' by setting logical !
! variable 'use_dw_surf' =.true. or .false. In any cases, we should avoid !
! double counting of surface interfacial layer and one single consistent way !
! should be used throughout the program. !
! -------------------------------------------------------------------------- !
if( extend ) then
ktop(i,ncv) = kt
kbase(i,ncv) = kb
! ------------------------------------------------------ !
! Step 1: Include surface interfacial layer contribution !
! ------------------------------------------------------ !
lbulk = zi(i,kt) - zi(i,kb)
dlint_surf = 0._r8
dl2n2_surf = 0._r8
dl2s2_surf = 0._r8
dw_surf = 0._r8
if( kb .eq. pver + 1 ) then
if( bflxs(i) .gt. 0._r8 ) then
! Calculate stability functions of surface interfacial layer
gg = 0.5_r8*vk*z(i,pver)*bprod(i,pver+1)/(tkes(i)**(3._r8/2._r8))
gh = gg/(alph5-gg*alph3)
! gh = min(max(gh,-0.28_r8),0.0233_r8)
gh = min(max(gh,-3.5334_r8),0.0233_r8)
sh = alph5/(1._r8+alph3*gh)
sm = (alph1 + alph2*gh)/(1._r8+alph3*gh)/(1._r8+alph4*gh)
! Calculate surface interfacial layer contribution. By construction,
! it exactly becomes 'dw_surf = -dl2n2_surf + ds2n2_surf'
dlint_surf = z(i,pver)
dl2n2_surf = -vk*(z(i,pver)**2._r8)*bprod(i,pver+1)/(sh*sqrt(tkes(i)))
dl2s2_surf = vk*(z(i,pver)**2._r8)*sprod(i,pver+1)/(sm*sqrt(tkes(i)))
dw_surf = (tkes(i)/b1)*z(i,pver)
else
lbulk = zi(i,kt) - z(i,pver)
end if
end if
lint = dlint_surf
l2n2 = dl2n2_surf
l2s2 = dl2s2_surf
wint = dw_surf
if( use_dw_surf ) then
l2n2 = 0._r8
l2s2 = 0._r8
else
wint = 0._r8
end if
! -------------------------------------------------------------- !
! Step 2. Include the contribution of 'pure internal interfaces' !
! -------------------------------------------------------------- !
do k = kt + 1, kb - 1
if( choice_tunl .eq. 'rampcl' ) then
tunlramp = 0.5_r8*(1._r8+ctunl)*tunl
elseif( choice_tunl .eq. 'rampsl' ) then
tunlramp = ctunl*tunl
! tunlramp = 0.765_r8
else
tunlramp = tunl
endif
if( choice_leng .eq. 'origin' ) then
lz = ( (vk*zi(i,k))**(-cleng) + (tunlramp*lbulk)**(-cleng) )**(-1._r8/cleng)
! lz = vk*zi(i,k) / (1._r8+vk*zi(i,k)/(tunlramp*lbulk))
else
lz = min( vk*zi(i,k), tunlramp*lbulk )
endif
dzinc = z(i,k-1) - z(i,k)
lint = lint + dzinc
l2n2 = l2n2 + lz*lz*n2(i,k)*dzinc
l2s2 = l2s2 + lz*lz*s2(i,k)*dzinc
end do
ricll = min(l2n2/max(l2s2,ntzero),ricrit)
trma = alph3*alph4*ricll+2._r8*b1*(alph2-alph4*alph5*ricll)
trmb = ricll*(alph3+alph4)+2._r8*b1*(-alph5*ricll+alph1)
trmc = ricll
det = max(trmb*trmb-4._r8*trma*trmc,0._r8)
gh = (-trmb + sqrt(det))/2._r8/trma
! gh = min(max(gh,-0.28_r8),0.0233_r8)
gh = min(max(gh,-3.5334_r8),0.0233_r8)
sh = alph5 / (1._r8+alph3*gh)
sm = (alph1 + alph2*gh)/(1._r8+alph3*gh)/(1._r8+alph4*gh)
! Even though the 'wint' after finishing merging was positive, it is
! possible that re-calculated 'wint' here is negative. In this case,
! correct 'wint' to be a small positive number
wint = max( wint - sh*l2n2 + sm*l2s2, 0.01_r8 )
end if
! ---------------------------------------------------------------------- !
! Calculate final output variables of each CL (either has merged or not) !
! ---------------------------------------------------------------------- !
lbrk(i,ncv) = lint
wbrk(i,ncv) = wint/lint
ebrk(i,ncv) = b1*wbrk(i,ncv)
ebrk(i,ncv) = min(ebrk(i,ncv),tkemax)
ricl(i,ncv) = ricll
ghcl(i,ncv) = gh
shcl(i,ncv) = sh
smcl(i,ncv) = sm
! Increment counter for next CL. I should check if the increament of 'ncv'
! below is reasonable or not, since whenever CL is merged during downward
! extension process, 'ncv' is lowered down continuously within 'do' loop.
! But it seems that below 'ncv = ncv + 1' is perfectly correct.
ncv = ncv + 1
end do ! End of loop over each CL regime, ncv.
! ---------------------------------------------------------- !
! Re-initialize external interface indices which are not CLs !
! ---------------------------------------------------------- !
do ncv = ncvfin(i) + 1, ncvmax
ktop(i,ncv) = 0
kbase(i,ncv) = 0
end do
! ------------------------------------------------ !
! Update CL interface identifiers, 'belongcv' !
! CL external interfaces are also identified as CL !
! ------------------------------------------------ !
do k = 1, pver + 1
belongcv(i,k) = .false.
end do
do ncv = 1, ncvfin(i)
do k = ktop(i,ncv), kbase(i,ncv)
belongcv(i,k) = .true.
end do
end do
return
end subroutine zisocl
real(r8) function compute_cubic(a,b,c) 3
! ------------------------------------------------------------------------- !
! Solve canonical cubic : x^3 + a*x^2 + b*x + c = 0, x = sqrt(e)/sqrt(<e>) !
! Set x = max(xmin,x) at the end !
! ------------------------------------------------------------------------- !
implicit none
real(r8), intent(in) :: a, b, c
real(r8) qq, rr, dd, theta, aa, bb, x1, x2, x3
real(r8), parameter :: xmin = 1.e-2_r8
qq = (a**2-3._r8*b)/9._r8
rr = (2._r8*a**3 - 9._r8*a*b + 27._r8*c)/54._r8
dd = rr**2 - qq**3
if( dd .le. 0._r8 ) then
theta = acos(rr/qq**(3._r8/2._r8))
x1 = -2._r8*sqrt(qq)*cos(theta/3._r8) - a/3._r8
x2 = -2._r8*sqrt(qq)*cos((theta+2._r8*3.141592)/3._r8) - a/3._r8
x3 = -2._r8*sqrt(qq)*cos((theta-2._r8*3.141592)/3._r8) - a/3._r8
compute_cubic = max(max(max(x1,x2),x3),xmin)
return
else
if( rr .ge. 0._r8 ) then
aa = -(sqrt(rr**2-qq**3)+rr)**(1._r8/3._r8)
else
aa = (sqrt(rr**2-qq**3)-rr)**(1._r8/3._r8)
endif
if( aa .eq. 0._r8 ) then
bb = 0._r8
else
bb = qq/aa
endif
compute_cubic = max((aa+bb)-a/3._r8,xmin)
return
endif
return
end function compute_cubic
END MODULE eddy_diff