!pbl_dry_contrgradient.f90
!>@brief implements mass-flux contr-gradient parametrization
module pbl_dry_contrgradient
implicit none
type pblContrGradDataType
real, allocatable :: wu(:), &
theta_up(:), &
thetav_up(:), &
ua_up(:), &
va_up(:), &
qv_up(:), &
entr(:)
real :: theta_up0, thetav_up0, qv_up0
real :: ua_up0, va_up0
real :: ua_upH, va_upH
real :: theta_upH, thetav_upH, qv_upH
end type pblContrGradDataType
real, parameter :: c_entr = 0.38 !< dry entrainment parameterization
real, parameter :: b1 = 1.8; !< vertical velocity in updraft Bernulli equation constant
real, parameter :: b2 = 3.5; !< vertical velocity in updraft Bernulli equation constant
real, parameter :: wstrmin = 1.0e-6 !< minimimal deardorff velocity
real, parameter :: lmin_entr = 1.0e6 !< maximum entrainement scale above CBL
real, parameter :: tau_dry_scale = 500.0 !< Time scale for entrainment
real, parameter :: a0 = 0.08 !< Updraft fraction area
real, parameter :: alph0 = 0.25 !< amount of surface dispersion to transfer to updraft
public cbl_allocate, cbl_deallocate
public cbl_get_entrainment, cbl_get_up
public cbl_get_wu, cbl_apply_cntrg
contains
subroutine cbl_allocate(cbl, kmax)
integer, intent(in):: kmax
type(pblContrGradDataType), intent(out):: cbl
allocate(cbl%entr(kmax))
allocate(cbl%theta_up(kmax))
allocate(cbl%thetav_up(kmax))
allocate(cbl%qv_up(kmax))
allocate(cbl%ua_up(kmax))
allocate(cbl%va_up(kmax))
allocate(cbl%wu(kmax))
end subroutine cbl_allocate
subroutine cbl_deallocate(cbl)
type(pblContrGradDataType), intent(inout):: cbl
deallocate(cbl%entr)
deallocate(cbl%theta_up)
deallocate(cbl%thetav_up)
deallocate(cbl%qv_up)
deallocate(cbl%ua_up)
deallocate(cbl%va_up)
deallocate(cbl%wu)
end subroutine cbl_deallocate
subroutine cbl_get_entrainment(cbl, bl, fluid, grid)
use scm_state_data, only : stateBLDataType
use pbl_turb_data, only : turbBLDataType
use phys_fluid, only: fluidParamsDataType
use pbl_grid, only : pblgridDataType
implicit none
type(pblContrGradDataType) :: cbl
type(stateBLDataType), intent(inout):: bl
type(fluidParamsDataType), intent(in) :: fluid
type(pblgridDataType), intent(in) :: grid
integer k
real dz
cbl%entr(:) = 0.0
do k = grid%kmax, 2, -1
dz =(grid%z_cell(k-1) - grid%z_cell(k)) + 1.0
if (k < bl%kpbl+2) then
cbl%entr(k) = 0.0
else
cbl%entr(k) = c_entr * ( 1.0/(grid%z_cell(k) + dz) &
+ 1.0/(bl%hpbla_diag - grid%z_cell(k) + dz) &
+ 1.0/ lmin_entr)
end if
write(*,*) 'entr, k = ' , cbl%entr(k), k, grid%z_cell(k)
end do
cbl%entr(1) = 0
end subroutine cbl_get_entrainment
subroutine cbl_get_up(cbl, bl, fluid, grid)
use scm_state_data, only : stateBLDataType
use pbl_turb_data, only : turbBLDataType
use phys_fluid, only: fluidParamsDataType
use pbl_grid, only : pblgridDataType
implicit none
type(pblContrGradDataType) :: cbl
type(stateBLDataType), intent(inout):: bl
type(fluidParamsDataType), intent(in) :: fluid
type(pblgridDataType), intent(in) :: grid
real phys_beta, wstr, dz, dzentrp, dzentrm, temp
integer k, kmax
cbl%theta_up(:) = 0.0
cbl%thetav_up(:) = 0
cbl%qv_up = 0.0
cbl%ua_up = 0.0
cbl%va_up = 0.0
kmax = grid%kmax
phys_beta = 0.5 * fluid%g /(bl%theta_v(kmax) + bl%theta_v(kmax-1))
write(*,*) 'bl%hs, ', (bl%surf%hs), phys_beta
if (bl%surf%hs > 0.0) then
wstr = (phys_beta * (bl%surf%hs/bl%rho(kmax)) &
* bl%hpbla_diag)**(0.33333)
wstr = max(wstrmin, wstr)
cbl%thetav_up0 = (bl%surf%hs/(bl%rho(kmax)*fluid%cp)) / wstr
cbl%theta_up0 = (bl%surf%hs/(bl%rho(kmax)*fluid%cp)) / wstr
cbl%qv_up0 = (bl%surf%es/bl%rho(kmax)) / wstr
else
cbl%thetav_up0 = 0.0
cbl%theta_up0 = 0.0
cbl%qv_up0 = 0.0
end if
cbl%ua_up0 = 0.0
cbl%va_up0 = 0.0
cbl%thetav_up(kmax) = cbl%thetav_up0 + bl%theta_v(kmax)
cbl%theta_up(kmax) = cbl%theta_up0 + bl%theta(kmax)
cbl%qv_up(kmax) = cbl%qv_up0 + bl%qv(kmax)
cbl%ua_up(kmax) = cbl%ua_up0 + bl%u(kmax)
cbl%va_up(kmax) = cbl%va_up0 + bl%v(kmax)
do k = kmax-1 ,1,-1
if (k <= bl%kpbl ) then
cbl%theta_up(k) = bl%theta(k)
cbl%thetav_up(k) = bl%theta_v(k)
cbl%qv_up(k) = bl%qv(k)
cbl%ua_up(k) = bl%u(k)
cbl%ua_up(k) = bl%u(k)
cbl%va_up(k) = bl%v(k)
else
dz = (grid%z_cell(k) - grid%z_cell(k+1))
cbl%thetav_up(k) = cbl%thetav_up(k+1) - &
dz * cbl%entr(k+1) &
* (cbl%thetav_up(k+1) - bl%theta_v(k+1))
cbl%theta_up(k) = cbl%theta_up(k+1) - &
dz * cbl%entr(k+1) &
* (cbl%theta_up(k+1) - bl%theta(k+1))
write(*,*) 'theta_up, k = ' , cbl%theta_up(k) - bl%theta(k), k
cbl%qv_up(k) = cbl%qv_up(k+1) - &
dz * cbl%entr(k+1) &
* (cbl%qv_up(k+1) - bl%qv(k+1))
cbl%ua_up(k) = cbl%ua_up(k+1) + &
dz * cbl%entr(k+1) &
* (cbl%ua_up(k+1) - bl%u(k+1))
cbl%va_up(k) = cbl%va_up(k+1) - &
dz * cbl%entr(k+1) &
* (cbl%va_up(k+1) - bl%v(k+1))
end if
end do
end subroutine cbl_get_up
subroutine cbl_get_wu(cbl, bl, fluid, grid)
use scm_state_data, only : stateBLDataType
use pbl_turb_data, only : turbBLDataType
use phys_fluid, only: fluidParamsDataType
use pbl_grid, only : pblgridDataType
implicit none
type(pblContrGradDataType) :: cbl
type(stateBLDataType), intent(inout):: bl
type(fluidParamsDataType), intent(in) :: fluid
type(pblgridDataType), intent(in) :: grid
real wu, phys_beta, umod, ustr, rhs, a, b, dz
integer k, kmax
kmax = grid%kmax
cbl%wu(:) = 0.0
umod = sqrt(bl%u(kmax)*bl%u(kmax) + bl%v(kmax)*bl%v(kmax))
ustr = sqrt(bl%surf%cm2u /bl%rho(kmax) * umod)
phys_beta = 0.5 * fluid%g /(bl%theta_v(kmax) + bl%theta_v(kmax-1))
cbl%wu(kmax) = 2.46 * ((ustr)**3 &
- 0.4 * phys_beta * bl%surf%hs &
* (grid%z_cell(k))/bl%rho(kmax))**(1.0/3.0) &
* sqrt(1.0 - grid%z_cell(k) / bl%hpbla_diag)
do k = kmax - 1, 1, -1
dz = (grid%z_cell(K) - grid%z_cell(K+1))
a = 0.0
if (abs(cbl%entr(k)) >= 1.0e-8 .and. abs(cbl%wu(k+1)) > 1.0e-6 ) then
a = b1 * cbl%entr(k) * cbl%wu(k+1) * dz
b = b2 * 9.81 * (dz/cbl%wu(k+1)) &
* (cbl%thetav_up(k) - bl%theta_v(k))/bl%theta_v(k);
rhs = cbl%wu(k+1) - a + b;
if (rhs > 0) then
cbl%wu(k) = rhs;
else
cbl%wu(k) = 0.0;
endif
else
cbl%wu(k) = 0.0;
endif
enddo
end subroutine cbl_get_wu
subroutine cbl_apply_cntrg(cbl, bl, fluid, grid, dt)
use scm_state_data, only : stateBLDataType
use pbl_turb_data, only : turbBLDataType
use phys_fluid, only: fluidParamsDataType
use pbl_grid, only : pblgridDataType
implicit none
type(pblContrGradDataType), intent(inout) :: cbl
type(stateBLDataType), intent(inout):: bl
type(fluidParamsDataType), intent(in) :: fluid
type(pblgridDataType), intent(in) :: grid
real, intent(in) :: dt
real, dimension(grid%kmax) :: rhs_up, rhs
real a0w0
integer kmax, kpbl, k
kmax = grid%kmax
kpbl = bl%kpbl
a0w0 = 0.15 * cbl%wu(kpbl)
call cbl_get_entrainment(cbl, bl, fluid, grid)
call cbl_get_up(cbl, bl, fluid, grid)
call cbl_get_wu(cbl, bl, fluid, grid)
!apply upwind
rhs_up(:) = 0
do k = kmax-1, 1, -1
if (abs(cbl%wu(k)) > 1.0e-7) then
rhs_up(k) = 0.1 * (cbl%wu(k)) * &
(cbl%theta_up(k+1) - cbl%theta_up(k) - bl%theta(k+1) + bl%theta(k)) &
/ (grid%z_cell(k) - grid%z_cell(k+1))
else
rhs_up(k)=0
end if
end do
bl%theta = bl%theta + dt * rhs_up
rhs_up = 0
do k = kmax-1, 1, -1
if (abs(cbl%wu(k)) > 1.0e-7) then
rhs_up(k) = 0.1 * (cbl%wu(k)) * &
(cbl%qv_up(+1) - cbl%qv_up(k) &
- bl%qv(k+1) + bl%qv(k)) / (grid%z_cell(k) -grid%z_cell(k+1))
else
rhs_up(k)=0
end if
end do
bl%qv(:) = bl%qv(:) + dt * rhs_up(:)
rhs_up(:) = 0
do k = kmax-1, 1, -1
if (abs(cbl%wu(k)) > 1.0e-8) then
rhs_up(k) = 0.1 * (cbl%wu(k)) * &
(cbl%ua_up(k+1) - cbl%ua_up(k) - bl%u(k+1) + bl%u(k)) &
/ (grid%z_cell(k) - grid%z_cell(k+1))
else
rhs_up(k)=0
end if
end do
bl%u(:) = bl%u(:) + dt * rhs_up(:)
rhs_up(:) = 0
do k = kmax-1, 1, -1
if (abs(cbl%wu(k)) > 1.0e-8) then
rhs_up(k) = 0.1 * (cbl%wu(k)) * &
(cbl%va_up(k+1) - cbl%va_up(k) - bl%v(k+1) + bl%v(k)) &
/ (grid%z_cell(k) - grid%z_cell(k+1))
else
rhs_up(k)=0
end if
end do
bl%v(:) = bl%v(:) + dt * rhs_up(:)
end subroutine cbl_apply_cntrg
subroutine new_cntrg(cbl, bl, fluid, grid, dt)
use scm_state_data, only : stateBLDataType
use pbl_turb_data, only : turbBLDataType
use phys_fluid, only: fluidParamsDataType
use pbl_grid, only : pblgridDataType
implicit none
type(pblContrGradDataType), intent(inout) :: cbl
type(stateBLDataType), intent(inout):: bl
type(fluidParamsDataType), intent(in) :: fluid
type(pblgridDataType), intent(in) :: grid
real, intent(in) :: dt
! local variables
real, save, allocatable :: rhs_up(:), rhs(:)
real, save, allocatable :: bouf(:)
real wu, phys_beta, umod, rhs_ws, a, b
real dz, dzentrp, dzentrm, temp,dth
real sigmaw, sigmath, sigmaqc
real wstr, ustr, thstar, thvstar, qstar
real z1, hpb, hpbmf
real entrint, entexp, entexpu
real wp, entw, wn2
real a0w0
integer kmax, kpbl, k
kmax = grid%kmax
kmax = grid%kmax
if (.not.(allocated(rhs_up))) then
allocate(rhs_up(grid%kmax), source=0.0)
end if
if (.not.(allocated(rhs))) then
allocate(rhs(grid%kmax), source=0.0)
end if
if (.not.(allocated(bouf))) then
allocate(bouf(grid%kmax), source=0.0)
end if
kpbl = bl%kpbl
cbl%theta_up(:) = 0.0
cbl%thetav_up(:) = 0
cbl%qv_up(:) = 0.0
cbl%ua_up(:) = 0.0
cbl%va_up(:) = 0.0
cbl%entr(:) = 0.0
cbl%wu(:) = 0.0
rhs_up(:) = 0.0
rhs(:) = 0.0
! Check if the flux is convective
if (bl%surf%hs > 0.0) then
! get surface properties
z1 = grid%z_cell(kmax)
hpb = bl%hpbla_diag
phys_beta = 0.5 * fluid%g /(bl%theta_v(kmax) + bl%theta_v(kmax-1))
wstr = (phys_beta * (bl%surf%hs/bl%rho(kmax)/fluid%cp) &
* bl%hpbla_diag)**(0.33333)
wstr = max(wstrmin, wstr)
! Initial condition for vertical velocity
umod = sqrt(bl%u(kmax)*bl%u(kmax) + bl%v(kmax)*bl%v(kmax))
ustr = sqrt(bl%surf%cm2u /bl%rho(kmax) * umod)
!cbl%wu(kmax) = 1.0 * ((ustr)**3.0 & !2.46
! + 0.4 * wstr**3.0)**(1.0/3.0) &
! * sqrt(1.0 - grid%z_cell(kmax) / bl%hpbla_diag)
sigmaw = 1.3 * (ustr**3.0 + 0.6 * wstr**3.0 * z1/hpb) * &
sqrt(1.0 - z1 / hpb)
thstar = (bl%surf%hs/(bl%rho(kmax))) / wstr
thvstar = (bl%surf%hs/(bl%rho(kmax))) / wstr
qstar = (bl%surf%es/bl%rho(kmax)) / wstr
cbl%wu(kmax) = 0.5 * sigmaw
! initial perturbation
cbl%thetav_up0 = (bl%surf%hs/(bl%rho(kmax))) / sigmaw
cbl%theta_up0 = (bl%surf%hs/(bl%rho(kmax))) / sigmaw
cbl%qv_up0 = (bl%surf%es/bl%rho(kmax)) / sigmaw
cbl%ua_up0 = 0.5 * (bl%u(kmax) + bl%u(kmax-1))
cbl%va_up0 = 0.5 * (bl%v(kmax) + bl%v(kmax-1))
cbl%thetav_up(kmax) = alph0 *cbl%thetav_up0 + bl%theta_v(kmax)
cbl%theta_up(kmax) = alph0 * cbl%theta_up0 + bl%theta(kmax)
cbl%qv_up(kmax) = alph0 * cbl%qv_up0 + bl%qv(kmax)
cbl%ua_up(kmax) = cbl%ua_up0 + bl%u(kmax)
cbl%va_up(kmax) = cbl%va_up0 + bl%v(kmax)
!Initial entrainment
!cbl%entr(kmax) = 1.0 / (cbl%wu(kmax) * tau_dry_scale) &
!+ c_entr / grid%z_cell(kmax)
dz = grid%z_cell(kmax) - grid%z_edge(kmax)
cbl%entr(kmax) = c_entr * ( 1.0/(grid%z_cell(kmax) + dz) &
+ 1.0/(bl%hpbla_diag - grid%z_cell(kmax) + dz))
bl%kpbld_mf = bl%kpbl
! get non-entraiened parcel height
!do k = kmax - 1, 2, -1
! dth = cbl%thetav_up(kmax) - bl%theta_v(k)
! if (bl%kpbld_mf == 0 .and. dth < 0.0 ) then
! bl%kpbld_mf = k
! end if
!end do
hpbmf = 0.5 * (grid%z_cell(bl%kpbld_mf) + &
bl%hpbla_diag)
write(*,*) 'hbp, hmf', grid%z_cell(bl%kpbld_mf), bl%hpbla_diag, bl%surf%hs
! get proper entrainment
do k = grid%kmax-1,1,-1
dz = (grid%z_cell(k) - grid%z_cell(k+1))
if (grid%z_cell(k) <= hpbmf) then
cbl%entr(k) = c_entr * ( 1.0/(grid%z_cell(k) + dz) &
+ 1.0/(hpbmf - grid%z_cell(k) + dz))
else
cbl%entr(k) = 0.0
end if
end do
!get updrafts
do k = grid%kmax-1,bl%kpbld_mf,-1
dz = (grid%z_cell(k) - grid%z_cell(k+1))
entexp = exp( - cbl%entr(k) * dz)
entexpu = exp( - cbl%entr(k) * dz / 3.0 )
cbl%thetav_up(k) = bl%theta_v(k) * (1.0 - entexp) + &
cbl%thetav_up(k+1) * entexp
cbl%theta_up(k) = bl%theta(k) * (1.0 - entexp) + &
cbl%theta_up(k+1) * entexp
cbl%qv_up(k) = bl%qv(k) * (1.0 - entexp) + &
cbl%qv_up(k+1) * entexp
cbl%ua_up(k) = bl%u(k) * (1.0 - entexpu) + &
cbl%ua_up(k+1) * entexpu
cbl%va_up(k) = bl%u(k) * (1.0 - entexpu) + &
cbl%va_up(k+1) * entexpu
bouf(k) = fluid%g * &
(0.5 * (cbl%thetav_up(k) + cbl%thetav_up(k+1)) / &
bl%theta_v(k) - 1.0)
enddo
!get vertical speed
do k = grid%kmax-1,bl%kpbld_mf,-1
dz = (grid%z_cell(k) - grid%z_cell(k+1))
wp = b1 * cbl%entr(k)
if (wp > 0.0) then
entw = exp( -2.0 * wp * dz )
wn2 = cbl%wu(k+1) * cbl%wu(k+1) * entw + &
b2* bouf(k)*(1.0-entw)/entw
else
wn2 = cbl%wu(k+1) * cbl%wu(k+1) + &
2.0 * b2 * bouf(k) * dz
end if
if ( wn2 > 0.0) then
cbl%wu(k) = sqrt(wn2)
else
cbl%wu(k) = 0.0
end if
end do
! apply upwind
rhs_up(:) = 0.0
do k = kmax-1, 1, -1
if (cbl%wu(k) > 0.0) then
rhs_up(k) = a0 * (cbl%wu(k)) * &
(cbl%theta_up(k+1) - cbl%theta_up(k) - bl%theta(k+1) + bl%theta(k)) &
/ (grid%z_cell(k) - grid%z_cell(k+1))
else
rhs_up(k)=0.0
end if
end do
bl%theta = bl%theta + dt * rhs_up
rhs_up(:) = 0.0
do k = kmax-1, 1, -1
if (cbl%wu(k) > 0.0) then
rhs_up(k) = a0 * (cbl%wu(k)) * &
(cbl%qv_up(k+1) - cbl%qv_up(k) &
- bl%qv(k+1) + bl%qv(k)) &
/ (grid%z_cell(k) -grid%z_cell(k+1))
else
rhs_up(k)=0.0
end if
end do
bl%qv(:) = bl%qv(:) + dt * rhs_up(:)
rhs_up(:) = 0.0
do k = kmax-1, 1, -1
if (cbl%wu(k) > 0.0) then
rhs_up(k) = a0 * (cbl%wu(k)) * &
(cbl%ua_up(k+1) - cbl%ua_up(k) - bl%u(k+1) + bl%u(k)) &
/ (grid%z_cell(k) - grid%z_cell(k+1))
else
rhs_up(k)=0.0
end if
end do
bl%u(:) = bl%u(:) + dt * rhs_up(:)
rhs_up(:) = 0.0
do k = kmax-1, 1, -1
if (cbl%wu(k) > 0.0) then
rhs_up(k) = a0 * (cbl%wu(k)) * &
(cbl%va_up(k+1) - cbl%va_up(k) - bl%v(k+1) + bl%v(k)) &
/ (grid%z_cell(k) - grid%z_cell(k+1))
else
rhs_up(k)=0.0
end if
end do
bl%v(:) = bl%v(:) + dt * rhs_up(:)
end if
end subroutine new_cntrg
end module pbl_dry_contrgradient