#include "../includeF/sfx_def.fi"
module sfx_sheba_coare
! modules used
! --------------------------------------------------------------------------------
#ifdef SFX_CHECK_NAN
use sfx_common
#endif
use sfx_data
use sfx_surface
use sfx_sheba_coare_param
#if defined(INCLUDE_CXX)
use iso_c_binding, only: C_LOC, C_PTR, C_INT, C_FLOAT
use C_FUNC
#endif
! --------------------------------------------------------------------------------
! directives list
! --------------------------------------------------------------------------------
implicit none
private
! --------------------------------------------------------------------------------
! public interface
! --------------------------------------------------------------------------------
public :: get_surface_fluxes
public :: get_surface_fluxes_vec
public :: get_psi_stable
public :: get_psi_a
public :: get_psi_convection
public :: get_psi_BD
integer z0m_id
integer z0t_id
! --------------------------------------------------------------------------------
! --------------------------------------------------------------------------------
type, public :: numericsType
integer :: maxiters_charnock = 10 !< maximum (actual) number of iterations in charnock roughness
integer :: maxiters_convection = 10 !< maximum (actual) number of iterations in charnock roughness
end type
! --------------------------------------------------------------------------------
#if defined(INCLUDE_CXX)
type, BIND(C), public :: sfx_sheba_coare_param_C
real(C_FLOAT) :: kappa
real(C_FLOAT) :: Pr_t_0_inv
real(C_FLOAT) :: Pr_t_inf_inv
real(C_FLOAT) :: alpha_m
real(C_FLOAT) :: alpha_h
real(C_FLOAT) :: gamma
real(C_FLOAT) :: zeta_a
real(C_FLOAT) :: a_m
real(C_FLOAT) :: b_m
real(C_FLOAT) :: a_h
real(C_FLOAT) :: b_h
real(C_FLOAT) :: c_h
real(C_FLOAT) :: beta_m
real(C_FLOAT) :: beta_h
end type
type, BIND(C), public :: sfx_sheba_coare_numericsType_C
integer(C_INT) :: maxiters_convection
integer(C_INT) :: maxiters_charnock
end type
INTERFACE
SUBROUTINE c_sheba_coare_compute_flux(sfx, meteo, model_param, surface_param, numerics, constants, grid_size) BIND(C, &
name="c_sheba_coare_compute_flux")
use sfx_data
use, intrinsic :: ISO_C_BINDING, ONLY: C_INT, C_PTR
Import :: sfx_sheba_coare_param_C, sfx_sheba_coare_numericsType_C
implicit none
integer(C_INT) :: grid_size
type(C_PTR), value :: sfx
type(C_PTR), value :: meteo
type(sfx_sheba_coare_param_C) :: model_param
type(sfx_surface_sheba_coare_param) :: surface_param
type(sfx_sheba_coare_numericsType_C) :: numerics
type(sfx_phys_constants) :: constants
END SUBROUTINE c_sheba_coare_compute_flux
END INTERFACE
#endif
contains
! --------------------------------------------------------------------------------
#if defined(INCLUDE_CXX)
subroutine set_c_struct_sfx_sheba_coare_param_values(sfx_model_param)
type (sfx_sheba_coare_param_C), intent(inout) :: sfx_model_param
sfx_model_param%kappa = kappa
sfx_model_param%Pr_t_0_inv = Pr_t_0_inv
sfx_model_param%Pr_t_inf_inv = Pr_t_inf_inv
sfx_model_param%alpha_m = alpha_m
sfx_model_param%alpha_h = alpha_h
sfx_model_param%gamma = gamma
sfx_model_param%zeta_a = zeta_a
sfx_model_param%a_m = a_m
sfx_model_param%b_m = b_m
sfx_model_param%a_h = a_h
sfx_model_param%b_h = b_h
sfx_model_param%c_h = c_h
sfx_model_param%c3 = beta_m
sfx_model_param%c4 = beta_h
end subroutine set_c_struct_sfx_sheba_coare_param_values
#endif
! --------------------------------------------------------------------------------
subroutine get_surface_fluxes_vec(sfx, meteo, numerics, n)
!< @brief surface flux calculation for array data
!< @details contains C/C++ & CUDA interface
! ----------------------------------------------------------------------------
type (sfxDataVecType), intent(inout) :: sfx
type (meteoDataVecType), intent(in) :: meteo
type (numericsType), intent(in) :: numerics
integer, intent(in) :: n
! ----------------------------------------------------------------------------
! --- local variables
type (meteoDataType) meteo_cell
type (sfxDataType) sfx_cell
integer i
! ----------------------------------------------------------------------------
#if defined(INCLUDE_CXX)
type (meteoDataVecTypeC), target :: meteo_c !< meteorological data (input)
type (sfxDataVecTypeC), target :: sfx_c !< surface flux data (output)
type(C_PTR) :: meteo_c_ptr, sfx_c_ptr
type (sfx_sheba_coare_param_C) :: model_param
type (sfx_surface_param) :: surface_param
type (sfx_sheba_coare_numericsType_C) :: numerics_c
type (sfx_phys_constants) :: phys_constants
numerics_c%maxiters_convection = numerics%maxiters_convection
numerics_c%maxiters_charnock = numerics%maxiters_charnock
phys_constants%Pr_m = Pr_m;
phys_constants%nu_air = nu_air;
phys_constants%g = g;
call set_c_struct_sfx_sheba_coare_param_values(model_param)
call set_c_struct_sfx_surface_param_values(surface_param)
call set_meteo_vec_c(meteo, meteo_c)
call set_sfx_vec_c(sfx, sfx_c)
meteo_c_ptr = C_LOC(meteo_c)
sfx_c_ptr = C_LOC(sfx_c)
call c_sheba_coare_compute_flux(sfx_c_ptr, meteo_c_ptr, model_param, surface_param, numerics_c, phys_constants, n)
#else
do i = 1, n
meteo_cell = meteoDataType(&
h = meteo%h(i), &
U = meteo%U(i), dT = meteo%dT(i), Tsemi = meteo%Tsemi(i), dQ = meteo%dQ(i), &
z0_m = meteo%z0_m(i), depth=meteo%depth(i), lai=meteo%lai(i), surface_type=meteo%surface_type(i))
call get_surface_fluxes(sfx_cell, meteo_cell, numerics)
call push_sfx_data(sfx, sfx_cell, i)
end do
#endif
end subroutine get_surface_fluxes_vec
! --------------------------------------------------------------------------------
! --------------------------------------------------------------------------------
subroutine get_surface_fluxes(sfx, meteo, numerics)
!< @brief surface flux calculation for single cell
!< @details contains C/C++ interface
! ----------------------------------------------------------------------------
#ifdef SFX_CHECK_NAN
use ieee_arithmetic
#endif
type (sfxDataType), intent(out) :: sfx
type (meteoDataType), intent(in) :: meteo
type (numericsType), intent(in) :: numerics
! ----------------------------------------------------------------------------
! --- meteo derived datatype name shadowing
! ----------------------------------------------------------------------------
real :: h !< constant flux layer height [m]
real :: U !< abs(wind speed) at 'h' [m/s]
real :: dT !< difference between potential temperature at 'h' and at surface [K]
real :: Tsemi !< semi-sum of potential temperature at 'h' and at surface [K]
real :: dQ !< difference between humidity at 'h' and at surface [g/g]
real :: z0_m !< surface aerodynamic roughness (should be < 0 for water bodies surface)
!real :: hpbl
real :: depth
real :: lai
integer :: surface_type
! ----------------------------------------------------------------------------
! --- local variables
! ----------------------------------------------------------------------------
real z0_t !< thermal roughness [m]
real B !< = ln(z0_m / z0_t) [n/d]
real h0_m, h0_t !< = h / z0_m, h / z0_h [n/d]
real u_dyn0 !< dynamic velocity in neutral conditions [m/s]
real Re !< roughness Reynolds number = u_dyn0 * z0_m / nu [n/d]
real zeta !< = z/L [n/d]
real Rib !< bulk Richardson number
real zeta_conv_lim !< z/L critical value for matching free convection limit [n/d]
real Rib_conv_lim !< Ri-bulk critical value for matching free convection limit [n/d]
real f_m_conv_lim !< stability function (momentum) value in free convection limit [n/d]
real f_h_conv_lim !< stability function (heat) value in free convection limit [n/d]
real psi_m, psi_h !< universal functions (momentum) & (heat) [n/d]
real psi0_m, psi0_h !< universal functions (momentum) & (heat) [n/d]
real z0_m1
! real psi_m_BD, psi_h_BD !< universal functions (momentum) & (heat) [n/d]
! real psi0_m_BD, psi0_h_BD !< universal functions (momentum) & (heat) [n/d]
! real psi_m_conv, psi_h_conv !< universal functions (momentum) & (heat) [n/d]
! real psi0_m_conv, psi0_h_conv !< universal functions (momentum) & (heat) [n/d]
real Udyn, Tdyn, Qdyn !< dynamic scales
real phi_m, phi_h !< stability functions (momentum) & (heat) [n/d]
real Km !< eddy viscosity coeff. at h [m^2/s]
real Pr_t_inv !< invese Prandt number [n/d]
real Cm, Ct !< transfer coeff. for (momentum) & (heat) [n/d]
!integer surface_type !< surface type = (ocean || land)
real c_wdyn
#ifdef SFX_CHECK_NAN
real NaN
#endif
! ----------------------------------------------------------------------------
#ifdef SFX_CHECK_NAN
! --- checking if arguments are finite
if (.not.(is_finite(meteo%U).and.is_finite(meteo%Tsemi).and.is_finite(meteo%dT).and.is_finite(meteo%dQ) &
.and.is_finite(meteo%z0_m).and.is_finite(meteo%h))) then
NaN = ieee_value(0.0, ieee_quiet_nan) ! setting NaN
sfx = sfxDataType(zeta = NaN, Rib = NaN, &
Re = NaN, B = NaN, z0_m = NaN, z0_t = NaN, &
Rib_conv_lim = NaN, &
Cm = NaN, Ct = NaN, Km = NaN, Pr_t_inv = NaN)
!Cm = NaN, Ct = NaN, Km = NaN, Pr_t_inv = NaN, c_wdyn = NaN)
return
end if
#endif
! --- shadowing names for clarity
U = meteo%U
Tsemi = meteo%Tsemi
dT = meteo%dT
dQ = meteo%dQ
h = meteo%h
z0_m1 = meteo%z0_m
depth = meteo%depth
lai = meteo%lai
surface_type=meteo%surface_type
!hpbl = meteo%hpbl
call get_dynamic_roughness_definition(surface_type, ocean_z0m_id, land_z0m_id, lake_z0m_id, snow_z0m_id, &
forest_z0m_id, usersf_z0m_id, ice_z0m_id, z0m_id)
call get_dynamic_roughness_all(z0_m, u_dyn0, U, depth, h, numerics%maxiters_charnock, z0_m1, z0m_id)
call get_thermal_roughness_definition(surface_type, ocean_z0t_id, land_z0t_id, lake_z0t_id, snow_z0t_id, &
forest_z0t_id, usersf_z0t_id, ice_z0t_id, z0t_id)
Re = u_dyn0 * z0_m / nu_air
call get_thermal_roughness_all(z0_t, B, z0_m, Re, u_dyn0, lai, z0t_id)
! --- define relative height
h0_m = h / z0_m
! --- define relative height [thermal]
h0_t = h / z0_t
! --- define Ri-bulk
Rib = (g / Tsemi) * h * (dT + 0.61e0 * Tsemi * dQ) / U**2
! --- define free convection transition zeta = z/L value
call get_convection_lim(zeta_conv_lim, Rib_conv_lim, f_m_conv_lim, f_h_conv_lim, &
h0_m, h0_t, B)
! --- get the fluxes
! ----------------------------------------------------------------------------
if (Rib > 0.0) then
! --- stable stratification block
! --- restrict bulk Ri value
! *: note that this value is written to output
! Rib = min(Rib, Rib_max)
call get_zeta_stable(zeta, Rib, h, z0_m, z0_t)
call get_psi_stable(psi_m, psi_h, zeta, zeta)
call get_psi_stable(psi0_m, psi0_h, zeta * z0_m / h, zeta * z0_t / h)
phi_m = 1.0 + (a_m * zeta * (1.0 + zeta)**(1.0 / 3.0)) / (1.0 + b_m * zeta)
phi_h = 1.0 + (a_h * zeta + b_h * zeta * zeta) / (1.0 + c_h * zeta + zeta * zeta)
Udyn = kappa * U / (log(h / z0_m) - (psi_m - psi0_m))
Tdyn = kappa * dT * Pr_t_0_inv / (log(h / z0_t) - (psi_h - psi0_h))
else if (Rib <= -0.001)then
call get_dynamic_scales(Udyn, Tdyn, Qdyn, zeta, psi_m, psi_h, psi0_m, psi0_h,&
U, Tsemi, dT, dQ, h, z0_m, z0_t, (g / Tsemi), numerics%maxiters_convection)
call get_phi_a(phi_m,phi_h,zeta)
!! call get_phi_a2(phi_m,phi_h,zeta)
!! call get_phi_a3(phi_m,phi_h,zeta)
!! print *, zeta,psi_m,psi_h,phi_m,phi_h
psi_m = (log(h / z0_m) - (psi_m - psi0_m))
psi_h = (log(h / z0_t) - (psi_h - psi0_h))
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!non-iterative version below is not debugged yet!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
! call get_zeta_conv(zeta,Rib,h,z0_m,z0_t)
!
! call get_psi_a(psi_m, psi_h, zeta,zeta)
! call get_psi_a(psi0_m, psi0_h, zeta * z0_m / h, zeta * z0_t / h)
!
! Udyn = kappa * U / (log(h / z0_m) - (psi_m - psi0_m))
! Tdyn = kappa * dT * Pr_t_0_inv / (log(h / z0_t) - (psi_h - psi0_h))
!
! call get_phi_a(phi_m,phi_h,zeta)
!print *, zeta,psi_m,psi_h,phi_m,phi_h
!
! psi_m = (log(h / z0_m) - (psi_m - psi0_m))
! psi_h = (log(h / z0_t) - (psi_h - psi0_h))
else
! --- nearly neutral [-0.001, 0] block
call get_psi_neutral(psi_m, psi_h, h0_m, h0_t, B)
zeta = 0.0
phi_m = 1.0
phi_h = 1.0 / Pr_t_0_inv
Udyn = kappa * U / log(h / z0_m)
Tdyn = kappa * dT * Pr_t_0_inv / log(h / z0_t)
end if
! ----------------------------------------------------------------------------
! --- define transfer coeff. (momentum) & (heat)
if(Rib > 0)then
Cm = 0.0
if (U > 0.0) then
Cm = Udyn / U
end if
Ct = 0.0
if (abs(dT) > 0.0) then
Ct = Tdyn / dT
end if
else
Cm = kappa / psi_m
Ct = kappa / psi_h
end if
! --- define eddy viscosity & inverse Prandtl number
Km = kappa * Cm * U * h / phi_m
Pr_t_inv = phi_m / phi_h
! --- setting output
sfx = sfxDataType(zeta = zeta, Rib = Rib, &
Re = Re, B = B, z0_m = z0_m, z0_t = z0_t, &
Rib_conv_lim = Rib_conv_lim, &
Cm = Cm, Ct = Ct, Km = Km, Pr_t_inv = Pr_t_inv)
! Cm = Cm, Ct = Ct, Km = Km, Pr_t_inv = Pr_t_inv, c_wdyn = 0)
end subroutine get_surface_fluxes
! --------------------------------------------------------------------------------
! universal functions
! --------------------------------------------------------------------------------
subroutine get_psi_neutral(psi_m, psi_h, h0_m, h0_t, B)
!< @brief universal functions (momentum) & (heat): neutral case
! ----------------------------------------------------------------------------
real, intent(out) :: psi_m, psi_h !< universal functions
real, intent(in) :: h0_m, h0_t !< = z/z0_m, z/z0_h
real, intent(in) :: B !< = log(z0_m / z0_h)
! ----------------------------------------------------------------------------
psi_m = log(h0_m)
psi_h = log(h0_t) / Pr_t_0_inv
!*: this looks redundant z0_t = z0_m in case |B| ~ 0
if (abs(B) < 1.0e-10) psi_h = psi_m / Pr_t_0_inv
end subroutine
subroutine get_zeta_stable(zeta, Rib, h, z0_m, z0_t)
real,intent(out) :: zeta
real,intent(in) :: Rib, h, z0_m, z0_t
real :: Ribl, C1, A1, A2, lne, lnet
real :: psi_m, psi_h, psi0_m, psi0_h
Ribl = (Rib * Pr_t_0_inv) * (1 - z0_t / h) / ((1 - z0_m / h)**2)
call get_psi_stable(psi_m, psi_h, zeta_a, zeta_a)
call get_psi_stable(psi0_m, psi0_h, zeta_a * z0_m / h, zeta_a * z0_t / h)
lne = log(h/z0_m)
lnet = log(h/z0_t)
C1 = (lne**2)/lnet
A1 = ((lne - psi_m + psi0_m)**(2*(gamma-1))) &
& / ((zeta_a**(gamma-1))*((lnet-(psi_h-psi0_h)*Pr_t_0_inv)**(gamma-1)))
A2 = ((lne - psi_m + psi0_m)**2) / (lnet-(psi_h-psi0_h)*Pr_t_0_inv) - C1
zeta = C1 * Ribl + A1 * A2 * (Ribl**gamma)
end subroutine get_zeta_stable
subroutine get_psi_stable(psi_m, psi_h, zeta_m, zeta_h)
!< @brief universal functions (momentum) & (heat): neutral case
! ----------------------------------------------------------------------------
real, intent(out) :: psi_m, psi_h !< universal functions
real, intent(in) :: zeta_m, zeta_h !< = z/L
! ----------------------------------------------------------------------------
! --- local variables
real :: x_m, x_h
real :: q_m, q_h
! ----------------------------------------------------------------------------
q_m = ((1.0 - b_m) / b_m)**(1.0 / 3.0)
x_m = (1.0 + zeta_m)**(1.0 / 3.0)
psi_m = -3.0 * (a_m / b_m) * (x_m - 1.0) + 0.5 * (a_m / b_m) * q_m * (&
2.0 * log((x_m + q_m) / (1.0 + q_m)) - &
log((x_m * x_m - x_m * q_m + q_m * q_m) / (1.0 - q_m + q_m * q_m)) + &
2.0 * sqrt(3.0) * (&
atan((2.0 * x_m - q_m) / (sqrt(3.0) * q_m)) - &
atan((2.0 - q_m) / (sqrt(3.0) * q_m))))
q_h = sqrt(c_h * c_h - 4.0)
x_h = zeta_h
psi_h = -0.5 * b_h * log(1.0 + c_h * x_h + x_h * x_h) + &
((-a_h / q_h) + ((b_h * c_h) / (2.0 * q_h))) * (&
log((2.0 * x_h + c_h - q_h) / (2.0 * x_h + c_h + q_h)) - &
log((c_h - q_h) / (c_h + q_h)))
end subroutine get_psi_stable
subroutine get_psi_convection(psi_m, psi_h, zeta_m, zeta_h)
!< @brief Carl et al. 1973 with Grachev et al. 2000 corrections of beta_m, beta_h
! ----------------------------------------------------------------------------
real, intent(out) :: psi_m, psi_h !< universal functions [n/d]
real, intent(in) :: zeta_m, zeta_h !< = z/L [n/d]
real y
! ----------------------------------------------------------------------------
! beta_m = 10, beta_h = 34
y = (1.0 - beta_m * zeta_m)**(1/3.)
psi_m = 3.0 * 0.5 *log((y*y + y + 1.0)/3.) - sqrt(3.0) *atan((2.0*y + 1)/sqrt(3.0)) + pi/sqrt(3.0)
y = (1.0 - beta_h * zeta_h)**(1/3.)
psi_h = 3.0 * 0.5 *log((y*y + y + 1.0)/3.) - sqrt(3.0) *atan((2.0*y + 1)/sqrt(3.0)) + pi/sqrt(3.0)
end subroutine
subroutine get_psi_BD(psi_m, psi_h, zeta_m, zeta_h)
!< @brief universal functions (momentum) & (heat): neutral case
! ----------------------------------------------------------------------------
real, intent(out) :: psi_m, psi_h !< universal functions
real, intent(in) :: zeta_m,zeta_h !< = z/L
! ----------------------------------------------------------------------------
! --- local variables
real :: x_m, x_h
! ----------------------------------------------------------------------------
x_m = (1.0 - alpha_m * zeta_m)**(0.25)
x_h = (1.0 - alpha_h * zeta_h)**(0.25)
psi_m = (4.0 * atan(1.0) / 2.0) + 2.0 * log(0.5 * (1.0 + x_m)) + log(0.5 * (1.0 + x_m * x_m)) - 2.0 * atan(x_m)
psi_h = 2.0 * log(0.5 * (1.0 + x_h * x_h))
end subroutine
subroutine get_phi_a(phi_m, phi_h, zeta)
!< @brief universal functions (momentum) & (heat): neutral case
! ----------------------------------------------------------------------------
real, intent(out) :: phi_m, phi_h !< universal functions
real, intent(in) :: zeta !< = z/L
! ----------------------------------------------------------------------------
! --- local variables
real :: x_m, x_h, y
real :: psi_m_bd,psi_h_bd,psi_m_conv,psi_h_conv
real :: dpsi_m_bd,dpsi_h_bd,dpsi_m_conv,dpsi_h_conv
! ----------------------------------------------------------------------------
call get_psi_BD(psi_m_bd,psi_h_bd,zeta,zeta)
call get_psi_convection(psi_m_conv,psi_h_conv,zeta,zeta)
x_m = (1.0 - alpha_m * zeta)**(0.25)
x_h = (1.0 - alpha_h * zeta)**(0.25)
dpsi_m_bd = -(alpha_m/(2.0*(x_m**3))) * (1/(1+x_m) + (x_m-1)/(1+x_m**2))
dpsi_h_bd = -alpha_h / ((x_h**2)*(1+x_h**2))
y = (1 - beta_m * zeta)**(1/3.)
dpsi_m_conv = -beta_m/(y*(y**2 + y + 1))
y = (1 - beta_h * zeta)**(1/3.)
dpsi_h_conv = -beta_h/(y*(y**2 + y + 1))
phi_m = 1.0 - zeta * (dpsi_m_bd/(1.0+zeta**2) - psi_m_bd*2.0*zeta/((1.0+zeta**2)**2) + &
dpsi_m_conv/(1.0+1.0/(zeta**2)) + 2.0*psi_m_conv/((zeta**3)*((1.0+1.0/(zeta**2))**2)))
phi_h = 1.0 - zeta * (dpsi_h_bd/(1.0+zeta**2) - psi_h_bd*2.0*zeta/((1.0+zeta**2)**2) + &
dpsi_h_conv/(1.0+1.0/(zeta**2)) + 2.0*psi_h_conv/((zeta**3)*((1.0+1.0/(zeta**2))**2)))
end subroutine
subroutine get_phi_a2(phi_m,phi_h,zeta)
! ----------------------------------------------------------------------------
real, intent(out) :: phi_m, phi_h !< universal functions
real, intent(in) :: zeta !< = z/L
! ----------------------------------------------------------------------------
! --- local variables
real :: phi_m_bd,phi_h_bd,phi_m_conv,phi_h_conv
call get_phi_convection(phi_m_conv, phi_h_conv, zeta)
call get_phi_BD(phi_m_BD, phi_h_BD, zeta)
phi_m = (phi_m_BD + (zeta**2) * phi_m_conv) / (1 + zeta**2)
phi_h = (phi_h_BD + (zeta**2) * phi_h_conv) / (1 + zeta**2)
end subroutine
subroutine get_phi_a3(phi_m,phi_h,zeta)
! ----------------------------------------------------------------------------
real, intent(out) :: phi_m, phi_h !< universal functions
real, intent(in) :: zeta !< = z/L
! ----------------------------------------------------------------------------
! --- local variables
real :: phi_m_bd,phi_h_bd,phi_m_conv,phi_h_conv
real :: psi_m_a,psi_h_a,psi_m_conv,psi_h_conv,psi_m_BD,psi_h_BD
call get_phi_convection(phi_m_conv, phi_h_conv, zeta)
call get_phi_BD(phi_m_BD, phi_h_BD, zeta)
call get_psi_convection(psi_m_conv, psi_h_conv, zeta,zeta)
call get_psi_BD(psi_m_BD, psi_h_BD, zeta,zeta)
! call get_psi_a(psi_m_a, psi_h_a, zeta,zeta)
phi_m = (1-phi_m_BD)/(zeta*(1+zeta**2)) + 2*zeta*(psi_m_conv-psi_m_BD)/((1+zeta**2)**2) &
+ zeta*(1-phi_m_conv)/((1+zeta**2)**2)
phi_h = (1-phi_h_BD)/(zeta*(1+zeta**2)) + 2*zeta*(psi_h_conv-psi_h_BD)/((1+zeta**2)**2) &
+ zeta*(1-phi_h_conv)/((1+zeta**2)**2)
end subroutine
subroutine get_phi_BD(phi_m, phi_h, zeta)
!< @brief stability functions (momentum) & (heat): neutral case
! ----------------------------------------------------------------------------
real, intent(out) :: phi_m, phi_h !< stability functions
real, intent(in) :: zeta !< = z/L
! ----------------------------------------------------------------------------
phi_m = (1.0 - alpha_m * zeta)**(-0.25)
phi_h = (1.0 - alpha_h * zeta)**(-0.5)
end subroutine
subroutine get_phi_convection(phi_m, phi_h, zeta)
!< @brief stability functions (momentum) & (heat): neutral case
! ----------------------------------------------------------------------------
real, intent(out) :: phi_m, phi_h !< stability functions
real, intent(in) :: zeta !< = z/L
! ----------------------------------------------------------------------------
phi_m = (1.0 - beta_m * zeta)**(-1.0/3.0)
phi_h = (1.0 - beta_h * zeta)**(-1.0/3.0)
end subroutine
!< @brief get dynamic scales
! --------------------------------------------------------------------------------
subroutine get_dynamic_scales(Udyn, Tdyn, Qdyn, zeta, psi_m, psi_h, &
psi0_m,psi0_h, U, Tsemi, dT, dQ, z, z0_m, z0_t, beta, maxiters)
! ----------------------------------------------------------------------------
real, intent(out) :: Udyn, Tdyn, Qdyn !< dynamic scales
real, intent(out) :: zeta !< = z/L
real, intent(out) :: psi_m,psi_h,psi0_m,psi0_h
real, intent(in) :: U !< abs(wind speed) at z
real, intent(in) :: Tsemi !< semi-sum of temperature at z and at surface
real, intent(in) :: dT, dQ !< temperature & humidity difference between z and at surface
real, intent(in) :: z !< constant flux layer height
real, intent(in) :: z0_m, z0_t !< roughness parameters
real, intent(in) :: beta !< buoyancy parameter
integer, intent(in) :: maxiters !< maximum number of iterations
! ----------------------------------------------------------------------------
! --- local variables
real :: Linv
integer :: i
! ----------------------------------------------------------------------------
Udyn = kappa * U / log(z / z0_m)
Tdyn = kappa * dT * Pr_t_0_inv / log(z / z0_t)
Qdyn = kappa * dQ * Pr_t_0_inv / log(z / z0_t)
zeta = 0.0
! --- no wind
if (Udyn < 1e-5) return
Linv = kappa * beta * (Tdyn + 0.61 * Qdyn * Tsemi) / (Udyn * Udyn)
zeta = z * Linv
psi_m = log(z/z0_m)
psi_h = log(z/z0_t) / Pr_t_0_inv
psi0_m = log(z/z0_m)
psi0_h = log(z/z0_t) / Pr_t_0_inv
! --- near neutral case
! if (Linv < 1e-5) return
do i = 1, maxiters
call get_psi_a(psi_m, psi_h, zeta, zeta)
call get_psi_a(psi0_m, psi0_h, z0_m * Linv, z0_t * Linv)
Udyn = kappa * U / (log(z / z0_m) - (psi_m - psi0_m))
Tdyn = kappa * dT * Pr_t_0_inv / (log(z / z0_t) - (psi_h - psi0_h))
Qdyn = kappa * dQ * Pr_t_0_inv / (log(z / z0_t) - (psi_h - psi0_h))
if (Udyn < 1e-5) exit
Linv = kappa * beta * (Tdyn + 0.61 * Qdyn * Tsemi) / (Udyn * Udyn)
zeta = z * Linv
end do
end subroutine get_dynamic_scales
subroutine get_psi_a(psi_m,psi_h,zeta_m, zeta_h)
! ----------------------------------------------------------------------------
real, intent(out) :: psi_m, psi_h !< universal functions
real, intent(in) :: zeta_m,zeta_h !< = z/L
! ----------------------------------------------------------------------------
! --- local variables
real :: psi_m_bd,psi_h_bd,psi_m_conv,psi_h_conv
call get_psi_convection(psi_m_conv, psi_h_conv, zeta_m, zeta_h)
call get_psi_BD(psi_m_BD, psi_h_BD, zeta_m, zeta_h)
psi_m = (psi_m_BD + (zeta_m**2) * psi_m_conv) / (1 + zeta_m**2)
psi_h = (psi_h_BD + (zeta_h**2) * psi_h_conv) / (1 + zeta_h**2)
end subroutine
subroutine get_convection_lim(zeta_lim, Rib_lim, f_m_lim, f_h_lim, &
h0_m, h0_t, B)
! ----------------------------------------------------------------------------
real, intent(out) :: zeta_lim !< limiting value of z/L
real, intent(out) :: Rib_lim !< limiting value of Ri-bulk
real, intent(out) :: f_m_lim, f_h_lim !< limiting values of universal functions shortcuts
real, intent(in) :: h0_m, h0_t !< = z/z0_m, z/z0_h [n/d]
real, intent(in) :: B !< = log(z0_m / z0_h) [n/d]
! ----------------------------------------------------------------------------
! --- local variables
real :: psi_m, psi_h
real :: f_m, f_h
real :: c
! ----------------------------------------------------------------------------
! --- define limiting value of zeta = z / L
c = (Pr_t_inf_inv / Pr_t_0_inv)**4
zeta_lim = (2.0 * alpha_h - c * alpha_m - &
sqrt((c * alpha_m)**2 + 4.0 * c * alpha_h * (alpha_h - alpha_m))) / (2.0 * alpha_h**2)
f_m_lim = f_m_conv(zeta_lim)
f_h_lim = f_h_conv(zeta_lim)
! --- universal functions
f_m = zeta_lim / h0_m
f_h = zeta_lim / h0_t
if (abs(B) < 1.0e-10) f_h = f_m
f_m = (1.0 - alpha_m * f_m)**0.25
f_h = sqrt(1.0 - alpha_h_fix * f_h)
psi_m = 2.0 * (atan(f_m_lim) - atan(f_m)) + alog((f_m_lim - 1.0) * (f_m + 1.0)/((f_m_lim + 1.0) * (f_m - 1.0)))
psi_h = alog((f_h_lim - 1.0) * (f_h + 1.0)/((f_h_lim + 1.0) * (f_h - 1.0))) / Pr_t_0_inv
! --- bulk Richardson number
Rib_lim = zeta_lim * psi_h / (psi_m * psi_m)
end subroutine
! convection universal functions shortcuts
! --------------------------------------------------------------------------------
function f_m_conv(zeta)
! ----------------------------------------------------------------------------
real :: f_m_conv
real, intent(in) :: zeta
! ----------------------------------------------------------------------------
f_m_conv = (1.0 - alpha_m * zeta)**0.25
end function f_m_conv
function f_h_conv(zeta)
! ----------------------------------------------------------------------------
real :: f_h_conv
real, intent(in) :: zeta
! ----------------------------------------------------------------------------
f_h_conv = (1.0 - alpha_h * zeta)**0.5
end function f_h_conv
subroutine get_zeta_conv(zeta,Rib,z,z0m,z0t)
!< @brief Srivastava and Sharan 2017, Abdella and Assefa 2005
! ----------------------------------------------------------------------------
real, intent(out) :: zeta !< = z/L [n/d]
real, intent(in) :: Rib !
real, intent(in) :: z,z0m,z0t !
real A,a0,a1,a2,r,q,s1,s2,theta,delta
real ksi_m,ksi_h,ksi_m_0,ksi_m_inf,ksi_h_0,ksi_h_inf
real f_m_inf,f_h_inf
real psi_m_zeta,psi_m_zeta0,psi_h_zeta,psi_h_zeta0
! ----------------------------------------------------------------------------
A = ( 1 / Pr_t_0_inv ) * ( (1 - z0m/z)**2) * log(z/z0t) / ( (1 - z0t/z) * ((log(z/z0m))**2) )
call get_psi_convection(psi_m_zeta,psi_h_zeta,Rib/A, Rib/A)
call get_psi_convection(psi_m_zeta0,psi_h_zeta0, (z0m/z) * (Rib/A),(z0t/z) * (Rib/A))
f_m_inf = 1 - (psi_m_zeta - psi_m_zeta0) / log(z/z0m)
f_h_inf = 1 - (psi_h_zeta - psi_h_zeta0) / log(z/z0t)
ksi_m_0 = ((z0m / z) - 1.0) / log(z0m/z)
ksi_h_0 = ((z0t / z) - 1.0) / log(z0t/z)
ksi_m_inf = (A / (beta_m * Rib)) * (1.0 - 1.0 / (f_m_inf**4))
ksi_h_inf = (A / (beta_h * Rib)) * (1.0 - ((1.0 / Pr_t_0_inv)**2) / (f_h_inf**2))
ksi_m = cc1 * ksi_m_inf + cc2 * ksi_m_0
ksi_h = cc3 * ksi_h_inf + cc4 * ksi_h_0
a0 = (1 / (beta_m * ksi_m)) * ((Rib / A)**2)
a1 = -1 * (beta_h * ksi_h / (beta_m * ksi_m)) * ((Rib / A)**2)
a2 = -1 / (beta_m * ksi_m)
r = (9.0 * (a1 * a2 - 3 * a0) - 2.0 * (a2**3)) / 54.0
q = (3.0 * a1 - a2*a2) / 9.0
delta = q**3 + r**2
s1 = (r + sqrt(delta))**(1./3.)
s2 = (r - sqrt(delta))**(1./3.)
theta = 1.0 / cos(r / sqrt(-1 * (q**3)))
if(delta <= 0.0)then
zeta = 2.0 * sqrt(-1.0 * q) * cos((theta + 2.0 * pi)/3.0) + 1 /(3.0 * beta_m * ksi_m)
else
s1 = cmplx(r + delta**0.5)**(1./3.)
s2 = cmplx(r - delta**0.5)**(1./3.)
zeta = -1*(real(real(s1)) + real(real(s2)) + 1.0 /(3.0 * beta_m * ksi_m))
endif
end subroutine
end module sfx_sheba_coare