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module sfx_z0t_all_surface
!< @brief surface thermal roughness parameterizations
implicit none
public
! --------------------------------------------------------------------------------
real, parameter, private :: kappa = 0.40 !< von Karman constant [n/d]
real, parameter, private :: Pr_m = 0.71 !< molecular Prandtl number (air) [n/d]
!< Re fully roughness minimum value [n/d]
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real, public, parameter :: Re_rough_min = 16.3
!< roughness model coeff. [n/d]
!< --- transitional mode
!< B = log(z0_m / z0_t) = B1 * log(B3 * Re) + B2
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real, public, parameter :: B1_rough = 5.0 / 6.0
real, public, parameter :: B2_rough = 0.45
real, parameter :: B3_rough = kappa * Pr_m
!< --- fully rough mode (Re > Re_rough_min)
!< B = B4 * Re^(B2)
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real, public, parameter :: B4_rough =(0.14 * (30.0**B2_rough)) * (Pr_m**0.8)
real, public, parameter :: B_max_ocean = 8.0
real, public, parameter :: B_max_land = 2.0
contains
! thermal roughness definition by Kazakov, Lykosov
! --------------------------------------------------------------------------------
subroutine get_thermal_roughness_kl_land(z0_t, B, &
z0_m, Re)
! ----------------------------------------------------------------------------
real, intent(out) :: z0_t !< thermal roughness [m]
real, intent(out) :: B !< = log(z0_m / z0_t) [n/d]
real, intent(in) :: z0_m !< aerodynamic roughness [m]
real, intent(in) :: Re !< roughness Reynolds number [n/d]
! ----------------------------------------------------------------------------
!--- define B = log(z0_m / z0_t)
if (Re <= Re_rough_min) then
B = B1_rough * alog(B3_rough * Re) + B2_rough
else
! *: B4 takes into account Re value at z' ~ O(10) z0
B = B4_rough * (Re**B2_rough)
end if
B = min(B, B_max_land)
z0_t = z0_m / exp(B)
end subroutine
! --------------------------------------------------------------------------------
! --------------------------------------------------------------------------------
subroutine get_thermal_roughness_kl_water(z0_t, B, &
z0_m, Re)
! ----------------------------------------------------------------------------
real, intent(out) :: z0_t !< thermal roughness [m]
real, intent(out) :: B !< = log(z0_m / z0_t) [n/d]
real, intent(in) :: z0_m !< aerodynamic roughness [m]
real, intent(in) :: Re !< roughness Reynolds number [n/d]
! ----------------------------------------------------------------------------
!--- define B = log(z0_m / z0_t)
if (Re <= Re_rough_min) then
B = B1_rough * alog(B3_rough * Re) + B2_rough
else
! *: B4 takes into account Re value at z' ~ O(10) z0
B = B4_rough * (Re**B2_rough)
end if
B = min(B, B_max_ocean)
z0_t = z0_m / exp(B)
end subroutine
! thermal roughness definition by Chen, F., Zhang, Y., 2009.
! --------------------------------------------------------------------------------
subroutine get_thermal_roughness_cz(z0_t, B, &
z0_m, Re)
! ----------------------------------------------------------------------------
real, intent(out) :: z0_t !< thermal roughness [m]
real, intent(out) :: B !< = log(z0_m / z0_t) [n/d]
real, intent(in) :: z0_m !< aerodynamic roughness [m]
real, intent(in) :: Re !< roughness Reynolds number [n/d]
B=(kappa*10.0**(-0.4*z0_m/0.07))*(Re**0.45) !Chen and Zhang
! --- define roughness [thermal]
z0_t = z0_m / exp(B)
end subroutine
! --------------------------------------------------------------------------------
! thermal roughness definition by Zilitinkevich, S., 1995.
! --------------------------------------------------------------------------------
subroutine get_thermal_roughness_zi(z0_t, B, &
z0_m, Re)
! ----------------------------------------------------------------------------
real, intent(out) :: z0_t !< thermal roughness [m]
real, intent(out) :: B !< = log(z0_m / z0_t) [n/d]
real, intent(in) :: z0_m !< aerodynamic roughness [m]
real, intent(in) :: Re !< roughness Reynolds number [n/d]
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B=0.1*kappa*(Re**0.5) !6-Zilitinkevich
! --- define roughness [thermal]
z0_t = z0_m / exp(B)
end subroutine
! --------------------------------------------------------------------------------
! thermal roughness definition by Cahill, A.T., Parlange, M.B., Albertson, J.D., 1997.
! It is better to use for dynamic surfaces such as sand
! --------------------------------------------------------------------------------
subroutine get_thermal_roughness_ca(z0_t, B, &
z0_m, Re)
! ----------------------------------------------------------------------------
real, intent(out) :: z0_t !< thermal roughness [m]
real, intent(out) :: B !< = log(z0_m / z0_t) [n/d]
real, intent(in) :: z0_m !< aerodynamic roughness [m]
real, intent(in) :: Re !< roughness Reynolds number [n/d]
B=2.46*(Re**0.25)-3.8 !4-Cahill et al.
! --- define roughness [thermal]
z0_t = z0_m / exp(B)
end subroutine
! --------------------------------------------------------------------------------
! thermal roughness definition by Brutsaert W., 2003.
! --------------------------------------------------------------------------------
subroutine get_thermal_roughness_br(z0_t, B, &
z0_m, Re)
! ----------------------------------------------------------------------------
real, intent(out) :: z0_t !< thermal roughness [m]
real, intent(out) :: B !< = log(z0_m / z0_t) [n/d]
real, intent(in) :: z0_m !< aerodynamic roughness [m]
real, intent(in) :: Re !< roughness Reynolds number [n/d]
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! --- define roughness [thermal]
z0_t = z0_m / exp(B)
end subroutine
! --------------------------------------------------------------------------------
! thermal roughness definition by Owen P. R., Thomson W. R., 1963.
! --------------------------------------------------------------------------------
subroutine get_thermal_roughness_ot(z0_t, B, &
z0_m, Re)
! ----------------------------------------------------------------------------
real, intent(out) :: z0_t !< thermal roughness [m]
real, intent(out) :: B !< = log(z0_m / z0_t) [n/d]
real, intent(in) :: z0_m !< aerodynamic roughness [m]
real, intent(in) :: Re !< roughness Reynolds number [n/d]
B=kappa*(Re**0.45) !Owen P. R., Thomson W. R.
! --- define roughness [thermal]
z0_t = z0_m / exp(B)
end subroutine
! --------------------------------------------------------------------------------
! thermal roughness definition by Duynkerke P. G., 1992.
!It is better to use for surfaces wiht forest
! --------------------------------------------------------------------------------
subroutine get_thermal_roughness_du(z0_t, B, &
z0_m, u_dyn, LAI)
! ----------------------------------------------------------------------------
real, intent(out) :: z0_t !< thermal roughness [m]
real, intent(out) :: B !< = log(z0_m / z0_t) [n/d]
real, intent(in) :: z0_m !< aerodynamic roughness [m]
real, intent(in) :: u_dyn !< dynamic velocity [m/s]
real, intent(in) :: LAI !< leaf-area index
B=(13*u_dyn**0.4)/LAI+0.85 !Duynkerke P. G., 1992.
! --- define roughness [thermal]
z0_t = z0_m / exp(B)
end subroutine
! --------------------------------------------------------------------------------
! thermal roughness definition z0_t = C*z0_m
! --------------------------------------------------------------------------------
subroutine get_thermal_roughness_zm(z0_t, B, &
z0_m, Czm)
! ----------------------------------------------------------------------------
real, intent(out) :: z0_t !< thermal roughness [m]
real, intent(out) :: B !< = log(z0_m / z0_t) [n/d]
real, intent(in) :: z0_m !< aerodynamic roughness [m]
real, intent(in) :: Czm !< proportionality coefficient
z0_t =Czm*z0_m
B=log(z0_m / z0_t)
end subroutine
! --------------------------------------------------------------------------------
! thermal roughness definition by Chen and Zhang and Zilitinkevich
! --------------------------------------------------------------------------------
subroutine get_thermal_roughness_mix(z0_t, B, &
z0_m, u_dyn, Re)
! ----------------------------------------------------------------------------
real, intent(out) :: z0_t !< thermal roughness [m]
real, intent(out) :: B !< = log(z0_m / z0_t) [n/d]
real, intent(in) :: z0_m !< aerodynamic roughness [m]
real, intent(in) :: u_dyn !< dynamic velocity [m/s]
real, intent(in) :: Re !< roughness Reynolds number [n/d]
real, parameter :: u_dyn_th=0.17 !< dynamic velocity treshhold [m/s]
if (u_dyn <= u_dyn_th) then
B=0.1*kappa*(Re**0.5) !Zilitinkevich
else
B=(kappa*10.0**(-0.4*z0_m/0.07))*(Re**0.45) !Chen and Zhang
end if
! --- define roughness [thermal]
z0_t = z0_m / exp(B)
end subroutine
! --------------------------------------------------------------------------------
subroutine get_thermal_roughness_re(z0_t, B, &
z0_m, Re)
! ----------------------------------------------------------------------------
real, intent(out) :: z0_t !< thermal roughness [m]
real, intent(out) :: B !< = log(z0_m / z0_t) [n/d]
real, intent(in) :: z0_m !< aerodynamic roughness [m]
real, intent(in) :: Re !< roughness Reynolds number [n/d]
z0_t = z0_m*(-0.56*(4.0*(Re1)**(0.5)-3.4))
if (z0_t<0) z0_t = z0_m*0.9
if (z0_m>z0_t) then
else
z0_t = z0_m*0.9
B=alog(z0_m/z0_t)
end if
end subroutine
end module sfx_z0t_all_surface