sfx_surface.f90

#include "../includeF/sfx_def.fi"

module sfx_surface
    !< @brief surface roughness parameterizations

    ! modules used
    ! --------------------------------------------------------------------------------
    use sfx_phys_const
    use sfx_z0m_all_surface
    use sfx_z0t_all_surface
    ! --------------------------------------------------------------------------------

    ! directives list
    ! --------------------------------------------------------------------------------
    implicit none
    ! --------------------------------------------------------------------------------

    ! public interface
    ! --------------------------------------------------------------------------------
#if defined(INCLUDE_CXX)
    public :: set_c_struct_sfx_surface_param_values
#endif
    !public :: get_charnock_roughness
    !public :: get_thermal_roughness
    public :: get_dynamic_roughness_all
    public :: get_dynamic_roughness_definition
    public :: get_thermal_roughness_all
    public :: get_thermal_roughness_definition
    ! --------------------------------------------------------------------------------


    ! *: add surface type as input value
    integer, public, parameter :: surface_ocean = 0     !< ocean surface
    integer, public, parameter :: surface_land = 1      !< land surface
    integer, public, parameter :: surface_lake = 2      !< lake surface
    integer, public, parameter :: surface_snow = 3      !< snow covered surface
    integer, public, parameter :: surface_forest = 4      !< forest covered surface
    integer, public, parameter :: surface_user = 5      !< coast covered surface
    integer, public, parameter :: surface_ice = 6      !< ice covered surface

    character(len = 16), parameter :: surface_ocean_tag = 'ocean'
    character(len = 16), parameter :: surface_land_tag = 'land'
    character(len = 16), parameter :: surface_lake_tag = 'lake'
    character(len = 16), parameter :: surface_snow_tag = 'snow'
    character(len = 16), parameter :: surface_forest_tag = 'forest'
    character(len = 16), parameter :: surface_user_tag = 'user'
    character(len = 16), parameter :: surface_ice_tag = 'ice'


    integer, public, parameter :: z0m_ch = 0 
    integer, public, parameter :: z0m_fe = 1   
    integer, public, parameter :: z0m_ow = 2  
    integer, public, parameter :: z0m_map_id = 3      
    integer, public, parameter :: z0m_user = 4 
    integer, public, parameter :: z0m_and = 5 
    integer, public, parameter :: z0m_cst1 = 6
    integer, public, parameter :: z0m_cst2 = 7
    integer, public, parameter :: z0m_cst3 = 8 

    integer, public, parameter :: z0t_kl_water = 0 
    integer, public, parameter :: z0t_kl_land = 1   
    integer, public, parameter :: z0t_re = 2      
    integer, public, parameter :: z0t_zi = 3         
    integer, public, parameter :: z0t_ca = 4    
    integer, public, parameter :: z0t_cz = 5      
    integer, public, parameter :: z0t_br = 6      
    integer, public, parameter :: z0t_ot = 7      
    integer, public, parameter :: z0t_du = 8      
    integer, public, parameter :: z0t_zm = 9      
    integer, public, parameter :: z0t_mix = 10      
    integer, public, parameter :: z0t_user = 11   


    character(len = 16), parameter :: z0m_tag_ch = 'charnock'
    character(len = 16), parameter :: z0m_tag_fe = 'fetch'
    character(len = 16), parameter :: z0m_tag_ow = 'owen'
    character(len = 16), parameter :: z0m_tag_map = 'map'
    character(len = 16), parameter :: z0m_tag_user = 'user'
    character(len = 16), parameter :: z0m_tag_and = 'andreas'
    character(len = 16), parameter :: z0m_tag_cst1 = 'coast1'
    character(len = 16), parameter :: z0m_tag_cst2 = 'coast2'
    character(len = 16), parameter :: z0m_tag_cst3 = 'coast3'


    character(len = 16), parameter :: z0t_tag_kl_water = 'kl_water'
    character(len = 16), parameter :: z0t_tag_kl_land = 'kl_land'
    character(len = 16), parameter :: z0t_tag_re = 're'
    character(len = 16), parameter :: z0t_tag_zi = 'zi'
    character(len = 16), parameter :: z0t_tag_ca = 'ca'
    character(len = 16), parameter :: z0t_tag_cz = 'cz'
    character(len = 16), parameter :: z0t_tag_br = 'br'
    character(len = 16), parameter :: z0t_tag_ot = 'ot'
    character(len = 16), parameter :: z0t_tag_du = 'du'
    character(len = 16), parameter :: z0t_tag_zm = 'zm'
    character(len = 16), parameter :: z0t_tag_mix = 'mix'
    character(len = 16), parameter :: z0t_tag_user = 'zt_user'
    

    integer, public, parameter :: ocean_z0m_id = z0m_ch     !< ocean surface
    integer, public, parameter :: land_z0m_id = z0m_map_id        !< land surface
    integer, public, parameter :: lake_z0m_id = z0m_map_id        !< lake surface
    integer, public, parameter :: snow_z0m_id = z0m_map_id       !< snow covered surface    
    integer, public, parameter :: forest_z0m_id = z0m_map_id     !< forest csurface  
    integer, public, parameter :: usersf_z0m_id = z0m_map_id      !< user surface  
    integer, public, parameter :: ice_z0m_id = z0m_map_id       !< ice surface  


    integer, public, parameter :: ocean_z0t_id = z0t_kl_water     !< ocean surface
    integer, public, parameter :: land_z0t_id = z0t_kl_land        !< land surface
    integer, public, parameter :: lake_z0t_id = z0t_kl_land        !< lake surface
    integer, public, parameter :: snow_z0t_id = z0t_kl_land         !< snow covered surface    
    integer, public, parameter :: forest_z0t_id = z0t_kl_land      !< forest csurface  
    integer, public, parameter :: usersf_z0t_id = z0t_kl_land      !< user surface  
    integer, public, parameter :: ice_z0t_id = z0t_kl_land     !< user surface  
    
    ! --------------------------------------------------------------------------------
    real, parameter, private :: kappa = 0.40         !< von Karman constant [n/d]
    ! --------------------------------------------------------------------------------

    !< Charnock parameters
    !<     z0 = Re_visc_min * (nu / u_dyn) + gamma_c * (u_dyn^2 / g)
    ! --------------------------------------------------------------------------------
    
    !real, parameter :: gamma_c = 0.0144
    !real, parameter :: Re_visc_min = 0.111

    !real, parameter :: h_charnock = 10.0
    !real, parameter :: c1_charnock = log(h_charnock * (g / gamma_c))
    !real, parameter :: c2_charnock = Re_visc_min * nu_air * (g / gamma_c)
    ! --------------------------------------------------------------------------------

    !< Re fully roughness minimum value [n/d]
    !real, parameter ::  Re_rough_min = 16.3

    !< roughness model coeff. [n/d]
    !< --- transitional mode
    !<     B = log(z0_m / z0_t) = B1 * log(B3 * Re) + B2
    !real, parameter :: B1_rough = 5.0 / 6.0
    !real, parameter :: B2_rough = 0.45
    !real, parameter :: B3_rough = kappa * Pr_m
    !< --- fully rough mode (Re > Re_rough_min)
    !<     B = B4 * Re^(B2)
    !real, parameter :: B4_rough =(0.14 * (30.0**B2_rough)) * (Pr_m**0.8)

    !real, parameter :: B_max_land = 2.0
    !real, parameter :: B_max_ocean = 8.0
    !real, parameter :: B_max_lake = 8.0

contains
   
    ! surface type definition
    ! --------------------------------------------------------------------------------
    function get_surface_id(tag) result(id)
        implicit none
        character(len=*), intent(in) :: tag
        integer :: id

        id = - 1
        if (trim(tag) == trim(surface_ocean_tag)) then
            id = surface_ocean
        else if (trim(tag) == trim(surface_land_tag)) then
            id = surface_land
        else if (trim(tag) == trim(surface_lake_tag)) then
            id = surface_lake
        else if (trim(tag) == trim(surface_snow_tag)) then
            id = surface_snow
        else if (trim(tag) == trim(surface_forest_tag)) then
            id = surface_forest
        else if (trim(tag) == trim(surface_user_tag)) then
            id = surface_user
        else if (trim(tag) == trim(surface_ice_tag)) then
            id = surface_ice
        end if

    end function

    function get_surface_tag(id) result(tag)
        implicit none
        integer :: id
        character(len=:), allocatable :: tag

        tag = 'undefined'
        if (id == surface_ocean) then
            tag = surface_ocean_tag
        else if (id == surface_land) then
            tag = surface_land_tag
        else if (id == surface_lake) then
            tag = surface_lake_tag
        else if (id == surface_snow) then
            tag = surface_snow_tag
        else if (id == surface_forest) then
            tag = surface_forest_tag
        else if (id == surface_user) then
            tag = surface_user_tag
        else if (id == surface_ice) then
            tag = surface_ice_tag
        end if 

    end function


    function get_surface_z0m_id(tag_z0m) result(z0m_id)
        implicit none
        character(len=*), intent(in) :: tag_z0m
        integer :: z0m_id

        z0m_id = - 1
        if (trim(tag_z0m) == trim(z0m_tag_ch)) then
            z0m_id = z0m_ch
        else if (trim(tag_z0m) == trim(z0m_tag_fe)) then
            z0m_id = z0m_fe
        else if (trim(tag_z0m) == trim(z0m_tag_ow)) then
            z0m_id = z0m_ow
        else if (trim(tag_z0m) == trim(z0m_tag_map)) then
            z0m_id = z0m_map_id
        else if (trim(tag_z0m) == trim(z0m_tag_user)) then
            z0m_id = z0m_user
        else if (trim(tag_z0m) == trim(z0m_tag_cst1)) then
            z0m_id = z0m_cst1
        else if (trim(tag_z0m) == trim(z0m_tag_cst2)) then
            z0m_id = z0m_cst2
        else if (trim(tag_z0m) == trim(z0m_tag_cst3)) then
            z0m_id = z0m_cst3
        end if

    end function

    function get_surface_z0m_tag(z0m_id) result(tag_z0m)
        implicit none
        integer :: z0m_id
        character(len=:), allocatable :: tag_z0m

        tag_z0m = 'undefined'
        if (z0m_id == z0m_ch) then
            tag_z0m = z0m_tag_ch
        else if (z0m_id == z0m_fe) then
            tag_z0m =  z0m_tag_fe
        else if (z0m_id == z0m_ow) then
            tag_z0m = z0m_tag_ow
        else if (z0m_id == z0m_map_id) then
            tag_z0m = z0m_tag_map
        else if (z0m_id == z0m_user) then
            tag_z0m = z0m_tag_user
        else if (z0m_id == z0m_cst1) then
            tag_z0m = z0m_tag_cst1
        else if (z0m_id == z0m_cst2) then
            tag_z0m = z0m_tag_cst2
        else if (z0m_id == z0m_cst3) then
            tag_z0m = z0m_tag_cst3
        end if 
     end function

     function get_surface_z0t_id(tag_z0t) result(z0t_id)
        implicit none
        character(len=*), intent(in) :: tag_z0t
        integer :: z0t_id

        z0t_id = - 1
        if (trim(tag_z0t) == trim(z0t_tag_kl_water)) then
            z0t_id = z0t_kl_water
        else if (trim(tag_z0t) == trim(z0t_tag_kl_land)) then
            z0t_id = z0t_kl_land
        else if (trim(tag_z0t) == trim(z0t_tag_re)) then
            z0t_id = z0t_re
        else if (trim(tag_z0t) == trim(z0t_tag_zi)) then
            z0t_id = z0t_zi
        else if (trim(tag_z0t) == trim(z0t_tag_ca)) then
            z0t_id = z0t_ca
        else if (trim(tag_z0t) == trim(z0t_tag_cz)) then
            z0t_id = z0t_cz
        else if (trim(tag_z0t) == trim(z0t_tag_br)) then
            z0t_id = z0t_br
        else if (trim(tag_z0t) == trim(z0t_tag_ot)) then
            z0t_id = z0t_ot
        else if (trim(tag_z0t) == trim(z0t_tag_du)) then
            z0t_id = z0t_du
        else if (trim(tag_z0t) == trim(z0t_tag_zm)) then
            z0t_id = z0t_zm
        else if (trim(tag_z0t) == trim(z0t_tag_mix)) then
            z0t_id = z0t_mix
        else if (trim(tag_z0t) == trim(z0t_tag_user)) then
            z0t_id = z0t_user
        end if
        
    end function

    function get_surface_z0t_tag(z0t_id) result(tag_z0t)
        implicit none
        integer :: z0t_id
        character(len=:), allocatable :: tag_z0t

        tag_z0t = 'undefined'
        if (z0t_id == z0t_kl_water) then
            tag_z0t = z0t_tag_kl_water
        else if (z0t_id == z0t_kl_land) then
            tag_z0t =  z0t_tag_kl_land
        else if (z0t_id == z0t_re) then
            tag_z0t = z0t_tag_re
        else if (z0t_id == z0t_zi) then
            tag_z0t = z0t_tag_zi
        else if (z0t_id == z0t_ca) then
            tag_z0t = z0t_tag_ca
        else if (z0t_id == z0t_cz) then
            tag_z0t = z0t_tag_cz
        else if (z0t_id == z0t_br) then
            tag_z0t = z0t_tag_br
        else if (z0t_id == z0t_ot) then
            tag_z0t = z0t_tag_ot
        else if (z0t_id == z0t_du) then
            tag_z0t = z0t_tag_du
        else if (z0t_id == z0t_zm) then
            tag_z0t = z0t_tag_zm
        else if (z0t_id == z0t_mix) then
            tag_z0t = z0t_tag_mix
        else if (z0t_id == z0t_user) then
            tag_z0t = z0t_tag_user
        end if 
     end function



#if defined(INCLUDE_CXX)
    subroutine set_c_struct_sfx_surface_param_values(surface_param)
        use sfx_data
        use sfx_z0m_all_surface
        use sfx_z0t_all_surface
        implicit none
        type (sfx_surface_param), intent(inout) :: surface_param
        surface_param%surface_ocean = surface_ocean
        surface_param%surface_land = surface_land
        surface_param%surface_lake = surface_lake

        surface_param%kappa = kappa
        surface_param%gamma_c = gamma_c
        surface_param%Re_visc_min = Re_visc_min
        surface_param%h_charnock = h_charnock
        surface_param%c1_charnock = c1_charnock
        surface_param%c2_charnock = c2_charnock
        surface_param%Re_rough_min = Re_rough_min
        surface_param%B1_rough = B1_rough
        surface_param%B2_rough = B2_rough
        surface_param%B3_rough = B3_rough
        surface_param%B4_rough = B4_rough
        surface_param%B_max_lake = B_max_lake
        surface_param%B_max_ocean = B_max_ocean
        surface_param%B_max_land = B_max_land
    end subroutine set_c_struct_sfx_surface_param_values
#endif

    ! dynamic roughness definition
    ! --------------------------------------------------------------------------------
      subroutine 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)
    ! ----------------------------------------------------------------------------
        integer, intent(out) :: z0m_id              

        integer, intent(in) :: surface_type             

        integer, intent(in) :: ocean_z0m_id            
        integer, intent(in) :: land_z0m_id             
        integer, intent(in) :: lake_z0m_id
        integer, intent(in) :: snow_z0m_id
        integer, intent(in) :: forest_z0m_id
        integer, intent(in) :: usersf_z0m_id
        integer, intent(in) :: ice_z0m_id
 ! ---------------------------------------------------------------------------

    if (surface_type == surface_ocean) then
     z0m_id = ocean_z0m_id
    else if (surface_type == surface_land) then
     z0m_id = land_z0m_id
    else if (surface_type == surface_snow) then
     z0m_id = snow_z0m_id
    else if (surface_type == surface_lake) then
    z0m_id = lake_z0m_id
    else if (surface_type == surface_forest) then
     z0m_id = forest_z0m_id
    else if (surface_type == surface_user) then
     z0m_id  = usersf_z0m_id
    else if (surface_type == surface_ice) then
    z0m_id  = ice_z0m_id
    end if 
    !write (*,*) z0m_id, surface_type
 end subroutine

    ! ----------------------------------------------------------------------------
 subroutine get_dynamic_roughness_all(z0_m, u_dyn0, U, depth, h,&
    maxiters, z0m_map, z0m_id)
! ----------------------------------------------------------------------------
       real, intent(out) :: z0_m           !< aerodynamic roughness [m]
       real, intent(out) :: u_dyn0         !< dynamic velocity in neutral conditions [m/s]

       real, intent(in) :: U               !< abs(wind speed) [m/s]
       real, intent(in) :: depth           !< depth [m]
       real, intent(in) :: h               !< constant flux layer height [m]
       real, intent(in) :: z0m_map          !< aerodynamic roughness from map [m]
       integer, intent(in) :: maxiters     !< maximum number of iterations
       
       integer, intent(in) :: z0m_id
! ---------------------------------------------------------------------------

      
  if (z0m_id == z0m_ch) then
      call get_dynamic_roughness_ch(z0_m, u_dyn0, U, h, maxiters)
   else if (z0m_id == z0m_fe) then
       call get_dynamic_roughness_fetch(z0_m, u_dyn0, U, depth, h, maxiters)
   else if (z0m_id == z0m_ow) then
       call get_dynamic_roughness_ow(z0_m, u_dyn0, U, h, maxiters)
   else if (z0m_id == z0m_map_id) then
       call get_dynamic_roughness_map(z0_m, u_dyn0, U, h, z0m_map)
    else if (z0m_id == z0m_and) then
        call get_dynamic_roughness_and(z0_m, u_dyn0, U, h, z0m_map)
   else if (z0m_id == z0m_user) then
       write(*, *) 'z0m_user'
    else if (z0m_id == z0m_cst1) then
        call get_dynamic_roughness_coast1(z0_m, u_dyn0, U, h, maxiters)
    else if (z0m_id == z0m_cst2) then
        call get_dynamic_roughness_coast2(z0_m, u_dyn0, U, h, maxiters)
    else if (z0m_id == z0m_cst3) then
        call get_dynamic_roughness_coast3(z0_m, u_dyn0, U, h, maxiters)
end if 
     
end subroutine
! --------------------------------------------------------------------------------  

! thermal roughness definition
    ! --------------------------------------------------------------------------------
subroutine 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)
! ----------------------------------------------------------------------------
    integer, intent(out) :: z0t_id              

    integer, intent(in) :: surface_type             

    integer, intent(in) :: ocean_z0t_id            
    integer, intent(in) :: land_z0t_id             
    integer, intent(in) :: lake_z0t_id
    integer, intent(in) :: snow_z0t_id
    integer, intent(in) :: forest_z0t_id
    integer, intent(in) :: usersf_z0t_id
    integer, intent(in) :: ice_z0t_id

! ---------------------------------------------------------------------------

    if (surface_type == surface_ocean) then
    z0t_id = ocean_z0t_id
    else if (surface_type == surface_land) then
    z0t_id = land_z0t_id
    else if (surface_type == surface_snow) then
    z0t_id = snow_z0t_id
    else if (surface_type == surface_lake) then
    z0t_id = lake_z0t_id
    else if (surface_type == surface_forest) then
    z0t_id = forest_z0t_id
    else if (surface_type == surface_user) then
    z0t_id  = usersf_z0t_id
    else if (surface_type == surface_ice) then
    z0t_id  = ice_z0t_id
    end if 
    
    end subroutine

!---------------------------------------------------------------
    subroutine get_thermal_roughness_all(z0_t, B, &
    z0_m, Re, u_dyn, LAI, z0t_id)
! ----------------------------------------------------------------------------
    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]
    real, intent(in) :: LAI                 !< leaf-area index
    real, intent(in) :: u_dyn              !< dynamic velocity [m/s]
    

    integer, intent(in) :: z0t_id
! ---------------------------------------------------------------------------
    real  Czm                 !< proportionality coefficient z0_t =Czm*z0_m
    Czm=1
    
    if (z0t_id == z0t_kl_water) then
    call get_thermal_roughness_kl_water(z0_t, B, z0_m, Re)
    else if (z0t_id == z0t_kl_land) then
    call get_thermal_roughness_kl_land(z0_t, B, z0_m, Re)
    else if (z0t_id == z0t_re) then
    call get_thermal_roughness_re(z0_t, B, z0_m, Re)
    else if (z0t_id == z0t_zi) then
    call get_thermal_roughness_zi(z0_t, B, z0_m, Re)
    else if (z0t_id == z0t_ca) then
    call get_thermal_roughness_ca(z0_t, B, z0_m, Re)
    else if (z0t_id == z0t_cz) then
    call get_thermal_roughness_cz(z0_t, B, z0_m, Re)
    else if (z0t_id == z0t_br) then
    call get_thermal_roughness_br(z0_t, B, z0_m, Re)
    else if (z0t_id == z0t_ot) then
    call get_thermal_roughness_ot(z0_t, B, z0_m, Re)
    else if (z0t_id == z0t_du) then
    call get_thermal_roughness_du(z0_t, B, z0_m, u_dyn, LAI)
    else if (z0t_id == z0t_zm) then
    call get_thermal_roughness_zm(z0_t, B, z0_m, Czm)
    else if (z0t_id == z0t_mix) then
    call get_thermal_roughness_mix(z0_t, B, z0_m, u_dyn, Re)
    else if (z0t_id == z0t_user) then
    write(*, *) 'z0t_user'
    end if
    

end subroutine



      subroutine get_charnock_roughness(z0_m, u_dyn0, U, h, maxiters)
        ! ----------------------------------------------------------------------------
        real, intent(out) :: z0_m           !< aerodynamic roughness [m]
        real, intent(out) :: u_dyn0         !< dynamic velocity in neutral conditions [m/s]

        real, intent(in) :: h               !< constant flux layer height [m]
        real, intent(in) :: U               !< abs(wind speed) [m/s]
        integer, intent(in) :: maxiters     !< maximum number of iterations
        ! ----------------------------------------------------------------------------

        ! --- local variables
        real :: Uc                  ! wind speed at h_charnock [m/s]

        real :: a, b, c, c_min
        real :: f

        integer :: i, j
        ! ----------------------------------------------------------------------------

        Uc = U
        a = 0.0
        b = 25.0
        c_min = log(h_charnock) / kappa

        do i = 1, maxiters
            f = c1_charnock - 2.0 * log(Uc)
            do j = 1, maxiters
                c = (f + 2.0 * log(b)) / kappa
                ! looks like the check should use U10 instead of U
                !   but note that a1 should be set = 0 in cycle beforehand
                if (U <= 8.0e0) a = log(1.0 + c2_charnock * ((b / Uc)**3)) / kappa
                c = max(c - a, c_min)
                b = c
            end do
            z0_m = h_charnock * exp(-c * kappa)
            z0_m = max(z0_m, 0.000015e0)
            Uc = U * log(h_charnock / z0_m) / log(h / z0_m)
        end do

        ! --- define dynamic velocity in neutral conditions
        u_dyn0 = Uc / c

    end subroutine
    ! --------------------------------------------------------------------------------

    ! thermal roughness definition
    ! --------------------------------------------------------------------------------
    subroutine get_thermal_roughness(z0_t, B, &
            z0_m, Re, surface_type)
        ! ----------------------------------------------------------------------------
        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]
        integer, intent(in) :: surface_type     !< = [ocean] || [land] || [lake]
        ! ----------------------------------------------------------------------------

        ! --- local variables
        ! ----------------------------------------------------------------------------

        ! --- 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

        !   --- apply max restriction based on surface type
        if (surface_type == surface_ocean) then
            B = min(B, B_max_ocean)
        else if (surface_type == surface_lake) then
            B = min(B, B_max_ocean)
        else if (surface_type == surface_land) then
            B = min(B, B_max_land)
        end if

        ! --- define roughness [thermal]
        z0_t = z0_m / exp(B)

    end subroutine
    ! --------------------------------------------------------------------------------

end module sfx_surface