ice_material_quantities.F90

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!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
!
!  Module :  i c e _ m a t e r i a l _ q u a n t i t i e s
!
!> @file
!!
!! Material quantities of ice:
!! Rate factor, heat conductivity, specific heat (heat capacity).
!!
!! @section Copyright
!!
!! Copyright 2009-2016 Ralf Greve
!!
!! @section License
!!
!! This file is part of SICOPOLIS.
!!
!! SICOPOLIS is free software: you can redistribute it and/or modify
!! it under the terms of the GNU General Public License as published by
!! the Free Software Foundation, either version 3 of the License, or
!! (at your option) any later version.
!!
!! SICOPOLIS is distributed in the hope that it will be useful,
!! but WITHOUT ANY WARRANTY; without even the implied warranty of
!! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
!! GNU General Public License for more details.
!!
!! You should have received a copy of the GNU General Public License
!! along with SICOPOLIS.  If not, see <http://www.gnu.org/licenses/>.
!<
!+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

!-------------------------------------------------------------------------------
!> Material quantities of ice:
!! Rate factor, heat conductivity, specific heat (heat capacity).
!<------------------------------------------------------------------------------
module ice_material_quantities

use sico_types

implicit none
save

!> RF(n): Tabulated values for the rate factor of cold ice
   real(dp), dimension(-256:255), private       :: rf
!> R_T: Coefficient of the water-content dependence in the rate factor
!>      for temperate ice
   real(dp)                     , private       :: r_t
!> KAPPA(n): Tabulated values for the heat conductivity of ice
   real(dp), dimension(-256:255), private       :: kappa
!> C(n): Tabulated values for the specific heat of ice
   real(dp), dimension(-256:255), private       :: c

!> RHO_I: Density of ice
   real(dp)                     , private       :: rho_i
                                                ! only for the Martian ice caps
!> RHO_C: Density of crustal material (dust)
   real(dp)                     , private       :: rho_c
                                                ! only for the Martian ice caps
!> KAPPA_C: Heat conductivity of crustal material (dust)
   real(dp)                     , private       :: kappa_c
                                                ! only for the Martian ice caps
!> C_C: Specific heat of crustal material (dust)
   real(dp)                     , private       :: c_c
                                                ! only for the Martian ice caps

public :: ice_mat_eqs_pars, ratefac_c, ratefac_t, ratefac_c_t, kappa_val, c_val

contains

!-------------------------------------------------------------------------------
!> Setting of required physical parameters.
!<------------------------------------------------------------------------------
subroutine ice_mat_eqs_pars(RF_table, R_T_val, KAPPA_table, C_table, &
                            n_temp_min, n_temp_max, &
                            rho_i_val, rho_c_val, kappa_c_val, c_c_val)

implicit none

integer(i4b),       intent(in) :: n_temp_min, n_temp_max
real(dp), dimension(n_temp_min:n_temp_max), &
                    intent(in) :: rf_table, kappa_table, c_table
real(dp),           intent(in) :: r_t_val
real(dp), optional, intent(in) :: rho_i_val, rho_c_val, kappa_c_val, c_c_val

integer(i4b) :: n

!-------- Initialisation --------

rf    = 0.0_dp
kappa = 0.0_dp
c     = 0.0_dp

if ((n_temp_min <= -256).or.(n_temp_max >= 255)) &
   stop ' ice_mat_eqs_pars: Temperature indices out of allowed range!'

!-------- Assignment --------

do n=n_temp_min, n_temp_max
   rf(n)    = rf_table(n)
   kappa(n) = kappa_table(n)
   c(n)     = c_table(n)
end do

do n=-256, n_temp_min-1
   rf(n)    = rf(n_temp_min)      ! dummy values
   kappa(n) = kappa(n_temp_min)   ! dummy values
   c(n)     = c(n_temp_min)       ! dummy values
end do

do n=n_temp_max+1, 255
   rf(n)    = rf(n_temp_max)      ! dummy values
   kappa(n) = kappa(n_temp_max)   ! dummy values
   c(n)     = c(n_temp_max)       ! dummy values
end do

r_t = r_t_val

!-------- Martian stuff --------

if ( present(rho_i_val) ) then
   rho_i = rho_i_val
else
   rho_i = 0.0_dp   ! dummy value
end if

if ( present(rho_c_val) ) then
   rho_c = rho_c_val
else
   rho_c = 0.0_dp   ! dummy value
end if

if ( present(kappa_c_val) ) then
   kappa_c = kappa_c_val
else
   kappa_c = 0.0_dp   ! dummy value
end if

if ( present(c_c_val) ) then
   c_c = c_c_val
else
   c_c = 0.0_dp   ! dummy value
end if

end subroutine ice_mat_eqs_pars

!-------------------------------------------------------------------------------
!> Rate factor for cold ice:
!! Linear interpolation of tabulated values in RF(.).
!<------------------------------------------------------------------------------
function ratefac_c(temp_val, temp_m_val)

use sico_types
use sico_variables
use sico_vars

implicit none
real(dp)             :: ratefac_c
real(dp), intent(in) :: temp_val, temp_m_val

real(dp) :: temp_h_val

temp_h_val = temp_val-temp_m_val

ratefac_c = rf(floor(temp_h_val)) &
              +(rf(floor(temp_h_val)+1)-rf(floor(temp_h_val))) &
               *(temp_h_val-real(floor(temp_h_val),dp))

end function ratefac_c

!-------------------------------------------------------------------------------
!> Rate factor for temperate ice.
!<------------------------------------------------------------------------------
function ratefac_t(omega_val)

use sico_types
use sico_variables
use sico_vars

implicit none
real(dp)             :: ratefac_t
real(dp), intent(in) :: omega_val

ratefac_t = rf(0)*(1.0_dp+r_t*(omega_val))

end function ratefac_t

!-------------------------------------------------------------------------------
!> Rate factor for cold and temperate ice:
!! Combination of ratefac_c and ratefac_t (only for the enthalpy method).
!<------------------------------------------------------------------------------
function ratefac_c_t(temp_val, omega_val, temp_m_val)

use sico_types
use sico_variables
use sico_vars

implicit none
real(dp)             :: ratefac_c_t
real(dp), intent(in) :: temp_val, temp_m_val, omega_val

real(dp) :: temp_h_val

temp_h_val = temp_val-temp_m_val

ratefac_c_t = ( rf(floor(temp_h_val)) &
                  +(rf(floor(temp_h_val)+1)-rf(floor(temp_h_val))) &
                   *(temp_h_val-real(floor(temp_h_val),dp)) ) &
              *(1.0_dp+r_t*(omega_val))

end function ratefac_c_t

!-------------------------------------------------------------------------------
!> Heat conductivity of ice:
!! Linear interpolation of tabulated values in KAPPA(.).
!<------------------------------------------------------------------------------
function kappa_val(temp_val)

use sico_types
use sico_variables
use sico_vars

implicit none
real(dp)             :: kappa_val
real(dp), intent(in) :: temp_val

real(dp) :: kappa_ice

!-------- Heat conductivity of pure ice --------

#if defined(FRAC_DUST)
kappa_ice = kappa(floor(temp_val)) &
           +(kappa(floor(temp_val)+1)-kappa(floor(temp_val))) &
            *(temp_val-real(floor(temp_val),dp))
#else
kappa_val = kappa(floor(temp_val)) &
           +(kappa(floor(temp_val)+1)-kappa(floor(temp_val))) &
            *(temp_val-real(floor(temp_val),dp))
#endif

!-------- If dust is present (polar caps of Mars):
!         Heat conductivity of ice-dust mixture --------

#if defined(FRAC_DUST)
kappa_val = (1.0_dp-frac_dust)*kappa_ice + frac_dust*kappa_c
#endif

end function kappa_val

!-------------------------------------------------------------------------------
!> Specific heat of ice:
!! Linear interpolation of tabulated values in C(.).
!<------------------------------------------------------------------------------
function c_val(temp_val)

use sico_types
use sico_variables
use sico_vars

implicit none
real(dp)             :: c_val
real(dp), intent(in) :: temp_val

real(dp) :: c_ice

!-------- Specific heat of pure ice --------

#if defined(FRAC_DUST)
c_ice = c(floor(temp_val)) &
        +(c(floor(temp_val)+1)-c(floor(temp_val))) &
         *(temp_val-real(floor(temp_val),dp))
#else
c_val = c(floor(temp_val)) &
        +(c(floor(temp_val)+1)-c(floor(temp_val))) &
         *(temp_val-real(floor(temp_val),dp))
#endif

!-------- If dust is present (polar caps of Mars):
!         Specific heat of ice-dust mixture --------

#if defined(FRAC_DUST)
c_val = rho_inv * ( (1.0_dp-frac_dust)*rho_i*c_ice + frac_dust*rho_c*c_c )
#endif

end function c_val

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

end module ice_material_quantities
!