!--------1---------2---------3---------4---------5---------6---------7---------8
subroutine flux_frez(flux_out) 
!--------1---------2---------3---------4---------5---------6---------7---------8
  use global_constants, only : rkind, dt, time, year, density
  use global_parameters, only : temp, radius, dr, surface_area, halfdr, surface_arear
  use heat_parameters, only : latent_heat_init, specific_heat
  use material_parameters, only : mn, iw, ii, i_irw &
    & , ice_reach_rock, melt, radius_ice, radius_water, frez_start &
    & , radius_ice_water, radius_rock, ice_rockice &
    & , material_select, mass_ratio_rock, mass_ratio_ice, mass_ratio_water
  use ice_parameters, only : temperature_melting_I
  use energy, only : lat_energy
  implicit none
  real(rkind) :: flux_out
  real(rkind) :: coef_latent, dlat_energy, dr_water
  if(.NOT.frez_start) then
    frez_start = .TRUE.
    radius_ice_water = radius_water
    i_irw = iw
  endif
  if(mn(ii) <= 3) then
    mn(ii) = 3
  elseif(mn(ii) == 8 .OR. mn(ii) == 9 .OR. mn(ii) == 11) then
    mn(ii) = 9
  elseif(mn(ii) == 5 .OR. mn(ii) == 12) then
    mn(ii) = 12
  else
    call log_error(ii,'flux_frez_mncheck')
    return
  endif
  coef_latent = latent_heat_init*density(1)*surface_arear(radius_water) 
  lat_energy(ii) = lat_energy(ii) - flux_out
  dr_water = flux_out*dt/coef_latent
  radius_water = radius_water - dr_water
  if(radius_water < radius(ii) - halfdr) then
    dlat_energy = coef_latent*((radius(ii)-halfdr)-radius_water)/dt
    lat_energy(ii) = lat_energy(ii) + dlat_energy
    if(mn(ii)==3) then
      mn(ii) = 2
      mass_ratio_water(ii) = 0._rkind
      mass_ratio_ice(ii) = 1._rkind
    elseif(mn(ii)==9) then
      mn(ii) = 10
      call ice_rockice(ii)
    endif
    if(mn(ii-1)<=3) then
      mn(ii-1) = 3
    elseif(mn(ii-1)==5) then
      mn(ii-1) = 12
    else
      write(999,*) 'error occurs at flux_frez_check! mn(ii-1)', mn(ii-1), ii-1
      call log_error(ii-1,'flux_frez_check mn(ii-1)')
      return
    endif
    melt(ii-1) = .FALSE.
    lat_energy(ii-1) = lat_energy(ii-1) - dlat_energy
  elseif(radius_water < radius_rock) then
    ice_reach_rock = .TRUE.
    dlat_energy = coef_latent*(radius_rock-radius_water)/dt
    lat_energy(ii) = lat_energy(ii) + dlat_energy
    temp(ii) = temp(ii) - dlat_energy*dt/(density(15)*specific_heat(15) &
      &*surface_area(ii)*dr)
    radius_water = radius_rock
    melt(ii) = .FALSE.
    mn(ii) =  13
    call material_select(ii)
    endif
  return
end subroutine flux_frez