| 1 | MODULE ice_table_mod |
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| 2 | |
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| 3 | implicit none |
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| 4 | |
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| 5 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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| 6 | !!! |
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| 7 | !!! Purpose: Ice table (pore-filling) variables and methods to compute it (dynamic and static) |
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| 8 | !!! Author: LL, 02/2023 |
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| 9 | !!! |
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| 10 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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| 11 | |
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| 12 | logical :: icetable_equilibrium ! Boolean to say if the PEM needs to recompute the icetable depth when at equilibrium |
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| 13 | logical :: icetable_dynamic ! Boolean to say if the PEM needs to recompute the icetable depth with the dynamic method |
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| 14 | real, allocatable, dimension(:,:) :: icetable_depth ! ngrid x nslope: Depth of the ice table [m] |
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| 15 | real, allocatable, dimension(:,:) :: icetable_thickness ! ngrid x nslope: Thickness of the ice table [m] |
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| 16 | real, allocatable, dimension(:,:,:) :: ice_porefilling ! the amout of porefilling in each layer in each grid [m^3/m^3] |
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| 17 | |
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| 18 | !----------------------------------------------------------------------- |
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| 19 | contains |
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| 20 | |
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| 21 | !----------------------------------------------------------------------- |
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| 22 | SUBROUTINE ini_ice_table(ngrid,nslope,nsoil) |
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| 23 | |
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| 24 | implicit none |
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| 25 | |
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| 26 | integer, intent(in) :: ngrid ! number of atmospheric columns |
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| 27 | integer, intent(in) :: nslope ! number of slope within a mesh |
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| 28 | integer, intent(in) :: nsoil ! number of soil layers |
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| 29 | |
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| 30 | allocate(icetable_depth(ngrid,nslope)) |
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| 31 | allocate(icetable_thickness(ngrid,nslope)) |
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| 32 | allocate(ice_porefilling(ngrid,nsoil,nslope)) |
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| 33 | |
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| 34 | END SUBROUTINE ini_ice_table |
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| 35 | |
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| 36 | !----------------------------------------------------------------------- |
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| 37 | SUBROUTINE end_ice_table |
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| 38 | |
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| 39 | implicit none |
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| 40 | |
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| 41 | if (allocated(icetable_depth)) deallocate(icetable_depth) |
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| 42 | if (allocated(icetable_thickness)) deallocate(icetable_thickness) |
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| 43 | if (allocated(ice_porefilling)) deallocate(ice_porefilling) |
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| 44 | |
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| 45 | END SUBROUTINE end_ice_table |
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| 46 | |
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| 47 | !------------------------------------------------------------------------------------------------------ |
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| 48 | SUBROUTINE computeice_table_equilibrium(ngrid,nslope,nsoil,watercaptag,rhowatersurf_ave,rhowatersoil_ave,regolith_inertia,ice_table_depth,ice_table_thickness) |
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| 49 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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| 50 | !!! |
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| 51 | !!! Purpose: Compute the ice table depth (pore-filling) knowing the yearly average water |
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| 52 | !!! density at the surface and at depth. |
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| 53 | !!! Computations are made following the methods in Schorgofer et al., 2005 |
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| 54 | !!! This subroutine only gives the ice table at equilibrium and does not consider exchange with the atmosphere |
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| 55 | !!! |
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| 56 | !!! Author: LL |
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| 57 | !!! |
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| 58 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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| 59 | use math_mod, only: findroot |
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| 60 | use comsoil_h_PEM, only: mlayer_PEM, layer_PEM ! Depth of the vertical grid |
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| 61 | use soil_thermalproperties_mod, only: ice_thermal_properties |
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| 62 | |
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| 63 | implicit none |
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| 64 | |
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| 65 | ! Inputs |
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| 66 | ! ------ |
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| 67 | integer, intent(in) :: ngrid, nslope, nsoil ! Size of the physical grid, number of subslope, number of soil layer in the PEM |
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| 68 | logical, dimension(ngrid), intent(in) :: watercaptag ! Boolean to check the presence of a perennial glacier |
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| 69 | real, dimension(ngrid,nslope), intent(in) :: rhowatersurf_ave ! Water density at the surface, yearly averaged [kg/m^3] |
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| 70 | real, dimension(ngrid,nsoil,nslope), intent(in) :: rhowatersoil_ave ! Water density at depth, computed from clapeyron law's (Murchy and Koop 2005), yearly averaged [kg/m^3] |
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| 71 | real, dimension(ngrid,nslope), intent(in) :: regolith_inertia ! Thermal inertia of the regolith layer [SI] |
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| 72 | ! Ouputs |
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| 73 | ! ------ |
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| 74 | real, dimension(ngrid,nslope), intent(out) :: ice_table_depth ! ice table depth [m] |
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| 75 | real, dimension(ngrid,nslope), intent(out) :: ice_table_thickness ! ice table thickness [m] |
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| 76 | ! Locals |
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| 77 | ! ------ |
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| 78 | integer :: ig, islope, isoil, isoilend ! loop variables |
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| 79 | real, dimension(nsoil) :: diff_rho ! difference of water vapor density between the surface and at depth [kg/m^3] |
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| 80 | real :: ice_table_end ! depth of the end of the ice table [m] |
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| 81 | real, dimension(ngrid,nslope) :: previous_icetable_depth ! Ice table computed at previous ice depth [m] |
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| 82 | real :: stretch ! stretch factor to improve the convergence of the ice table |
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| 83 | real :: wice_inertia ! Water Ice thermal Inertia [USI] |
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| 84 | ! Code |
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| 85 | ! ---- |
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| 86 | previous_icetable_depth = ice_table_depth |
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| 87 | do ig = 1,ngrid |
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| 88 | if (watercaptag(ig)) then |
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| 89 | ice_table_depth(ig,:) = 0. |
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| 90 | ice_table_thickness(ig,:) = layer_PEM(nsoil) ! Let's assume an infinite ice table (true when geothermal flux is set to 0.) |
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| 91 | else |
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| 92 | do islope = 1,nslope |
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| 93 | ice_table_depth(ig,islope) = -1. |
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| 94 | ice_table_thickness(ig,islope) = 0. |
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| 95 | do isoil = 1,nsoil |
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| 96 | diff_rho(isoil) = rhowatersurf_ave(ig,islope) - rhowatersoil_ave(ig,isoil,islope) |
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| 97 | enddo |
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| 98 | if (diff_rho(1) > 0.) then ! ice is at the surface |
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| 99 | ice_table_depth(ig,islope) = 0. |
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| 100 | do isoilend = 2,nsoil - 1 |
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| 101 | if (diff_rho(isoilend) > 0 .and. diff_rho(isoilend + 1) < 0.) then |
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| 102 | call findroot(diff_rho(isoilend),diff_rho(isoilend + 1),mlayer_PEM(isoilend - 1),mlayer_PEM(isoilend),ice_table_end) |
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| 103 | ice_table_thickness(ig,islope) = ice_table_end - ice_table_depth(ig,islope) |
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| 104 | exit |
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| 105 | endif |
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| 106 | enddo |
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| 107 | else |
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| 108 | do isoil = 1,nsoil - 1 ! general case, we find the ice table depth by doing a linear approximation between the two depth, and then solve the first degree equation to find the root |
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| 109 | if (diff_rho(isoil) < 0. .and. diff_rho(isoil + 1) > 0.) then |
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| 110 | call findroot(diff_rho(isoil),diff_rho(isoil + 1),mlayer_PEM(isoil),mlayer_PEM(isoil + 1),ice_table_depth(ig,islope)) |
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| 111 | ! Now let's find the end of the ice table |
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| 112 | ice_table_thickness(ig,islope) = layer_PEM(nsoil) ! Let's assume an infinite ice table (true when geothermal flux is set to 0.) |
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| 113 | do isoilend = isoil + 1,nsoil - 1 |
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| 114 | if (diff_rho(isoilend) > 0. .and. diff_rho(isoilend + 1) < 0.) then |
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| 115 | call findroot(diff_rho(isoilend),diff_rho(isoilend + 1),mlayer_PEM(isoilend - 1),mlayer_PEM(isoilend),ice_table_end) |
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| 116 | ice_table_thickness(ig,islope) = ice_table_end - ice_table_depth(ig,islope) |
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| 117 | exit |
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| 118 | endif |
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| 119 | enddo |
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| 120 | endif ! diff_rho(z) <0 & diff_rho(z+1) > 0 |
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| 121 | enddo |
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| 122 | endif ! diff_rho(1) > 0 |
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| 123 | enddo |
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| 124 | endif ! watercaptag |
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| 125 | enddo |
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| 126 | |
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| 127 | ! Small trick to speed up the convergence, Oded's idea. |
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| 128 | do islope = 1,nslope |
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| 129 | do ig = 1,ngrid |
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| 130 | if (ice_table_depth(ig,islope) > previous_icetable_depth(ig,islope) .and. previous_icetable_depth(ig,islope) >= 0) then |
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| 131 | call ice_thermal_properties(.false.,1.,regolith_inertia(ig,islope),wice_inertia) |
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| 132 | stretch = (regolith_inertia(ig,islope)/wice_inertia)**2 |
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| 133 | ice_table_thickness(ig,islope) = ice_table_thickness(ig,islope) + (ice_table_depth(ig,islope) - & |
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| 134 | previous_icetable_depth(ig,islope) + (ice_table_depth(ig,islope) - previous_icetable_depth(ig,islope))/stretch) |
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| 135 | ice_table_depth(ig,islope) = previous_icetable_depth(ig,islope) + (ice_table_depth(ig,islope) - previous_icetable_depth(ig,islope))/stretch |
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| 136 | endif |
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| 137 | enddo |
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| 138 | enddo |
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| 139 | |
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| 140 | END SUBROUTINE computeice_table_equilibrium |
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| 141 | |
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| 142 | !----------------------------------------------------------------------- |
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| 143 | SUBROUTINE compute_massh2o_exchange_ssi(ngrid,nslope,nsoil,icetable_thickness_old,ice_porefilling_old,tsurf,tsoil,delta_m_h2o) |
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| 144 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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| 145 | !!! |
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| 146 | !!! Purpose: Compute the mass of H2O that has sublimated from the ice table / condensed |
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| 147 | !!! |
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| 148 | !!! Author: LL |
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| 149 | !!! |
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| 150 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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| 151 | use comsoil_h_PEM, only: mlayer_PEM |
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| 152 | use comslope_mod, only: subslope_dist, def_slope_mean |
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| 153 | use constants_marspem_mod, only: porosity |
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| 154 | use comcstfi_h, only: pi |
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| 155 | |
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| 156 | implicit none |
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| 157 | |
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| 158 | ! Inputs |
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| 159 | ! ------ |
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| 160 | integer, intent(in) :: ngrid, nslope, nsoil ! Size of the physical grid, number of subslope, number of soil layer in the PEM |
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| 161 | real, dimension(ngrid,nslope), intent(in) :: icetable_thickness_old ! Ice table thickness at the previous iteration [m] |
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| 162 | real, dimension(ngrid,nsoil,nslope), intent(in) :: ice_porefilling_old ! Ice pore filling at the previous iteration [m] |
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| 163 | real, dimension(ngrid,nslope), intent(in) :: tsurf ! Surface temperature [K] |
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| 164 | real, dimension(ngrid,nsoil,nslope), intent(in) :: tsoil ! Soil temperature [K] |
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| 165 | ! Outputs |
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| 166 | ! ------- |
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| 167 | real, dimension(ngrid), intent(out) :: delta_m_h2o ! Mass of H2O ice that has been condensed on the ice table / sublimates from the ice table [kg/m^2] |
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| 168 | ! Locals |
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| 169 | !------- |
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| 170 | integer :: ig, islope, isoil ! loop index |
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| 171 | real :: rho ! density of water ice [kg/m^3] |
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| 172 | real :: Tice ! ice temperature [k] |
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| 173 | ! Code |
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| 174 | ! ---- |
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| 175 | |
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| 176 | ! Let's compute the amount of ice that has sublimated in each subslope |
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| 177 | if (icetable_equilibrium) then |
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| 178 | delta_m_h2o = 0. |
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| 179 | do ig = 1,ngrid |
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| 180 | do islope = 1,nslope |
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| 181 | call compute_Tice_pem(nsoil,tsoil(ig,:,islope),tsurf(ig,islope),icetable_depth(ig,islope),Tice) |
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| 182 | delta_m_h2o(ig) = delta_m_h2o(ig) + porosity*rho_ice(Tice,'h2o')*(icetable_thickness(ig,islope) - icetable_thickness_old(ig,islope)) & ! convention > 0. <=> it condenses |
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| 183 | *subslope_dist(ig,islope)/cos(def_slope_mean(islope)*pi/180.) |
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| 184 | enddo |
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| 185 | enddo |
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| 186 | else if (icetable_dynamic) then |
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| 187 | delta_m_h2o = 0. |
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| 188 | do ig = 1,ngrid |
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| 189 | do islope = 1,nslope |
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| 190 | do isoil = 1,nsoil |
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| 191 | call compute_Tice_pem(nsoil,tsoil(ig,:,islope),tsurf(ig,islope),mlayer_PEM(isoil - 1),Tice) |
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| 192 | delta_m_h2o(ig) = delta_m_h2o(ig) + rho_ice(Tice,'h2o')*(ice_porefilling(ig,isoil,islope) - ice_porefilling_old(ig,isoil,islope)) & ! convention > 0. <=> it condenses |
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| 193 | *subslope_dist(ig,islope)/cos(def_slope_mean(islope)*pi/180.) |
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| 194 | enddo |
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| 195 | enddo |
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| 196 | enddo |
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| 197 | endif |
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| 198 | |
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| 199 | END SUBROUTINE compute_massh2o_exchange_ssi |
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| 200 | |
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| 201 | !----------------------------------------------------------------------- |
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| 202 | SUBROUTINE find_layering_icetable(porefill,psat_soil,psat_surf,pwat_surf,psat_bottom,B,index_IS,depth_filling,index_filling,index_geothermal,depth_geothermal,dz_etadz_rho) |
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| 203 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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| 204 | !!! |
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| 205 | !!! Purpose: Compute layering between dry soil, pore filling ice, and ice sheet based on Schorgofer, Icarus (2010). Adapted from NS MSIM |
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| 206 | !!! |
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| 207 | !!! Author: LL |
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| 208 | !!! |
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| 209 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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| 210 | use comsoil_h_PEM, only: nsoilmx_PEM, mlayer_PEM |
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| 211 | use math_mod, only: deriv1, deriv1_onesided, colint, findroot, deriv2_simple |
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| 212 | |
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| 213 | implicit none |
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| 214 | |
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| 215 | ! Inputs |
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| 216 | ! ------ |
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| 217 | real, dimension(nsoilmx_PEM), intent(in) :: porefill ! Fraction of pore space filled with ice [Unitless] 0 <= f <= 1 for pore ice |
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| 218 | real, dimension(nsoilmx_PEM), intent(in) :: psat_soil ! Soil water pressure at saturation, yearly averaged [Pa] |
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| 219 | real, intent(in) :: psat_surf ! surface water pressure at saturation, yearly averaged [Pa] |
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| 220 | real, intent(in) :: pwat_surf ! Water vapor pressure at the surface, not necesseraly at saturation, yearly averaged [Pa] |
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| 221 | real, intent(in) :: psat_bottom ! Boundary conditions for soil vapor pressure [Pa] |
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| 222 | real, intent(in) :: B ! constant (Eq. 8 from Schorgofer, Icarus (2010).) |
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| 223 | integer, intent(in) :: index_IS ! index of the soil layer where the ice sheet begins [1] |
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| 224 | real, intent(inout) :: depth_filling ! depth where pore filling begins [m] |
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| 225 | ! Outputs |
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| 226 | ! ------- |
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| 227 | integer, intent(out) :: index_filling ! index where the pore filling begins [1] |
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| 228 | integer, intent(out) :: index_geothermal ! index where the ice table stops [1] |
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| 229 | real, intent(out) :: depth_geothermal ! depth where the ice table stops [m] |
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| 230 | real, dimension(nsoilmx_PEM), intent(out) :: dz_etadz_rho ! \partial z(eta \partial z rho), eta is the constriction, used later for pore filling increase |
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| 231 | ! Locals |
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| 232 | !------- |
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| 233 | real, dimension(nsoilmx_PEM) :: eta ! constriction |
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| 234 | real, dimension(nsoilmx_PEM) :: dz_psat ! first derivative of the vapor pressure at saturation |
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| 235 | real, dimension(nsoilmx_PEM) :: dz_eta ! \partial z \eta |
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| 236 | real, dimension(nsoilmx_PEM) :: dzz_psat ! \partial \partial psat |
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| 237 | integer :: ilay, index_tmp ! index for loop |
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| 238 | real :: old_depth_filling ! depth_filling saved |
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| 239 | real :: Jdry ! flux trought the dry layer |
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| 240 | real :: Jsat ! flux trought the ice layer |
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| 241 | real :: Jdry_prevlay, Jsat_prevlay ! same but for the previous ice layer |
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| 242 | integer :: index_firstice ! first index where ice appears (i.e., f > 0) |
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| 243 | real :: massfillabove, massfillafter ! h2O mass above and after index_geothermal |
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| 244 | ! Constant |
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| 245 | !--------- |
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| 246 | real, parameter :: pvap2rho = 18.e-3/8.314 |
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| 247 | ! Code |
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| 248 | !----- |
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| 249 | ! 0. Compute constriction over the layer |
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| 250 | ! Within the ice sheet, constriction is set to 0. Elsewhere, constriction = (1-porefilling)**2 |
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| 251 | if (index_IS < 0) then |
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| 252 | index_tmp = nsoilmx_PEM |
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| 253 | do ilay = 1,nsoilmx_PEM |
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| 254 | eta(ilay) = constriction(porefill(ilay)) |
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| 255 | enddo |
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| 256 | else |
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| 257 | index_tmp = index_IS |
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| 258 | do ilay = 1,index_IS - 1 |
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| 259 | eta(ilay) = constriction(porefill(ilay)) |
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| 260 | enddo |
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| 261 | do ilay = index_IS,nsoilmx_PEM |
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| 262 | eta(ilay) = 0. |
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| 263 | enddo |
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| 264 | endif |
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| 265 | |
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| 266 | ! 1. Depth at which pore filling occurs. We solve Eq. 9 from Schorgofer, Icarus (2010) |
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| 267 | old_depth_filling = depth_filling |
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| 268 | |
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| 269 | call deriv1(mlayer_PEM,nsoilmx_PEM,psat_soil,psat_surf,psat_bottom,dz_psat) |
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| 270 | |
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| 271 | do ilay = 1,index_tmp |
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| 272 | Jdry = (psat_soil(ilay) - pwat_surf)/mlayer_PEM(ilay) ! left member of Eq. 9 from Schorgofer, Icarus (2010) |
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| 273 | Jsat = eta(ilay)*dz_psat(ilay) !right member of Eq. 9 from Schorgofer, Icarus (2010) |
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| 274 | if (Jdry - Jsat <= 0) then |
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| 275 | index_filling = ilay |
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| 276 | exit |
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| 277 | endif |
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| 278 | enddo |
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| 279 | |
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| 280 | if (index_filling == 1) then |
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| 281 | depth_filling = mlayer_PEM(1) |
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| 282 | else if (index_filling > 1) then |
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| 283 | Jdry_prevlay = (psat_soil(index_filling - 1) - pwat_surf)/mlayer_PEM(index_filling - 1) |
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| 284 | Jsat_prevlay = eta(index_filling - 1)*dz_psat(index_filling - 1) |
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| 285 | call findroot(Jdry - Jsat,Jdry_prevlay - Jsat_prevlay,mlayer_PEM(index_filling),mlayer_PEM(index_filling - 1),depth_filling) |
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| 286 | endif |
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| 287 | |
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| 288 | ! 2. Compute d_z (eta* d_z(rho)) (last term in Eq. 13 of Schorgofer, Icarus (2010)) |
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| 289 | ! 2.0 preliminary: depth to shallowest ice (discontinuity at interface) |
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| 290 | index_firstice = -1 |
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| 291 | do ilay = 1,nsoilmx_PEM |
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| 292 | if (porefill(ilay) <= 0.) then |
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| 293 | index_firstice = ilay ! first point with ice |
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| 294 | exit |
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| 295 | endif |
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| 296 | enddo |
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| 297 | |
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| 298 | ! 2.1: now we can compute |
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| 299 | call deriv1(mlayer_PEM,nsoilmx_PEM,eta,1.,eta(nsoilmx_PEM - 1),dz_eta) |
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| 300 | |
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| 301 | if (index_firstice > 0 .and. index_firstice < nsoilmx_PEM - 2) call deriv1_onesided(index_firstice,mlayer_PEM,nsoilmx_PEM,eta,dz_eta(index_firstice)) |
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| 302 | |
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| 303 | call deriv2_simple(mlayer_PEM,nsoilmx_PEM,psat_soil,psat_surf,psat_bottom,dzz_psat) |
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| 304 | dz_etadz_rho = pvap2rho*(dz_eta*dz_psat + eta*dzz_psat) |
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| 305 | |
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| 306 | ! 3. Ice table boundary due to geothermal heating |
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| 307 | if (index_IS > 0) index_geothermal = -1 |
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| 308 | if (index_geothermal < 0) depth_geothermal = -1. |
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| 309 | if ((index_geothermal > 0).and.(index_IS < 0)) then ! Eq. 21 from Schorfoger, Icarus (2010) |
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| 310 | index_geothermal = -1 |
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| 311 | do ilay = 2,nsoilmx_PEM |
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| 312 | if (dz_psat(ilay) > 0.) then ! first point with reversed flux |
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| 313 | index_geothermal = ilay |
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| 314 | call findroot(dz_psat(ilay - 1),dz_psat(ilay),mlayer_PEM(ilay - 1),mlayer_PEM(ilay),depth_geothermal) |
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| 315 | exit |
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| 316 | endif |
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| 317 | enddo |
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| 318 | else |
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| 319 | index_geothermal = -1 |
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| 320 | endif |
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| 321 | if (index_geothermal > 0 .and. index_IS < 0) then ! Eq. 24 from Schorgofer, Icarus (2010) |
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| 322 | call colint(porefill/eta,mlayer_PEM,nsoilmx_PEM,index_geothermal - 1,nsoilmx_PEM,massfillabove) |
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| 323 | index_tmp = -1 |
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| 324 | do ilay = index_geothermal,nsoilmx_PEM |
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| 325 | if (minval(eta(ilay:nsoilmx_PEM)).le.0.) cycle ! eta=0 means completely full |
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| 326 | call colint(porefill/eta,mlayer_PEM,nsoilmx_PEM,ilay,nsoilmx_PEM,massfillafter) |
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| 327 | if (massfillafter < dz_psat(ilay)*pvap2rho*B) then ! usually executes on i=typeG |
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| 328 | if (ilay > index_geothermal) then |
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| 329 | ! write(34,*) '# adjustment to geotherm depth by',ilay-index_geothermal |
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| 330 | call findroot(dz_psat(ilay - 1)*pvap2rho*B - massfillabove, & |
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| 331 | dz_psat(ilay)*pvap2rho*B - massfillafter,mlayer_PEM(ilay - 1),mlayer_PEM(ilay),depth_geothermal) |
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| 332 | ! if (depth_geothermal > mlayer_PEM(ilay) .or. depth_geothermal < mlayer_PEM(ilay - 1)) write(*,*) '# WARNING: zdepthG interpolation failed',ilay,mlayer_PEM(ilay - 1),depth_geothermal,mlayer_PEM(ilay) |
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| 333 | index_tmp = ilay |
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| 334 | endif |
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| 335 | ! otherwise leave depth_geothermal unchanged |
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| 336 | exit |
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| 337 | endif |
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| 338 | massfillabove = massfillafter |
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| 339 | enddo |
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| 340 | if (index_tmp > 0) index_geothermal = index_tmp |
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| 341 | end if |
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| 342 | |
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| 343 | END SUBROUTINE find_layering_icetable |
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| 344 | |
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| 345 | !----------------------------------------------------------------------- |
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| 346 | FUNCTION constriction(porefill) RESULT(eta) |
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| 347 | |
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| 348 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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| 349 | !!! |
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| 350 | !!! Purpose: Compute the constriction of vapor flux by pore ice |
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| 351 | !!! |
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| 352 | !!! Author: LL |
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| 353 | !!! |
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| 354 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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| 355 | |
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| 356 | implicit none |
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| 357 | |
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| 358 | real, intent(in) :: porefill ! pore filling fraction |
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| 359 | real :: eta ! constriction |
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| 360 | |
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| 361 | if (porefill <= 0.) then |
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| 362 | eta = 1. |
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| 363 | else if (0 < porefill .and. porefill < 1.) then |
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| 364 | eta = (1-porefill)**2 ! Hudson et al., JGR, 2009 |
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| 365 | else |
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| 366 | eta = 0. |
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| 367 | endif |
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| 368 | |
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| 369 | END FUNCTION constriction |
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| 370 | |
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| 371 | !----------------------------------------------------------------------- |
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| 372 | SUBROUTINE compute_Tice_pem(nsoil,ptsoil,ptsurf,ice_depth,Tice) |
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| 373 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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| 374 | !!! |
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| 375 | !!! Purpose: Compute subsurface ice temperature by interpolating the temperatures between the two adjacent cells. |
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| 376 | !!! |
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| 377 | !!! Author: LL |
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| 378 | !!! |
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| 379 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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| 380 | |
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| 381 | use comsoil_h_PEM, only: mlayer_PEM |
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| 382 | use abort_pem_mod, only: abort_pem |
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| 383 | |
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| 384 | implicit none |
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| 385 | |
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| 386 | ! Inputs |
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| 387 | ! ------ |
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| 388 | integer, intent(in) :: nsoil ! Number of soil layers |
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| 389 | real, dimension(nsoil), intent(in) :: ptsoil ! Soil temperature (K) |
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| 390 | real, intent(in) :: ptsurf ! Surface temperature (K) |
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| 391 | real, intent(in) :: ice_depth ! Ice depth (m) |
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| 392 | |
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| 393 | ! Outputs |
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| 394 | ! ------- |
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| 395 | real, intent(out) :: Tice ! Ice temperatures (K) |
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| 396 | |
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| 397 | ! Locals |
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| 398 | ! ------ |
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| 399 | integer :: ik ! Loop variables |
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| 400 | integer :: indexice ! Index of the ice |
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| 401 | |
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| 402 | ! Code |
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| 403 | !----- |
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| 404 | indexice = -1 |
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| 405 | if (ice_depth >= mlayer_PEM(nsoil - 1)) then |
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| 406 | Tice = ptsoil(nsoil) |
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| 407 | else |
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| 408 | if(ice_depth < mlayer_PEM(0)) then |
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| 409 | indexice = 0. |
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| 410 | else |
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| 411 | do ik = 0,nsoil - 2 ! go through all the layers to find the ice locations |
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| 412 | if (mlayer_PEM(ik) <= ice_depth .and. mlayer_PEM(ik + 1) > ice_depth) then |
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| 413 | indexice = ik + 1 |
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| 414 | exit |
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| 415 | endif |
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| 416 | enddo |
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| 417 | endif |
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| 418 | if (indexice < 0) then |
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| 419 | call abort_pem("compute_Tice_pem","Subsurface ice is below the last soil layer!",1) |
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| 420 | else |
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| 421 | if(indexice >= 1) then ! Linear inteprolation between soil temperature |
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| 422 | Tice = (ptsoil(indexice) - ptsoil(indexice + 1))/(mlayer_PEM(indexice - 1) - mlayer_PEM(indexice))*(ice_depth - mlayer_PEM(indexice)) + ptsoil(indexice + 1) |
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| 423 | else ! Linear inteprolation between the 1st soil temperature and the surface temperature |
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| 424 | Tice = (ptsoil(1) - ptsurf)/mlayer_PEM(0)*(ice_depth - mlayer_PEM(0)) + ptsoil(1) |
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| 425 | endif ! index ice >= 1 |
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| 426 | endif !indexice < 0 |
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| 427 | endif ! icedepth > mlayer_PEM(nsoil - 1) |
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| 428 | |
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| 429 | END SUBROUTINE compute_Tice_pem |
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| 430 | |
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| 431 | !----------------------------------------------------------------------- |
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| 432 | FUNCTION rho_ice(T,ice) RESULT(rho) |
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| 433 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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| 434 | !!! |
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| 435 | !!! Purpose: Compute subsurface ice density |
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| 436 | !!! |
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| 437 | !!! Author: JBC |
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| 438 | !!! |
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| 439 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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| 440 | |
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| 441 | use abort_pem_mod, only: abort_pem |
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| 442 | |
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| 443 | implicit none |
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| 444 | |
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| 445 | real, intent(in) :: T |
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| 446 | character(3), intent(in) :: ice |
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| 447 | real :: rho |
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| 448 | |
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| 449 | select case (trim(adjustl(ice))) |
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| 450 | case('h2o') |
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| 451 | rho = -3.5353e-4*T**2 + 0.0351*T + 933.5030 ! Rottgers 2012 |
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| 452 | case('co2') |
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| 453 | rho = (1.72391 - 2.53e-4*T-2.87*1e-7*T**2)*1.e3 ! Mangan et al. 2017 |
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| 454 | case default |
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| 455 | call abort_pem("rho_ice","Type of ice not known!",1) |
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| 456 | end select |
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| 457 | |
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| 458 | END FUNCTION rho_ice |
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| 459 | |
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| 460 | END MODULE ice_table_mod |
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