rdb_ice_enthalpy Module

Specific-enthalpy <-> temperature inversions for the sea-ice thermodynamic column model.

  • The thermodynamic prognostic of the ice model is SPECIFIC ENTHALPY (J/kg), never temperature; these are the exact T<->E inversions every later rung (PR 3 Winton column, PR 4 transport re-layering) consumes.
  • Source: ../SIS2/src/SIS2_ice_thm.F90 (Apache-2.0) — T_Freeze (:1622), enth_from_TS (:1647), enthalpy_liquid_freeze (:1679), enthalpy_liquid (:1691), Temp_from_En_S (:1830); constant defaults from ice_thermo_init (:1534-1617).
  • THE SIMPLIFICATION (ratified in PLAN_SEA_ICE.md): Cp_brine == Cp_ice. SIS2’s default Cp_brine = Cp_water makes Temp_from_En_S transcendental (a T_fr*log(T_fr/T) term) and needs the 20-iteration Newton/false-position solve at SIS2_ice_thm.F90: 1876-1933; with Cp_brine = Cp_ice the log term vanishes and the T<->E map is a closed-form quadratic, invertible EXACTLY. Only the Cp_ice == Cp_brine branches are ported; the else branches are deliberately NOT.
  • WHY THE ROUND-TRIP IS EXACT: for S > 0, T < t_fr, substituting ice_enth_from_ts’s En into ice_temp_from_en_s gives BB = 0.5(ICE_LAT_FUSt_fr/T + ICE_CP_ICET), and the quadratic ICE_CP_ICET2 - 2BBT + ICE_LAT_FUS*t_fr = 0 has T as its smaller root by construction — so ice_temp_from_en_s(ice_enth_from_ts(T,S), S) == T to machine precision, not merely to a solver tolerance. The fresh-water and melted branches invert trivially.
  • Everything pure elemental + !$acc routine seq: host scalars, whole-array elemental calls, or per-point inside a do concurrent device kernel.

Uses

  • module~~rdb_ice_enthalpy~~UsesGraph module~rdb_ice_enthalpy rdb_ice_enthalpy module~rdb_constants rdb_constants module~rdb_ice_enthalpy->module~rdb_constants pic_types pic_types module~rdb_constants->pic_types

Used by

  • module~~rdb_ice_enthalpy~~UsedByGraph module~rdb_ice_enthalpy rdb_ice_enthalpy module~rdb_config rdb_config module~rdb_config->module~rdb_ice_enthalpy module~rdb_ice_init rdb_ice_init module~rdb_config->module~rdb_ice_init module~rdb_ice_column rdb_ice_column module~rdb_ice_column->module~rdb_ice_enthalpy module~rdb_ice_mass rdb_ice_mass module~rdb_ice_column->module~rdb_ice_mass module~rdb_ice_optics rdb_ice_optics module~rdb_ice_column->module~rdb_ice_optics module~rdb_ice_frazil_uptake rdb_ice_frazil_uptake module~rdb_ice_frazil_uptake->module~rdb_ice_enthalpy module~rdb_ice_frazil_uptake->module~rdb_ice_column module~rdb_ice_frazil_uptake->module~rdb_ice_mass module~rdb_ice_state rdb_ice_state module~rdb_ice_frazil_uptake->module~rdb_ice_state module~rdb_ice_init->module~rdb_ice_enthalpy module~rdb_ice_init->module~rdb_ice_column module~rdb_ice_init->module~rdb_ice_state module~rdb_ice_mass->module~rdb_ice_enthalpy module~rdb_ice_optics->module~rdb_ice_enthalpy module~rdb_ice_snow rdb_ice_snow module~rdb_ice_snow->module~rdb_ice_enthalpy module~rdb_ice_snow->module~rdb_ice_state module~rdb_ice_state->module~rdb_ice_enthalpy module~rdb_ice_state->module~rdb_ice_column module~rdb_config_schema rdb_config_schema module~rdb_config_schema->module~rdb_config module~rdb_decomp rdb_decomp module~rdb_decomp->module~rdb_config module~rdb_driver rdb_driver module~rdb_driver->module~rdb_config module~rdb_ocean_console_stats rdb_ocean_console_stats module~rdb_driver->module~rdb_ocean_console_stats module~rdb_ocean_engine rdb_ocean_engine module~rdb_driver->module~rdb_ocean_engine module~rdb_ocean_state rdb_ocean_state module~rdb_driver->module~rdb_ocean_state module~rdb_halo rdb_halo module~rdb_driver->module~rdb_halo module~rdb_ocean_dyn rdb_ocean_dyn module~rdb_driver->module~rdb_ocean_dyn module~rdb_handle rdb_handle module~rdb_handle->module~rdb_config module~rdb_handle->module~rdb_ocean_engine module~rdb_handle->module~rdb_ocean_state module~rdb_ice_atm_forcing rdb_ice_atm_forcing module~rdb_ice_atm_forcing->module~rdb_ice_state module~rdb_ice_basal_flux rdb_ice_basal_flux module~rdb_ice_basal_flux->module~rdb_ice_column module~rdb_ice_basal_flux->module~rdb_ice_state module~rdb_ice_evp rdb_ice_evp module~rdb_ice_evp->module~rdb_ice_column module~rdb_ice_evp->module~rdb_ice_state module~rdb_ocean_halo rdb_ocean_halo module~rdb_ice_evp->module~rdb_ocean_halo module~rdb_ice_itd rdb_ice_itd module~rdb_ice_itd->module~rdb_ice_state module~rdb_ice_ocean_coupler rdb_ice_ocean_coupler module~rdb_ice_ocean_coupler->module~rdb_ice_state module~rdb_ocean_halo_state rdb_ocean_halo_state module~rdb_ice_ocean_coupler->module~rdb_ocean_halo_state module~rdb_ice_thermo_driver rdb_ice_thermo_driver module~rdb_ice_thermo_driver->module~rdb_ice_column module~rdb_ice_thermo_driver->module~rdb_ice_state module~rdb_ice_transport rdb_ice_transport module~rdb_ice_transport->module~rdb_ice_column module~rdb_ice_transport->module~rdb_ice_state module~rdb_ice_transport->module~rdb_ice_itd module~rdb_ice_transport->module~rdb_ocean_halo_state module~rdb_ice_transport->module~rdb_halo module~rdb_ice_transport->module~rdb_ocean_halo module~rdb_continuity rdb_continuity module~rdb_ice_transport->module~rdb_continuity module~rdb_ocean_api rdb_ocean_api module~rdb_ocean_api->module~rdb_config module~rdb_ocean_api->module~rdb_handle module~rdb_ocean_diag_fills rdb_ocean_diag_fills module~rdb_ocean_api->module~rdb_ocean_diag_fills module~rdb_ocean_api->module~rdb_ocean_engine module~rdb_ocean_diag_derived rdb_ocean_diag_derived module~rdb_ocean_api->module~rdb_ocean_diag_derived module~rdb_ocean_api->module~rdb_ocean_dyn module~rdb_ocean_fold_apply rdb_ocean_fold_apply module~rdb_ocean_api->module~rdb_ocean_fold_apply module~rdb_ocean_console_stats->module~rdb_ice_column module~rdb_ocean_console_stats->module~rdb_halo module~rdb_ocean_data_forcing rdb_ocean_data_forcing module~rdb_ocean_data_forcing->module~rdb_config module~rdb_ocean_data_input rdb_ocean_data_input module~rdb_ocean_data_forcing->module~rdb_ocean_data_input module~rdb_ocean_data_forcing->module~rdb_ocean_halo_state module~rdb_ocean_data_input->module~rdb_config module~rdb_ocean_diag_fills->module~rdb_ice_column module~rdb_ocean_diag_fills->module~rdb_ocean_state module~rdb_ocean_engine->module~rdb_config module~rdb_ocean_engine->module~rdb_ice_frazil_uptake module~rdb_ocean_engine->module~rdb_ice_init module~rdb_ocean_engine->module~rdb_ice_snow module~rdb_ocean_engine->module~rdb_decomp module~rdb_ocean_engine->module~rdb_ice_atm_forcing module~rdb_ocean_engine->module~rdb_ice_basal_flux module~rdb_ocean_engine->module~rdb_ice_evp module~rdb_ocean_engine->module~rdb_ice_itd module~rdb_ocean_engine->module~rdb_ice_ocean_coupler module~rdb_ocean_engine->module~rdb_ice_thermo_driver module~rdb_ocean_engine->module~rdb_ice_transport module~rdb_ocean_engine->module~rdb_ocean_data_forcing module~rdb_ocean_engine->module~rdb_ocean_data_input module~rdb_ocean_engine->module~rdb_ocean_diag_fills module~rdb_ocean_engine->module~rdb_ocean_halo_state module~rdb_ocean_setup rdb_ocean_setup module~rdb_ocean_engine->module~rdb_ocean_setup module~rdb_ocean_stability_audit rdb_ocean_stability_audit module~rdb_ocean_engine->module~rdb_ocean_stability_audit module~rdb_ocean_engine->module~rdb_ocean_state module~rdb_state rdb_state module~rdb_ocean_engine->module~rdb_state module~rdb_ocean_engine->module~rdb_halo module~rdb_ocean_engine->module~rdb_ocean_diag_derived module~rdb_ocean_engine->module~rdb_ocean_dyn module~rdb_ocean_fold_exchange rdb_ocean_fold_exchange module~rdb_ocean_engine->module~rdb_ocean_fold_exchange module~rdb_ocean_engine->module~rdb_ocean_halo module~rdb_ocean_engine->module~rdb_ocean_fold_apply module~rdb_ocean_halo_state->module~rdb_ice_state module~rdb_ocean_halo_state->module~rdb_ocean_halo module~rdb_ocean_halo_state->module~rdb_ocean_fold_apply module~rdb_ocean_setup->module~rdb_config module~rdb_ocean_setup->module~rdb_decomp module~rdb_ocean_setup->module~rdb_ocean_halo_state module~rdb_ocean_setup->module~rdb_ocean_state module~rdb_ocean_setup->module~rdb_halo module~rdb_ocean_setup->module~rdb_ocean_dyn module~rdb_ocean_setup->module~rdb_ocean_fold_exchange module~rdb_ocean_setup->module~rdb_ocean_halo module~rdb_ocean_setup->module~rdb_ocean_fold_apply module~rdb_ocean_stability_audit->module~rdb_config module~rdb_ocean_state->module~rdb_config module~rdb_ocean_state->module~rdb_ice_state module~rdb_ocean_state->module~rdb_decomp module~rdb_ocean_state->module~rdb_ocean_data_forcing module~rdb_ocean_state->module~rdb_ocean_data_input module~rdb_ocean_z_init rdb_ocean_z_init module~rdb_ocean_state->module~rdb_ocean_z_init module~rdb_ocean_state->module~rdb_ocean_dyn module~rdb_ocean_restart_io rdb_ocean_restart_io module~rdb_ocean_state->module~rdb_ocean_restart_io module~rdb_ocean_state->module~rdb_continuity module~rdb_ocean_z_init->module~rdb_config module~rdb_state->module~rdb_config module~rdb_halo->module~rdb_decomp module~rdb_ocean_diag_derived->module~rdb_ocean_diag_fills module~rdb_ocean_diag_derived->module~rdb_ocean_state module~rdb_ocean_dyn->module~rdb_ocean_console_stats module~rdb_ocean_dyn->module~rdb_ocean_halo_state module~rdb_ocean_dyn->module~rdb_ocean_halo module~rdb_barotropic_substep rdb_barotropic_substep module~rdb_ocean_dyn->module~rdb_barotropic_substep module~rdb_ocean_dyn->module~rdb_continuity module~rdb_ocean_bt_wide rdb_ocean_bt_wide module~rdb_ocean_dyn->module~rdb_ocean_bt_wide module~rdb_ocean_chksum rdb_ocean_chksum module~rdb_ocean_dyn->module~rdb_ocean_chksum module~rdb_ocean_dyn->module~rdb_ocean_fold_apply module~rdb_ocean_fold_exchange->module~rdb_decomp module~rdb_ocean_halo->module~rdb_decomp module~rdb_ocean_restart_io->module~rdb_decomp module~rdb_barotropic_substep->module~rdb_ocean_fold_exchange module~rdb_barotropic_substep->module~rdb_ocean_halo module~rdb_continuity->module~rdb_ocean_fold_exchange module~rdb_continuity->module~rdb_ocean_halo module~rdb_continuity->module~rdb_ocean_fold_apply module~rdb_ocean_bt_wide->module~rdb_ocean_halo module~rdb_ocean_bt_wide->module~rdb_barotropic_substep module~rdb_ocean_chksum->module~rdb_halo module~rdb_ocean_fold_apply->module~rdb_ocean_fold_exchange proc~ocean_cavity_mass_step ocean_cavity_mass_step proc~ocean_cavity_mass_step->module~rdb_halo

Variables

Type Visibility Attributes Name Initial
real(kind=wp), public, parameter :: ICE_CP_BRINE = ICE_CP_ICE

Heat capacity of brine pockets (J/kg/K). THE simplification: set equal to ICE_CP_ICE (SIS2’s documented computational- convenience option for CP_BRINE, not its default Cp_water) so the T<->E map closes in quadratic form with no Newton loop.
real(kind=wp), public, parameter :: ICE_CP_ICE = 2100.0_wp

Heat capacity of fresh ice (J/kg/K) — SIS2 CP_ICE.
real(kind=wp), public, parameter :: ICE_CP_WATER = 4200.0_wp

Heat capacity of seawater as carried by the ICE model (J/kg/K) — SIS2 CP_SEAWATER. Deliberately DISTINCT from the ocean’s SEAWATER_CP = 3992 (rdb_ocean_surface_flux): SIS2’s ice model owns its own Cp_water = 4200 as the enthalpy zero-of-reference, and reusing 3992 here would break bit-parity with SIS2’s enthalpy and mis-close the PR-3 frazil energy handshake. Do not “unify” them.
real(kind=wp), public, parameter :: ICE_DTF_DS = -0.054_wp

Liquidus slope dT_f/dS (degC/PSU) — SIS2 DTFREEZE_DS. Same value as the ocean-side TFR_S_COEFF (rdb_eos) by construction — SIS2 parity on both sides of the seam.

DELIBERATELY NOT switched by &ocean_eos_nml tfreeze_set. That knob selects the OCEAN-side liquidus that eos_freezing_point returns (the sea-surface freezing temperature the frazil / basal-flux seam works against); THIS constant is internal to the SIS2 enthalpy relation, where it fixes the brine-pocket melting temperature inside the ice and is baked into the closed-form quadratic T<->E map (and into SIS2 bit-parity). Retuning it is an ice-thermodynamics change, not an ocean-liquidus one. Consequence, documented rather than papered over: under tfreeze_set = "isomip" the ocean surface freezing point and the ice-internal brine liquidus disagree by ~0.03 degC. The ISOMIP+ set exists for ICE-SHELF-CAVITY work, where the sea-ice column model is normally off; running both at once is legal but means accepting that offset.
real(kind=wp), public, parameter :: ICE_ENTH_LIQ_0 = 0.0_wp

Enthalpy of liquid fresh water at 0 degC (J/kg) — SIS2 ENTHALPY_LIQUID_0. Zero-point of the enthalpy scale; kept in the algebra (even though it is 0) so a future non-zero reference is a one-line change.
real(kind=wp), public, parameter :: ICE_LAT_FUS = 3.34e5_wp

Latent heat of fusion (J/kg) — SIS2 LATENT_HEAT_FUSION.
real(kind=wp), public, parameter :: ICE_LIQ_LIM = 0.99_wp

LIQUID_LIMIT (PR 3a) — max liquid fraction before the excess-enthalpy clamp (SIS2_ice_thm.F90:500-524) and the bottom-freeze min_dEnth_freeze floor (:1164-1188). Co-located here (not rdb_ice_column) so both rdb_ice_column and rdb_ice_mass can depend on this leaf module without a cycle.
integer, public, parameter :: ICE_NK_MAX = 8

Compile-time cap on per-column local-array size (kappa-shear NZ_STACK_MAX precedent). nk_ice <= ICE_NK_MAX is asserted at slot init (ocean_sea_ice_init, rdb_ice_state). Co-located on this leaf (not rdb_ice_column) — like ICE_LIQ_LIM — so rdb_ice_mass can size its fixed device-stack locals by it without a rdb_ice_column → rdb_ice_mass → rdb_ice_column cycle. rdb_ice_column re-exports it for existing importers.

Functions

public pure elemental function ice_enth_from_ts(t, s) result(enth)

Ice specific enthalpy (J/kg) from temperature + bulk salinity — SIS2 enth_from_TS (SIS2_ice_thm.F90:1647). NOTE: here (and only here) the freezing point uses max(0, s), per SIS2. The SIS2 else branch at :1667-1671 (Cp_brine /= Cp_ice, the T_fr*log(T_fr/T) form) is deliberately NOT ported — with ICE_CP_BRINE == ICE_CP_ICE it is unreachable, and dropping it keeps the map closed-form-invertible (see module docstring).

Arguments

Type IntentOptional Attributes Name
real(kind=wp), intent(in) :: t

Ice temperature (degC).
real(kind=wp), intent(in) :: s

Ice bulk salinity (PSU).

Return Value real(kind=wp)

public pure elemental function ice_enthalpy_liquid(t, s) result(enth)

Enthalpy (J/kg) of liquid water at temperature t — SIS2 enthalpy_liquid (SIS2_ice_thm.F90:1691). s is unused in this linear form; the argument is kept for SIS2 call-site parity (enthalpy_liquid(T, S, ITV)).

Arguments

Type IntentOptional Attributes Name
real(kind=wp), intent(in) :: t

Water temperature (degC).
real(kind=wp), intent(in) :: s

Ice bulk salinity (PSU) — unused, kept for call-site parity.

Return Value real(kind=wp)

public pure elemental function ice_enthalpy_liquid_freeze(s) result(enth)

Enthalpy (J/kg) of liquid water at the freezing point for salinity s — SIS2 enthalpy_liquid_freeze (SIS2_ice_thm.F90:1679).

Arguments

Type IntentOptional Attributes Name
real(kind=wp), intent(in) :: s

Ice bulk salinity (PSU).

Return Value real(kind=wp)

public pure elemental function ice_t_freeze(s) result(t_fr)

Freezing temperature (degC) of the ice brine at bulk salinity s — SIS2 T_Freeze (SIS2_ice_thm.F90:1622), linear liquidus. RAW s (no max(0,s) clamp) — faithful to SIS2, which clamps only in enth_from_TS. Do not unify with ice_enth_from_ts’s internal t_fr.

Arguments

Type IntentOptional Attributes Name
real(kind=wp), intent(in) :: s

Ice bulk salinity (PSU).

Return Value real(kind=wp)

public pure elemental function ice_temp_from_en_s(en, s) result(t)

Ice temperature (degC) from specific enthalpy + bulk salinity — SIS2 Temp_from_En_S (SIS2_ice_thm.F90:1830), Cp_ice == Cp_brine path only: the quadratic ICE_CP_ICET2 - 2BBT + ICE_LAT_FUSt_fr = 0 solved for its smaller root. The SIS2 Newton/false-position refinement (:1876-1933) is only needed when Cp_brine /= Cp_ice and is deliberately NOT ported. Uses RAW s for t_fr (no max), faithful to SIS2.

Arguments

Type IntentOptional Attributes Name
real(kind=wp), intent(in) :: en

Ice specific enthalpy (J/kg).
real(kind=wp), intent(in) :: s

Ice bulk salinity (PSU).

Return Value real(kind=wp)