Thermodynamic evaluators#

Internal energy, enthalpy, thermal conductivity, etc used for both surface and subsurface transport of energy.

Internal energy#

src/physics/ats/src/pks/energy/constitutive_relations/internal_energy/iem_evaluator.hh

Computes (specific) internal energy of as a function of temperature.

“evaluator type” = “iem”

evaluator-iem-spec

  • “IEM parameters” [iem-typedinline-spec-list]

KEYS:

  • “temperature”

Linear#

src/physics/ats/src/pks/energy/constitutive_relations/internal_energy/iem_linear.hh

Internal energy based on a linear fit.

Linear internal energy model – function of Cv and temperature

\[u = L_f + C_v * (T - T_{ref})\]

“IEM type” = “linear”

iem-linear-spec

  • “reference temperature [K]” [double] 273.15 The phase transition point, \(T_{ref}\) above

ONE OF

  • “latent heat [J kg^-1]” [double] Latent heat of fusion, \(L_f\) above

  • “heat capacity [J kg^-1 K^-1]” [double] \(C_v\) above

OR

  • “latent heat [J mol^-1]” [double] Latent heat of fusion, \(L_f\) above.

  • “heat capacity [J mol^-1 K^-1]” [double] \(C_v\) above

END

Quadratic#

src/physics/ats/src/pks/energy/constitutive_relations/internal_energy/iem_quadratic.hh

Internal energy based on a quadratic fit to data.

Quadratic internal energy model – function of Cv and temperature

\[u = L_f + C_v * (T - T_{ref}) + b(T - T_{ref})^2\]

“IEM type” = “quadratic”

iem-quadratic-spec

  • “reference temperature [K]” [double] 273.15 The phase transition point, \(T_{ref}\) above.

ONE OF

  • “latent heat [J kg^-1]” [double] Latent heat of fusion, \(L_f\) above

  • “heat capacity [J kg^-1 K^-1]” [double] \(C_v\) above

  • “quadratic b [J kg^-1 K^-2]” [double] \(b\) above

OR

  • “latent heat [J mol^-1]” [double] Latent heat of fusion, \(L_f\) above.

  • “heat capacity [J mol^-1 K^-1]” [double] \(C_v\) above

  • “quadratic b [J mol^-1 K^-2]” [double] \(b\) above

END

Water Vapor#

src/physics/ats/src/pks/energy/constitutive_relations/internal_energy/iem_water_vapor_evaluator.hh

Computes (specific) internal energy of as a function of temperature and molar fraction of water vapor in the gaseous phase.

“evaluator type” = “iem water vapor”

evaluator-iem-water-vapor-spec

  • “IEM parameters” [iem-water-vapor-spec]

KEYS:

  • “temperature”

  • “vapor molar fraction”

src/physics/ats/src/pks/energy/constitutive_relations/internal_energy/iem_water_vapor.hh

Internal energy model for air and water vapor.

\[u = (1 + 0.622 \omega) C_v^{air} (T - 273.15) + \omega L_v\]

iem-water-vapor-spec

  • “latent heat [J mol^-1]” [double] Latent heat of vaporization, \(L_v\)

  • “heat capacity [J mol^-1 K^-1]” [double] Heat capacity of air, \(C_v^{air}\)

Enthalpy#

src/physics/ats/src/pks/energy/constitutive_relations/enthalpy/enthalpy_evaluator.hh

Computes enthalpy [MJ mol^-1] of as a function of internal energy, pressure, and density.

\[e = u + 10^{-6} * \frac{p}{n_l}\]

“evaluator type” = “enthalpy”

evaluator-enthalpy-spec

  • “include work term” [bool] false If false, e = u, ignoring the work term.

KEYS:

  • “internal energy”

  • “pressure”

  • “mass density”

Thermal Conductivity, Two Phases#

src/physics/ats/src/pks/energy/constitutive_relations/thermal_conductivity/thermal_conductivity_twophase_evaluator.hh

Thermal conductivity based on two-phases (air,liquid) composition of the porous media.

“evaluator type” = “two-phase thermal conductivity”

evaluator-two-phase-thermal-conductivity-spec

  • “thermal conductivity parameters” [thermal-conductivity-twophase-typed-spec-list]

KEYS:

  • “porosity”

  • “saturation liquid”

Wet-Dry Model#

src/physics/ats/src/pks/energy/constitutive_relations/thermal_conductivity/thermal_conductivity_twophase_wetdry.hh

Simple model of two-phase thermal conductivity, based upon:

  • Interpolation between saturated and dry conductivities via a Kersten number.

  • Power-law Kersten number.

“thermal conductivity type” = “two-phase wet/dry”

thermal-conductivity-twophase-wetdry-spec

  • “thermal conductivity, wet [W m^-1 K^-1]” [double] Thermal conductivity of saturated soil

  • “thermal conductivity, dry [W m^-1 K^-1]” [double] Thermal conductivity of dry soil

  • “unsaturated alpha [-]” [double] Interpolating exponent

  • “epsilon” [double] 1e-10 Epsilon to keep saturations bounded away from 0.

Example:

<ParameterList name="thermal conductivity model">
  <Parameter name="thermal conductivity type" type="string" value="two-phase wet/dry"/>
  <Parameter name="thermal conductivity, wet [W m^-1 K^-1]" type="double" value=""/>
  <Parameter name="thermal conductivity, dry [W m^-1 K^-1]" type="double" value=""/>
  <Parameter name="epsilon" type="double" value="1.e-10"/>
  <Parameter name="unsaturated alpha" type="double" value="1.0"/>
</ParameterList>

Units: [W m^-1 K^-1]

Peters-Lidard Model#

src/physics/ats/src/pks/energy/constitutive_relations/thermal_conductivity/thermal_conductivity_twophase_peterslidard.hh

A two-phase thermal conductivity, based upon:

  • Interpolation between saturated and dry conductivities via a Kersten number.

  • Power-law Kersten number.

  • Emperical fit for dry conductivity from Peters-Lidard et al ‘98.

See Atchley et al GMD 2015 Supplementary Material for equations.

“thermal conductivity type” = “two-phase Peters-Lidard”

thermal-conductivity-twophase-peterslidard-spec

  • “region” [string] Region name on which to apply these parameters.

  • “thermal conductivity of soil [W m^-1 K^-1]” [double] Thermal conductivity of soil grains (not bulk soil)

  • “thermal conductivity of liquid [W m^-1 K^-1]” [double] Thermal conductivity of liquid (water)

  • “thermal conductivity of gas [W m^-1 K^-1]” [double] Thermal conductivity of gas (air)

  • “unsaturated alpha [-]” [double] Interpolating exponent

  • “epsilon” [double] 1e-10 Epsilon to keep saturations bounded away from 0.

Example:

<ParameterList name="Thermal Conductivity Model">
  <Parameter name="thermal conductivity type" type="string" value="two-phase Peters-Lidard"/>
  <Parameter name="thermal conductivity of soil [W m^-1 K^-1]" type="double" value=""/>
  <Parameter name="thermal conductivity of liquid [W m^-1 K^-1]" type="double" value=""/>
  <Parameter name="thermal conductivity of gas [W m^-1 K^-1]" type="double" value=""/>
  <Parameter name="unsaturated alpha" type="double" value="1.0"/>
  <Parameter name="epsilon" type="double" value="1.e-10"/>
</ParameterList>

Units: [W m^-1 K^-1]

Thermal Conductivity, Three Phases#

src/physics/ats/src/pks/energy/constitutive_relations/thermal_conductivity/thermal_conductivity_threephase_evaluator.hh

Thermal conductivity based on a three-phase (air,liquid,ice) composition of the porous media.

“evaluator type” = “three-phase thermal conductivity”

evaluator-three-phase-thermal-conductivity-spec

  • “thermal conductivity parameters” [thermal-conductivity-threephase-typed-spec-list]

KEYS:

  • “porosity”

  • “saturation liquid”

  • “second saturation”

  • “temperature”

Wet-Dry Model#

src/physics/ats/src/pks/energy/constitutive_relations/thermal_conductivity/thermal_conductivity_threephase_wetdry.hh

Three-phase thermal conductivity based on paper by Peters-Lidard.

A three-phase thermal conductivity, based upon:

  • Interpolation between saturated and dry conductivities via a Kersten number.

  • Power-law Kersten number.

  • Empirical relationship for frozen soil based on Peters-Lidard

See Atchley et al GMD 2015 Supplementary Material for equations.

“thermal conductivity type” = “three-phase wet/dry”

thermal-conductivity-threephase-wetdry-spec

  • “region” [string] Region name on which to apply these parameters.

  • “thermal conductivity, saturated (unfrozen) [W m^-1 K^-1]” [double] Thermal conductivity of fully saturated, unfrozen bulk soil.

  • “thermal conductivity, dry [W m^-1 K^-1]” [double] Thermal conductivity of fully dried bulk soil.

  • “unsaturated alpha unfrozen [-]” [double] Interpolating exponent

  • “unsaturated alpha frozen [-]” [double] Interpolating exponent

  • “saturated beta frozen [-]” [double] 1.0 Interpolating exponent

  • “epsilon” [double] 1e-10 Epsilon to keep saturations bounded away from 0.

Peters-Lidard Model#

src/physics/ats/src/pks/energy/constitutive_relations/thermal_conductivity/thermal_conductivity_threephase_peterslidard.hh

Three-phase thermal conductivity based on paper by Peters-Lidard.

A three-phase thermal conductivity, based upon:

  • A mixture model using interpolation across various components.

  • Power-law Kersten number.

See Atchley et al GMD 2015 Supplementary Material for equations.

“thermal conductivity type” = “three-phase Peters-Lidard”

thermal-conductivity-threephase-peterslidard-spec

  • “thermal conductivity of soil [W m^-1 K^-1]” [double] Thermal conductivity of soil grains (not bulk soil)

  • “thermal conductivity of liquid [W m^-1 K^-1]” [double] Thermal conductivity of liquid (water)

  • “thermal conductivity of gas [W m^-1 K^-1]” [double] Thermal conductivity of gas (air)

  • “thermal conductivity of ice [W m^-1 K^-1]” [double] Thermal conductivity of ice

  • “unsaturated alpha unfrozen [-]” [double] Interpolating exponent

  • “unsaturated alpha frozen [-]” [double] Interpolating exponent

  • “epsilon” [double] 1e-10 Epsilon to keep saturations bounded away from 0.

Example:

<ParameterList name="thermal_conductivity">
  <Parameter name="thermal conductivity type" type="string" value="three-phase Peters-Lidard"/>
  <Parameter name="thermal conductivity of soil [W m^-1 K^-1]" type="double" value=""/>
  <Parameter name="thermal conductivity of liquid [W m^-1 K^-1]" type="double" value=""/>
  <Parameter name="thermal conductivity of gas [W m^-1 K^-1]" type="double" value=""/>
  <Parameter name="thermal conductivity of ice [W m^-1 K^-1]" type="double" value=""/>

  <Parameter name="unsaturated alpha unfrozen [-]" type="double" value=""/>
  <Parameter name="unsaturated alpha frozen [-]" type="double" value=""/>

  <Parameter name="epsilon" type="double" value="1.e-10"/>
</ParameterList>

Volume-averaged Model#

src/physics/ats/src/pks/energy/constitutive_relations/thermal_conductivity/thermal_conductivity_threephase_volume_averaged.hh

A volume-averaged thermal conductivity based on TCs of raw components.

A simple model of three-phase thermal conductivity, based upon volume-averaging of four consitutive components.

“thermal conductivity type” = “three-phase volume averaged”

See Atchley et al GMD 2015 Supplementary Material for equations.

thermal-conductivity-volume-averaged-spec

  • “thermal conductivity of soil [W m^-1 K^-1]” [double] Thermal conductivity of soil grains

  • “thermal conductivity of liquid [W m^-1 K^-1]” [double] Thermal conductivity of liquid water.

  • “thermal conductivity of gas [W m^-1 K^-1]” [double] Thermal conductivity of air.

  • “thermal conductivity of ice [W m^-1 K^-1]” [double] Thermal conductivity of frozen water.

Sutra-ICE model#

src/physics/ats/src/pks/energy/constitutive_relations/thermal_conductivity/thermal_conductivity_threephase_sutra_hacked.hh

Thermal conductivity model with constant values as a function of temperature, requires the sutra model for permafrost WRM to also be used. This only exists to support the INTERFROST comparison.

Usage:

<ParameterList name="Thermal Conductivity Model">
  <Parameter name="Thermal Conductivity Type" type="string" value="sutra hacked"/>
  <Parameter name="thermal conductivity of frozen" type="double" value=""/>
  <Parameter name="thermal conductivity of mushy" type="double" value=""/>
  <Parameter name="thermal conductivity of unfrozen" type="double" value=""/>
  <Parameter name="residual saturation" type="double" value=""/>
</ParameterList>

Units: [W m^-1 K^-1]

Thermal Conductivity, Surface#

src/physics/ats/src/pks/energy/constitutive_relations/thermal_conductivity/thermal_conductivity_surface_evaluator.hh

Thermal conductivity of surface water that can be either frozen or liquid phase.

“evaluator type” = “surface thermal conductivity”

evaluator-thermal-conductivity-surface-spec

  • “thermal conductivity parameters” [thermal-conductivity-surface-spec]

KEYS:

  • “unfrozen fraction”

  • “ponded depth”

thermal-conductivity-surface-spec

  • “thermal conductivity of water [W m^-1 K^-1]” [double] 0.58

  • “thermal conductivity of ice [W m^-1 K^-1]” [double] 2.18

  • “minimum thermal conductivity” [double] 1.e-14

Advected Energy Source#

src/physics/ats/src/pks/energy/constitutive_relations/source_terms/advected_energy_source_evaluator.hh

Active Layer Averaged Temperature#

src/physics/ats/src/constitutive_relations/column_integrators/activelayer_average_temp_evaluator.hh

Water Table#

src/physics/ats/src/constitutive_relations/column_integrators/water_table_depth_evaluator.hh

Computes the depth to the water table.

“evaluator type” = “water table depth”

water-table-depth-spec

  • “interpolate depth from pressure” [bool] false Default to calculate water table depth by locating the top face of the last continuously saturated cell from bottom upward. If true, use the height and pressure at the centroids of the last continuously saturated cell and its adjacent unsaturated cell to determine the water table depth through interpolation.

KEYS:

  • “saturation of gas” SUBSURFACE_DOMAIN-saturation-gas

  • “pressure” SUBSURFACE_DOMAIN-pressure

  • “subsurface cell volume” SUBSURFACE_DOMAIN-cell_volume

  • “surface cell volume” DOMAIN-cell_volume

Thaw Depth#

src/physics/ats/src/constitutive_relations/column_integrators/thaw_depth_evaluator.hh

Computes the depth to a saturated water table.

“evaluator type” = “thaw depth”

thaw-depth-spec

KEYS:

  • “temperature” SUBSURFACE_DOMAIN-temperature

  • “subsurface cell volume” SUBSURFACE_DOMAIN-cell_volume

  • “surface cell volume” DOMAIN-cell_volume