Thermodynamic evaluators#

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

Internal energy#

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

“evaluator type” = “iem”

iem-evaluator-spec

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

KEYS:

  • “temperature”

Linear#

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-model-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#

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-model-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#

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”

iem-water-vapor-evaluator-spec

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

KEYS:

  • “temperature”

  • “vapor molar fraction”

Internal energy model for air and water vapor.

iem-water-vapor-model-spec

  • “latent heat [J mol^-1]” [double] Latent heat of vaporization

  • “heat capacity [J mol^-1 K^-1]” [double] C_v

Enthalpy#

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

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

“evaluator type” = “enthalpy”

enthalpy-evaluator-spec

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

KEYS:

  • “internal energy”

  • “pressure”

  • “mass density”

Thermal Conductivity, two phases#

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

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

thermal-conductivity-twophase-evaluator-spec

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

KEYS:

  • “porosity”

  • “saturation liquid”

Wet-Dry Model#

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

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

  • “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#

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#

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

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

thermal-conductivity-threephase-evaluator-spec

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

KEYS:

  • “porosity”

  • “saturation liquid”

  • “second saturation”

  • “temperature”

Wet-Dry Model#

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#

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

  • “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)

  • “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#

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

  • “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

  • “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#

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#

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

“evaluator type” = “surface thermal conductivity”

thermal-conductivity-surface-evaluator-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#

Active Layer Averaged Temperature#

Water Table#

Computes the depth to a saturated water table.

“evaluator type” = “water table depth”

water-table-depth-spec

KEYS:

  • “saturation of gas” SUBSURFACE_DOMAIN-saturation-gas

  • “subsurface cell volume” SUBSURFACE_DOMAIN-cell_volume

  • “surface cell volume” DOMAIN-cell_volume

Thaw Depth#

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