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Module enthalpy

Warning: this rather complex module was not much tested so far, use it with care!

Description:

This IGM module models the ice enthalpy, which permits to jointly model the ice temperature, as well as the water content created when the temperature hits the pressure melting points, and therefore energy conservation, which is not the case when modelling the sole temperature variable. The model is described in (Aschwanden and al, JOG, 2012). Check at the IGM technical paper for further details [1].

[1] Concepts and capabilities of the Instructed Glacier Model 3.X.X, Jouvet and al.

The enthalpy module builds upon the iceflow module. To ensure proper functionality, follow these requirements:

  • Activate the vertical_iceflow module to provide the vertical velocity.
  • Set params.dim_arrhenius = 3.
  • Set params.new_friction_param = true.
  • Ensure sufficient retraining by setting retrain_iceflow_emulator_freq = 1. Optionally, set retrain_iceflow_emulator_nbit to a value greater than 1 for improved performance.

Contributors: G. Jouvet

This implementation is largely inspired from the one implemented in PISM. Other references that have helped are (Kleiner and al, TC, 2015) and (Wang and al, 2020).

Config Structure

enthalpy:  
  water_density: 1000.0
  spy: 31556926.0
  gas_constant: 8.314
  ci: 2009.0
  ki: 2.1
  Lh: 3.34e+5
  KtdivKc: 1e-1
  claus_clape: 7.9e-8
  melt_temp: 273.15
  ref_temp: 223.15
  min_temp: 243.15
  temperature_offset_air_to_ice: 0.0
  arrhenius_temp_threshold: 263.15
  arrhenius_A_cold: 3.985e-13
  arrhenius_A_warm: 1.916e+3
  arrhenius_Q_cold: 60000.0
  arrhenius_Q_warm: 139000.0
  omega_enhancement_factor: 181.25
  max_omega_enhancement: 0.01
  till_void_ratio: 0.69
  till_compressibility: 0.12
  till_delta: 0.02
  till_reference_pressure: 1000.0
  till_friction_angle: 30.0
  till_friction_angle_bed_min: null
  till_friction_angle_bed_max: null
  till_friction_angle_phi_min: 15.0
  till_friction_angle_phi_max: 45.0
  uthreshold: 100.0
  tauc_min: 1.0e+5
  tauc_max: 1.0e+10
  drain_rate: 0.001
  till_wat_max: 2.0
  drain_ice_column: True
  drainage_omega_threshold_1: 0.01
  drainage_omega_threshold_2: 0.02
  drainage_omega_threshold_3: 0.03
  target_water_fraction: 0.01
  default_bheatflx: 0.065

Parameters

Name Type Units Description Default Value
water_density float \( kg m^{-3} \) Water density constant. 1000.0
spy float \( s y^{-1} \) Number of seconds per year (for unit conversions). 31556926.0
gas_constant float \( J mol^{-1} K^{-1} \) Universal gas constant for Arrhenius law. 8.314
ci float \( J kg^{-1} K^{-1} \) Specific heat capacity of ice [@Aschwanden2012]. 2009.0
ki float \( W m^{-1} K^{-1} \) Thermal conductivity of cold ice [@Aschwanden2012]. 2.1
Lh float \( J kg^{-1} \) Latent heat of fusion [@Aschwanden2012]. 334000.0
KtdivKc float \( dimless \) Ratio of temperate vs cold ice thermal diffusivity [@Aschwanden2012]. 1e-1
claus_clape float \( K Pa^{-1} \) Clausius-Clapeyron constant for pressure melting [@Aschwanden2012]. 7.9e-08
melt_temp float \( K \) Melting point temperature at standard pressure [@Aschwanden2012]. 273.15
ref_temp float \( K \) Reference temperature for enthalpy calculations [@Aschwanden2012]. 223.15
min_temp float \( K \) Minimum temperature bound for enthalpy solver. 243.15
temperature_offset_air_to_ice float \( K \) Offset between air temperature and ice surface temperature. 0.0
arrhenius_temp_threshold float \( K \) Temperature threshold separating cold and warm ice regimes in Arrhenius law. 263.15
arrhenius_A_cold float \( s^{-1} Pa^{-3} \) Pre-exponential factor for cold ice (T < threshold) [@Paterson1994]. 3.985e-13
arrhenius_A_warm float \( s^{-1} Pa^{-3} \) Pre-exponential factor for warm ice (T >= threshold) [@Paterson1994]. 1916.0
arrhenius_Q_cold float \( J mol^{-1} \) Activation energy for cold ice (T < threshold) [@Paterson1994]. 60000.0
arrhenius_Q_warm float \( J mol^{-1} \) Activation energy for warm ice (T >= threshold) [@Paterson1994]. 139000.0
omega_enhancement_factor float \( dimless \) Enhancement factor for water content effect on ice softness. 181.25
max_omega_enhancement float \( dimless \) Maximum water fraction for enhancement calculation. 0.01
till_void_ratio float \( dimless \) Void ratio at reference effective pressure [@Tulaczyk2000]. 0.69
till_compressibility float \( dimless \) Till compressibility coefficient [@Tulaczyk2000]. 0.12
till_delta float \( dimless \) Transition parameter for effective pressure calculation [@Bueler2009]. 0.02
till_reference_pressure float \( Pa \) Reference effective pressure for till mechanics [@Bueler2009]. 1000.0
till_friction_angle float \( degree \) Till friction angle in Mohr-Coulomb friction law (uniform case). 30.0
till_friction_angle_bed_min float \( m \) Bed elevation for minimum friction angle (spatially variable case). None
till_friction_angle_bed_max float \( m \) Bed elevation for maximum friction angle (spatially variable case). None
till_friction_angle_phi_min float \( degree \) Minimum till friction angle (spatially variable case). 15.0
till_friction_angle_phi_max float \( degree \) Maximum till friction angle (spatially variable case). 45.0
uthreshold float \( m y^{-1} \) Threshold velocity for sliding coefficient calculation. 100.0
tauc_min float \( Pa \) Minimum basal yield stress. 100000.0
tauc_max float \( Pa \) Maximum basal yield stress. 10000000000.0
drain_rate float \( m y^{-1} \) Till water drainage rate [@Bueler2015]. 0.001
till_wat_max float \( m \) Maximum till water thickness [@Bueler2015]. 2.0
drain_ice_column boolean \( dimless \) Enable water drainage through ice column (transforms water content beyond threshold into basal melt). True
drainage_omega_threshold_1 float \( dimless \) First water fraction threshold for drainage function. 0.01
drainage_omega_threshold_2 float \( dimless \) Second water fraction threshold for drainage function. 0.02
drainage_omega_threshold_3 float \( dimless \) Third water fraction threshold for drainage function. 0.03
target_water_fraction float \( dimless \) Target water fraction after drainage in ice column. 0.01
default_bheatflx float \( W m^{-2} \) Default geothermal heat flux (used when not specified in state). 0.065