Skip to content

Module smb_accpdd

Module smb_accpdd implements a combined accumulation and temperature-index model [Hock, 2003]. In this model, surface accumulation equals solid precipitation when the temperature is below a threshold and decreases linearly to zero in a transition zone. Conversely, surface ablation is computed proportionally to the number of Positive Degree Days (PDD). The model also tracks snow layer depth and applies different PDD proportionality factors for snow and ice.

The computation of PDD uses the expectation integration formulation [Calov and Greve, 2005]. Additionally, the computation of the snowpack and refreezing parameters is adapted from the PyPDD and PISM implementations.

Input

  • state.precipitation [Unit: \(kg \, m^{-2} \, y^{-1}\) water equivalent]
  • state.air_temp [Unit: \(^{\circ}C\)]

Output

  • state.smb [Unit: \(m \, ice \, eq. \, y^{-1}\)]

References

  • Hock, R. (2003). Temperature index melt modelling in mountain areas. Journal of Hydrology.
  • Calov, R., & Greve, R. (2005). A semi-analytical solution for the positive degree-day model with stochastic temperature variations. Journal of Glaciology.

Contributors: G. Jouvet

Note: This implementation is a TensorFlow re-implementation inspired by the one used in the Aletsch 1880–2100 example. It has been adapted to closely align (though not strictly) with the Positive Degree Day model implemented in PyPDD [Seguinot, 2019], which is utilized in the Parallel Ice Sheet Model (PISM) [Khroulev and the PISM Authors, 2020].

Config Structure

smb_accpdd:
  update_freq: 1
  refreeze_factor: 0.6
  thr_temp_snow: 0.0
  thr_temp_rain: 2.0
  melt_factor_snow: 1.095726596343
  melt_factor_ice:  2.921937590248
  shift_hydro_year: 0.75
  ice_density: 910.0
  wat_density: 1000.0
  smb_maximum_accumulation: 6.0

Parameters

Name Type Units Description Default Value
update_freq float y Update the mass balance each X years 1
refreeze_factor float dimless Refreezing factor 0.6
thr_temp_snow float ^{\circ}C Threshold temperature for solid precipitation 0.0
thr_temp_rain float ^{\circ}C Threshold temperature for liquid precipitation 2.0
melt_factor_snow float m yr^{-1} K^{-1} Degree-day factor for snow (ice eq.) 1.095726596343
melt_factor_ice float m yr^{-1} K^{-1} Degree-day factor for ice (ice eq.) 2.921937590248
shift_hydro_year float dimless This serves to start Oct 1. the acc/melt computation 0.75
ice_density float kg m^{-3} Density of ice for conversion of SMB into ice equivalent 910.0
wat_density float kg m^{-3} Density of water 1000.0
smb_maximum_accumulation float m yr^{-1} Maximum accumulation rate (m yr^{-1}) 6.0