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Module smb_accpdd

Module smb_accpdd implements a combined accumulation and temperature-index model (Hock, 2003)1. 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 & Greve, 2005)2. 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\(^{-1}\)]

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)3, which is utilized in the Parallel Ice Sheet Model (PISM; www.pism-docs.org)

Parameters

Default configuration file (smb_accpdd.yaml): 

smb_accpdd:
  update_freq: 1.0
  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

Description of the parameters:

Name Description Default value Units
update_freq Update the mass balance each X years. 1.0 y
refreeze_factor Refreezing factor. 0.6 —
thr_temp_snow Threshold temperature for solid precipitation. 0.0 \( ^{\circ} \)C
thr_temp_rain Threshold temperature for liquid precipitation. 2.0 \( ^{\circ} \)C
melt_factor_snow Degree-day factor for snow (ice eq.). 1.095726596343 m yr\( ^{-1} \) K\( ^{-1} \)
melt_factor_ice Degree-day factor for ice (ice eq.). 2.921937590248 m yr\( ^{-1} \) K\( ^{-1} \)
shift_hydro_year This serves to start Oct 1. the acc/melt computation. 0.75 —
ice_density Density of ice for conversion of SMB into ice equivalent. 910.0 kg m\( ^{-3} \)
wat_density Density of water. 1000.0 kg m\( ^{-3} \)
smb_maximum_accumulation Maximum accumulation rate. 6.0 m yr\( ^{-1} \)

  1. Hock, R. (2003). Temperature index melt modelling in mountain areas. Journal of Hydrology, 282(1--4), 104--115. https://doi.org/10.1016/s0022-1694(03)00257-9 ↩

  2. Calov, R., & Greve, R. (2005). A semi-analytical solution for the positive degree-day model with stochastic temperature variations. Journal of Glaciology, 51(172), 173--175. https://doi.org/10.3189/172756505781829601 ↩

  3. Seguinot, J. (2019). PyPDD: A positive degree day model for glacier surface mass balance. https://doi.org/10.5281/ZENODO.3467639 ↩