The model code is a 3D englacial and supraglacial debris transport model. It is written in Fortran90. The model is used in Verhaegen and Huybrechts (2025), where it is applied to a synthetic, idealized glacier. It builds further upon earlier work in Anderson & Anderson (2016) and Verhaegen et al. (2020).
The model code consists of the following elemennts:
a) debris_cover_main_supraglacial.f90: supraglacial debris advection model
This model code solves for the debris thickness, including advection by surface ice flow, melt-out of englacial debris, gravitational transport, and off-glacier debris removal at the margin. The advection submodule uses a second-order upwind transport scheme, a Smolarkiewicz-based anti-diffusion correction and also uses a mass conservation correction.
b) debris_cover_main_englacial.f90: englacial debris advection model
This model advects debris mass concentration within the ice column, using a second-order upwind scheme + Smolarkiewicz anti-diffusion correction and also uses a mass conservation correction. It provides the melt-out mass that is used as input into the supraglacial debris model.
The model requieres certain input variables and parameters.
The following input variables are needed to run the model:
- H (ice thickness - m)
- HT (surface elevation - m)
- G (surface mass balance - m i.e. yr-1)
- mask (ice mask - 0 or 1)
- VX (horizontal velocity x - m yr-1)
- VY (horizontal velocity y - m yr-1)
- VZ (vertical velocity z - m yr-1)
- DHTDT_yearly (surface elevation change rate - m yr-1)
- DHDT_yearly (ice thickness change rate - m yr-1)
- margin (marginal pixels of glacier - 0 or 1)
Debris input locations are X,Y positions of the pixels within the domain and should be set in debris_cover_main_englacial.f90 (if in the accumulation zone) or debris_cover_main_supraglacial.f90 (if in the ablation zone).
The following parameter values were inserted to obtain the debris-covered reference glacier in Verhaegen & Huybrechts (2025):
INTEGER, PARAMETER :: NY=178 ! Number of pixels in y (-)
INTEGER, PARAMETER :: NX=300 ! Number of pixels in x (-)
INTEGER, PARAMETER :: NZ=21 ! Number of layers in z (-)
INTEGER, PARAMETER :: DX=25 ! Spatial resolution ice flow model x (m)
INTEGER, PARAMETER :: DY=DX ! Spatial resolution ice flow model y (m)
integer,parameter :: tdebris=5 ! Time of debris source release (yr)
integer,parameter :: deltax_d=DX ! Spatial resolution debris model x (m)
integer,parameter :: deltay_d=deltax_d ! Spatial resolution debris model y (m)
real,parameter :: deltat_d=0.005 ! Time step supraglacial debris model (yr)
real,parameter :: dt_eng=0.005 ! Time step englacial debris model (yr)
integer,parameter :: dtdiag_d=1 ! Diagnostic time step debris models (yr)
integer,parameter :: nyears_d=1 ! Number of years supragglacial debris (yr)
integer,parameter :: nyears_deng=1 ! Number of years englacial debris (yr)
real,parameter :: deposition_mass_debris_abl=0.0 ! Deposition mass in kg/yr (ABLATION AREA)
real,parameter :: deposition_mass_debris_acc=2000000. ! Deposition mass in kg/yr (ACCUMULATION AREA)
real,parameter :: phi_debris=0.3 ! Debris cover porosity (-)
real,parameter :: rho_debris=2650 ! Debris cover density (kg m-3)
real,parameter :: epsilon_d = 1e-15 ! Ensuring finite values (-)
real,parameter :: n_iter_smolar = 1 ! Number of iterations for numerical diffusion correction (-)
real,parameter :: c_deb_slope = 0.0001 ! Debris removal efficiency parameter (Pa-1 m2 yr-1)
real,parameter :: max_iters_mc = 10 ! For mass conservation check (-)
real,parameter :: lchar_d = 25 ! Characteristic marginal length scale for debris removal (m)
Anderson, L. S. and Anderson, R. S.: Modeling debris-covered glaciers: response to steady debris deposition, The Cryosphere, 10, 1105–1124, https://doi.org/10.5194/tc-10-1105-2016, 2016.
Verhaegen, Y., Huybrechts, P., Rybak, O., and Popovnin, V. V.: Modelling the evolution of Djankuat Glacier, North Caucasus, from 1752 until 2100 CE, The Cryosphere, 14, 4039–4061, https://doi.org/10.5194/tc-14-4039-2020, 2020.
If you use this model, please cite:
Verhaegen, Y. & Huybrechts, P. (2025). Coupling debris transport to 3D higher-order ice flow dynamics to model the behavior and climate change response of debris-covered glaciers. Journal of Geophysical Research – Earth Surface.
The corresponding Zenodo folder can be found here: http://doi.org/10.5281/zenodo.17693004.