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Aletsch: parameter calibration with Optuna

A glacier model is only as good as its parameters. For the realistic Aletsch setup of forward modelling, Step 3, the key unknowns are the accumulation and ablation scale factors (weight_accumulation, weight_ablation) and the basal friction (tau_ref). Choosing them by hand is tedious; letting an optimiser search automatically is faster and more rigorous.

This is Part B of the Aletsch example — data assimilation by hyperparameter tuning. Rather than inverting a spatial field, it treats a few scalar parameters as unknowns and uses Optuna to search the values that best reproduce observations. The forward model is the realistic climate/SMB pipeline of Part A (clim_aletsch + smb_accmelt + observation tracking), run from 1880 to 2020.

Setup

git clone https://github.com/instructed-glacier-model/igm-examples.git
cd igm-examples/aletsch

Input data (the observed DEMs and the surface-velocity field) ships in data/. The Optuna sweeper is bundled with IGM; the interactive Optuna dashboard is a separate web app installed on demand (pip install optuna-dashboard).

How the calibration works

Two custom modules turn the forward simulation into a calibration objective:

  • track_usurf_obs — compares the modelled surface elevation against 7 observed DEMs (1880–2017) and writes the mean standard deviation across all years into state.score as cost_usurf.
  • track_velsurf_obs — at the final time step (2020) computes the RMSE between modelled and observed surface speeds where observations exist, written as cost_velsurf (used in Step 2 only).

Optuna calls igm_run repeatedly, proposing new parameter values each trial based on previous results, and records every trial in an SQLite database.

Step 1: Single-objective optimisation

Finds the weight_accumulation and weight_ablation that minimise the DEM misfit (cost_usurf).

Parameter Meaning Search range Sampler
processes.smb_accmelt.weight_accumulation Scale factor on accumulation 0.5 – 3.0 TPE
processes.smb_accmelt.weight_ablation Scale factor on melt 0.5 – 3.0 TPE

The optimisation settings live in optuna/optuna_1obj_params.yaml (50 trials, 4 in parallel, TPE sampler — a Tree-structured Parzen Estimator that models the objective from completed trials and samples promising regions, far more efficient than random search).

# Single run (no optimisation), to verify the setup:
igm_run +experiment=params_B_1obj

# With Optuna optimisation (50 trials, 4 in parallel):
igm_run -m +experiment=params_B_1obj \
        hydra/sweeper=igm_optuna \
        hydra.sweeper.optuna_config=optuna/optuna_1obj_params.yaml

Results are stored under multirun/, and the study is persisted in optuna_1obj.db so you can resume or inspect it any time. Explore it interactively:

pip install optuna-dashboard          # one-off install
optuna-dashboard sqlite:///optuna_1obj.db

Best parameters found: weight_accumulation = 1.84, weight_ablation = 2.01. These optimised values are the defaults used in the realistic forward runs (Part A, Steps 3–4).

Step 2: Multi-objective optimisation

Same model as Step 1, but optimises two objectives simultaneously:

  • cost_usurf — mean STD between modelled and observed DEMs (as in Step 1)
  • cost_velsurf — RMSE between modelled and observed surface speeds at 2020 (from track_velsurf_obs)

The config optuna/optuna_2obj_params.yaml declares both objectives, switches the sampler from TPE to NSGA-II (a genetic algorithm suited to Pareto-front exploration), and adds a third free parameter:

Parameter Meaning Search range
processes.iceflow.physics.sliding.tau_ref Basal shear stress (MPa) at u_ref = 100 m/yr 0.08 – 0.50

With u_ref = 100 m/yr, tau_ref is the basal shear stress at a typical Aletsch trunk speed, so fitting velocities well requires tuning it alongside the SMB weights.

# Single run (no optimisation):
igm_run +experiment=params_B_2obj

# With NSGA-II multi-objective optimisation (200 trials, 4 in parallel):
igm_run -m +experiment=params_B_2obj \
        hydra/sweeper=igm_optuna \
        hydra.sweeper.optuna_config=optuna/optuna_2obj_params.yaml

The study is persisted in optuna_2obj.db (study aletsch_2obj).

Analyse and visualise

A Pareto-front plot reads the database directly:

python tools/plot_pareto_front.py
# or with explicit arguments:
python tools/plot_pareto_front.py --storage sqlite:///optuna_2obj.db \
                                  --study   aletsch_2obj \
                                  --out     pareto_front.png --show

The Pareto front reveals the trade-off: trials that fit surface elevation best tend to fit velocities less well, and vice versa — choosing a point on it is a modelling decision. To inspect the spatial misfit of a chosen trial (each trial writes output.nc + output_ts.nc):

# a single run saved under outputs/<timestamp>:
python tools/plot_misfit_maps.py --run outputs/<timestamp>

# a Pareto-optimal trial from the optimisation:
python tools/plot_misfit_maps.py --run multirun/<date>/<trial_number>

Next steps