Simulation of snowpack formation using a ballistic deposition model with spatially correlated snowfall to study weak-layer formation and avalanche risk.
Avalanches are one of the most dangerous natural hazards in mountainous regions, often triggered by weak layers within the snowpack. These weak layers arise when successive snowfall events deposit structurally distinct layers with poor cohesion.
This project models snowpack formation using a 1D ballistic deposition framework, extended to include:
- Spatially correlated snowfall (storm structure)
- Realistic storm size distributions (log-normal)
- Layer-by-layer statistical analysis
The goal is to understand how storm spatial structure influences snowpack heterogeneity and whether this can help identify avalanche-prone conditions.
How does spatial correlation in snowfall deposition affect the structure of snowpack layers, and can this be used to identify weak-layer formation associated with avalanche risk?
- 1D lattice of width
L - Particles fall vertically and stick according to:
[ h_i = \max(h_{i-1}, h_i, h_{i+1}) + 1 ]
- Produces rough, correlated surfaces consistent with the KPZ universality class
- Uncorrelated case (
σ = 0): uniform random deposition - Correlated case (
σ > 0):- Gaussian-smoothed noise determines deposition probabilities
- Mimics storm systems depositing snow unevenly across space
- Storm sizes drawn from a log-normal distribution
- Captures real-world snowfall behavior:
- Many small storms
- Few extreme events
Each storm creates a layer:
[ l^{(k)}(x) = h^{(k)}(x) - h^{(k-1)}(x) ]
- Measures spatial unevenness within a layer
- Measures difference between consecutive layers
[ WLI = \frac{\Delta h}{\sigma_{\text{layer}}} ]
- High WLI → structurally distinct layers → potential instability
ballistic_deposition(...)ballistic_deposition_variable_storms(...)
extract_beta(...)– growth exponent (KPZ validation)extract_alpha(...)– roughness exponentcompute_layer_statistics(...)– layer metrics
- Surface growth scaling plots
- Layer-by-layer statistics
- Snowpack stratigraphy heatmaps
The model is validated against KPZ theory:
| Exponent | Theory | Observed |
|---|---|---|
| β (growth) | 1/3 | ~0.33 |
| α (roughness) | 1/2 | ~0.5 |
This confirms correct implementation before introducing correlations.
- Surface growth follows expected power laws
- Validates baseline (σ = 0)
- Higher σ leads to:
- Increased intra-layer variance
- Increased inter-layer contrast
- More spatially coherent deposition
- High variance obscures clear trends
- Suggests WLI is better as a relative metric rather than absolute predictor
- Uncorrelated snowfall → irregular, inconsistent layers
- Correlated snowfall → smoother, more uniform stratigraphy
- Spatially correlated storms produce systematically different snowpack structures
- Weak layers emerge from structural mismatch between consecutive deposits
- Realistic storm distributions (log-normal) significantly improve model realism
- Visual stratigraphy reveals patterns not captured by scalar metrics alone
This model simplifies real snowpack physics:
- 1D geometry (no lateral 2D effects)
- No temperature-driven metamorphism
- No wind redistribution
- No compaction or sintering processes
Separating validation from feature development is critical for debugging and correctness.
- Naive implementation: O(L³) complexity
- Optimization via sparse measurement drastically improved runtime
- Larger systems improve accuracy but increase runtime
- Model realism vs computational feasibility is a constant balance
- Extend to 2D deposition models
- Incorporate temperature and wind effects
- Use real snowfall data for calibration
- Develop improved weak-layer detection metrics
pip install numpy matplotlib scipy