Gobet et al. (2025) Interpretable seasonal multisite hidden Markov model for stochastic rain generation in France

Identification

• Journal: Advances in statistical climatology, meteorology and oceanography
• Year: 2025
• Date: 2025-09-08
• Authors: Emmanuel Gobet, David Métivier, Sylvie Parey
• DOI: 10.5194/ascmo-11-159-2025

Research Groups

• CMAP, CNRS, École Polytechnique, Institut Polytechnique de Paris, Route de Saclay, Palaiseau, France
• MISTEA, Université de Montpellier, INRAE, Institut Agro, Montpellier, France
• EDF R&D, Chatou CEDEX, France

Short Summary

This paper introduces a lightweight seasonal hierarchical hidden Markov model (SHHMM) for multisite stochastic rain generation in France, demonstrating its ability to accurately capture spatiotemporal precipitation patterns, seasonality, and dry/wet spell distributions, with interpretable weather regimes.

Objective

• Develop an interpretable parametric model for efficient, spatially coherent simulation of rainfall occurrences and amounts across France, incorporating self-taught large-scale weather patterns.

Study Configuration

• Spatial Scale: France, using 10 weather stations selected to be representative of French weather. The model focuses on large-scale patterns rather than high-resolution fields.
• Temporal Scale: Daily resolution, covering a 64-year historical period (1956–2019) for training and validation, and future climate projections (e.g., 2032–2096) for application. Model parameters are T-periodic (366 days).

Methodology and Data

• Models used: Seasonal Hierarchical Hidden Markov Model (SHHMM) with autoregressive (local memory) Markov dependence for rain occurrences and a Gaussian copula for multisite rain amounts. Compared against WGEN-type models.
• Data sources: European Climate Assessment & Dataset (ECA&D) for daily rainfall observations (1956–2019). ERA5 reanalysis for mean sea level pressure (1979–2017) for hidden state interpretation. DRIAS (French climate service) for downscaled and bias-adjusted climate projections (Euro-CORDEX, CMIP5, RCP scenarios) for future climate applications.

Main Results

• The SHHMM successfully captures spatiotemporal precipitation patterns, seasonality, and accurately reproduces dry and wet spell distributions across France.
• The model's four hidden states are interpretable as large-scale weather regimes, correlating well with mean sea level pressure anomalies (approximately 10 hPa) over the North Atlantic, learned solely from rain occurrence data.
• It effectively reproduces observed spatial correlations (Mean Square Error of Conditional Independence, MSECI = 0.003) and the bulk and tails of nonzero precipitation amount distributions, including 5-day aggregated rainfall.
• The SHHMM outperforms WGEN-type models in reproducing large-scale dry/wet spell distributions.
• The model demonstrates robustness in its hidden states and parameters when trained on future climate projections (e.g., RCP8.5), revealing projected changes like longer heavy rain spells.
• The autocorrelation function (ACF) for daily rainfall is underestimated at lag 1 but better reproduced for larger lags. Tail correlations for extreme events are underestimated for some station pairs.

Contributions

• Introduction of the Seasonal Hierarchical Hidden Markov Model (SHHMM), a lightweight, multisite stochastic weather generator for precipitation.
• Demonstration of naturally emerging, interpretable large-scale weather regimes from data, achieved by enforcing conditional independence of rain occurrences given hidden states, avoiding exogenous inputs or ambiguous model identification.
• Integration of autoregressive (local memory) Markov dependence for improved wet/dry spell persistence and a Gaussian copula for conditional rainfall amount generation, showing significant improvements over previous methods.
• Unique combination of local memory, seasonal parameter variation at low computational cost, and interpretable conditional rainfall generation in a multisite HMM.
• Development of an efficient heuristic initialization method for the Baum–Welch algorithm, addressing known convergence issues in HMM training.
• Extensive validation demonstrating superior performance in reproducing dry/wet spells and areal dry spells compared to WGEN-type models.
• Proof-of-concept application for climate change projections, enabling robust evaluation of climate models and analysis of future parameter evolution and extreme events.
• Provision of open-source Julia package StochasticWeatherGenerators.jl for reproducibility.

Funding

• Fondation de l’École Polytechnique (Chaire Stress Test: Risk management and Financial Steering, BNP Paribas, École polytechnique)
• EDF Energy Research and Development (Chaire Énergies Durables, CEA-EDF-École polytechnique)

Citation

@article{Gobet2025Interpretable,
  author = {Gobet, Emmanuel and Métivier, David and Parey, Sylvie},
  title = {Interpretable seasonal multisite hidden Markov model for stochastic rain generation in France},
  journal = {Advances in statistical climatology, meteorology and oceanography},
  year = {2025},
  doi = {10.5194/ascmo-11-159-2025},
  url = {https://doi.org/10.5194/ascmo-11-159-2025}
}