Modelling short- and long-term flooding levels in the Venice lagoon: A hierarchical hidden Markov model approach

We develop a nested (two-scale) hidden Markov framework for sea level in the Venice lagoon in which a coarse-scale monthly background sets the context and fine-scale daily regimes describe day-to-day conditions within each month. The daily regimes are ordered and evolve with near tri-diagonal transitions, while emissions at both scales are heavy-tailed (Student-t), capturing both level shifts and tail behaviour. We validate the model with a compact diagnostics “scoreboard”. Empirically, we uncover a persistent higher-risk monthly background under which all daily regimes are lifted and day-to-day evolution is predominantly incremental, producing multi-day clusters in the upper regimes; these features map cleanly to probability-based alerting and barrier rules.