Interpretable Machine Learning Surrogates for Short-Term Water-Level Forecasting at Ports: A Case Study of the Varna Hydromast Station

The water level at ports governs under-keel clearance, pilotage windows, cargo operations and local flood risk, yet regional ocean forecasting systems resolve it at kilometre scales that may lie outside the harbour basin. This study evaluates a station-only machine learning surrogate that forecasts a single low-cost hydromast water-level sensor at the port of Varna (Bulgarian Black Sea) 1 to 24 h ahead, using only the sensor’s own recent history and deterministic harmonic (tidal and diurnal) cyclic features. The target is framed as a residual relative to the current observation, which keeps it bounded regardless of season or tidal phase. Persistence, ridge regression, random forest, XGBoost, a multilayer perceptron, a long short-term memory network and PySR symbolic regression are compared at horizons of 1, 3, 6, 12 and 24 h on a chronological hold-out period. Ridge regression is the most accurate model at 1–6 h, random forest is marginally best at 12 h, and PySR is best at 24 h, where all methods lie close to persistence. PySR reduces the residual problem to short closed-form expressions dominated by harmonic phase terms, at four of five horizons without any lagged water-level input. Grouping the methods into four interpretability tiers shows that, at this site, the intrinsically interpretable models are competitive with or better than the black-box alternatives at four of the five horizons.