An explainable, uncertainty-aware ensemble soft-sensor for real-time dissolved oxygen estimation in rivers from routine in-situ monitoring streams

Abstract

Dissolved oxygen (DO) is the single most informative indicator of the ecological state of running waters, yet the optical probes used to record it are also the most prone to fouling, drift and outright failure among the routine sensors deployed at gauging stations. The resulting gaps interrupt exactly the early-warning function that continuous monitoring is meant to serve. This study develops a DO soft-sensor that reconstructs the concentration from the more robust and inexpensive variables recorded alongside it — water temperature and discharge — without recourse to the DO record itself, so that it remains usable while the oxygen probe is offline. A compact set of physically motivated predictors, including the temperature-dependent oxygen-solubility term of Benson and Krause, seasonal harmonics and short-memory hydrological statistics, is passed to a non-negativity-constrained stacked ensemble that combines five tree-based learners through a super-learner meta-model. The framework is evaluated on a nine-year daily record (n = 3357; 2012–2021) from a large lowland river under a strictly chronological train–validation–test partition. On the held-out final 504 days the ensemble attains R² = 0.877, RMSE = 0.697 mg L⁻¹, Nash–Sutcliffe efficiency 0.877 and Kling–Gupta efficiency 0.899, improving on a temperature-only physical baseline (RMSE 0.942 mg L⁻¹) and on multiple linear regression, and performing on par with the best individual learner while providing a single robust predictor. SHAP attribution recovers the correct physical hierarchy — the smoothed water-temperature signal and oxygen solubility dominate, with discharge and seasonality secondary — confirming that the model is physically consistent rather than an opaque fit. Split-conformal prediction intervals deliver near-nominal empirical coverage (0.82, 0.90 and 0.93 against nominal 0.80, 0.90 and 0.95), and the reconstructed series flags low-DO days with a recall of 0.97 and an F₁-score of 0.85. A rolling-origin backtest over four successive out-of-period blocks confirms that this performance is not an artefact of a single split, with a mean out-of-period R² of 0.854. The complete computational pipeline, the exact data-retrieval script, the preprocessed feature matrix, all model predictions with intervals, the SHAP values and the pinned software environment are released so that every table and figure below can be regenerated with a single command.