Machine learning-driven imputation and short-term forecasting of water levels in the karstic system of the Bükk Mountains, Northern Hungary

Abstract Karstic systems supply more than a quarter of the drinking water needs in the world, yet modeling these aquifer systems is constrained by their complexity and the extensive data requirements. Advances in data collection technologies enabled access to high-resolution hydrogeological data, but gaps in these datasets continue to limit their utility. To address this challenge, this study introduces a novel hybrid methodology that integrates self-organizing maps (SOM) and bidirectional long short-term memory (Bi-LSTM) networks to impute missing water level intervals and forecast future water levels in karstic systems. The feasibility of the proposed approach is demonstrated through its successful application in analyzing the spatiotemporal dynamics of karst water levels in the Bükk Mountains, Northern Hungary. Initially the Bi-LSTM model was employed to impute missing intervals in the precipitation and water level datasets. The SOM analysis revealed that spring water levels are correlated with precipitation, reflecting immediate recharge dynamics. In contrast, the wells displayed a delayed response due to slower recharge processes. Subsequently, the SOM features, including grid coordinates and distances, were incorporated into the Bi-LSTM model to add contextual information and improve its predictive capability. To assess the reliability of the forecasts, a bootstrap uncertainty analysis was conducted. This enabled reliable prediction and forecasting of karst water levels, achieving predictive accuracy exceeding 92% while also providing estimates of potential uncertainty. The overall trend of the forecasted water levels showed spatial variability, with most monitoring stations exhibiting increasing trends and gradual decline observed at one site, underscoring the importance of site-specific management.