Data-driven modeling of spring discharge in a dynamic karst aquifer using multivariate models and spectral analysis

Karst aquifers are highly sensitive to climate change due to their complex internal structure, which makes them both reactive and difficult to model. This study proposes a transdisciplinary decision-support analytical framework to support long-term groundwater management in a dynamic karst system in northwestern Tuscany (Italy). The approach combines time- and frequency-domains techniques - multivariate regression models and singular spectrum analysis, respectively - to characterize both short-term system memory and the low-frequency variability of the spring discharge. The methodology was applied to the Cartaro spring (Apuan Alps) using a 18-year dataset of discharge and meteorological variables (precipitation and temperature). Time-domain analysis showed that meteorological variables alone cannot fully explain the long-term variability of spring discharge, and that accounting for the short memory of the karst system (about five days) significantly improved the performance of the classical models. Furthermore, spectral decomposition allowed us to extract the significant annual and semi-annual oscillatory components with modulated amplitude, highlighting the role of low-frequency climatic variability in controlling spring behavior. By combining the results from the time and frequency domains, we fine‑tuned a forecasting procedure that enables statistically reliable annual predictions of long‑term average discharge trends, while limiting noise propagation and without relying on physical governing equations. The research is transdisciplinary, as it was developed from its preliminary phases in collaboration with stakeholders and local managers. The methodological workflow can be applied to other karst aquifers, provided that it is recalibrated using the site-specific hydro-climatic and discharge data.