Karst aquifer discharge response to rainfall interpreted as anomalous transport

Abstract. The discharge measured in karst springs is known to exhibit distinctive long tails during recession times following distinct discharge peaks of short duration. The long-tail behavior is generally attributed to the occurrence of tortuous, ramified flow paths that develop in the underground structure of karst systems. Modeling the discharge behavior poses unique difficulties because of the poorly-delineated flow path geometry and generally scarce information on the hydraulic properties of catchment-scale systems. In a different context, modeling of long-tailed behavior has been addressed in studies of chemical transport. Here, an adaptation of a continuous time random walk – particle tracking (CTRW-PT) framework for anomalous transport is proposed, which offers a robust means to quantify long-tailed breakthrough curves that often arise during chemical species transport under various flow scenarios. A theoretical analogy is first established between partially water-saturated karst flow, characterized by temporally varying water storage, and chemical transport involving accumulation and release of a chemical tracer. This analogy is then used to develop and implement a CTRW-PT model. Application of this numerical model to examination of three years of summer rainfall and discharge data from a karst aquifer system – the Disnergschroef high alpine site in the Austrian Alps – is shown to yield robust fits between modeled and measured discharge values. In particular, the analysis underscores the predominance of slow diffusive flow over rapid conduit flow. The study affirms the analogy between partially saturated karst flow and chemical transport, exemplifying the compatibility of the CTRW-PT model for this purpose. Within the specific context of the Disnergschroef karst system, these findings highlight the predominance of slow diffusive flow over rapid conduit flow. The agreement between measured and simulated data supports the proposed analogy between partially saturated karst flow and chemical transport; it also highlights the potential ability of the anomalous transport framework to further enhance modeling of flow and transport in karst systems.