Abstract
Documenting and understanding water balances in a karst watershed in which groundwater and surface water resources are strongly interconnected are important aspects for managing regional water resources. Assessing water balances in karst watersheds can be difficult, however, because karst watersheds are so very strongly affected by groundwater flows through solution conduits that are often connected to one or more sinkholes. In this paper we develop a mathematical model to approximate sinkhole porosity from discharge at a downstream spring. The model represents a combination of a traditional linear reservoir model with turbulent hydrodynamics in the solution conduit connecting the downstream spring with the upstream sinkhole, which allows for the simulation of spring discharges and estimation of sinkhole porosity. Noting that spring discharge is an integral of all aspects of water storage and flow, it is mainly dependent on the behavior of the karst aquifer as a whole and can be adequately simulated using the analytical model described in this paper. The model is advantageous in that it obviates the need for a sophisticated numerical model that is much more costly to calibrate and operate. The model is demonstrated using the St. Marks River Watershed in northwestern Florida.
Zusammenfassung
Die Bestimmung von Wasserbilanzen in Karsteinzugsgebieten, in welchen Grundwasser und Oberflächenwasser miteinander in Kontakt stehen, ist ein wichtiger Aspekt für die Bewirtschaftung regionaler Grundwasserressourcen. Das Abschätzen der Wasserbilanzen kann allerdings schwierig sein, denn die Grundwasserströmung in Karsteinzugsgebieten wird sehr stark durch hochdurchlässige Karströhren beeinflusst, die oft mit einer oder mehreren Dolinen verbunden sind. In diesem Artikel wird die Entwicklung eines mathematischen Modells zur Abschätzung der Dolinendichte (Anteil von Dolinen an der Einzugsgebietsfläche) aus dem Schüttungsverhalten einer Quelle präsentiert. Das Modell ist eine Kombination aus einem traditionellen linearen Reservoirmodell unter Berücksichtigung turbulenter Verhältnisse der Karströhre, welche die Quelle und die Doline miteinander verbindet. Der Quellabfluss repräsentiert als integrales Gebietssignal alle Aspekte von Strömung und Wasserspeicherung und hängt von der Summe der Systemeigenschaften des Quelleinzugsgebietes ab. Er kann durch das in diesem Artikel beschriebene analytische Modell simuliert werden. Das Modell kann den Einsatz aufwendiger numerischer Modelle überflüssig machen, welche einen höheren Aufwand für Kalibrierung und Anwendung benötigen. Die Anwendung des Modells wird am Beispiel des St. Marks Flusseinzugsgebietes im Nordwesten Floridas demonstriert.
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Acknowledgements
Funding support of this study was provided in part by the National Science Foundation of China under grant 41162008. Special gratitude to the Editor, Tobias Geyer, and two anonymous reviewers for their insightful comments and constructive suggestions.
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Li, G., Field, M.S. A mathematical model for simulating spring discharge and estimating sinkhole porosity in a karst watershed. Grundwasser 19, 51–60 (2014). https://doi.org/10.1007/s00767-013-0243-3
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DOI: https://doi.org/10.1007/s00767-013-0243-3