PROCESS LENGTH SCALES: A CONCEPTUAL TOOL FOR KARST HYDROGEOLOGY, GEOMORPHOLOGY, AND HYDROECOLOGY

Simple mathematical models often allow an intuitive grasp of the function of physical systems and provide a useful tool for conceptualizing them. In this work, we derive a simple mathematical framework that can be applied to a wide variety of processes that occur in karst conduits, including heat transport, dissolution, matrix input, sediment transport, and degradation of organic matter. We show that, as the result of advection along the conduit, any process that occurs over a characteristic time scale results in a characteristic length scale. We analytically derive length scales for heat transport and dissolution in karst conduits and relate these scales to the information content of temperature and conductivity signals at karst springs. Additionally, we use the length scale conceptual framework to quantify the importance of dispersion and diffuse input in determining spring signals. Because process length scales are a ubiquitous feature of karst systems and surface streams, we discuss several other potential applications of this simple idea in fields such as geomorphology and hydroecology.