Relationships Between Conduit Properties and the Damping and Retardation of Thermal Pulses in Karst Conduits

Abstract:

The general lack of information concerning karst conduit network geometry is a crucial problem for the management of karst aquifers. Many prior studies have used a variety of statistical and physics-based approaches to understand relationships between aquifer structure and the variations in discharge, chemistry, and temperature observed at karst springs. In particular, previous work has shown that temperature signals at karst springs contain substantial information about the flow network and modes of recharge. Thermal pulses have also been fit to numerical transport simulations to constrain conduit diameter. The peaks of temperature curves observed at multiple points along a flow path are sometimes employed to estimate flow-through time. However, thermal peaks exhibit retardation as a result of heat exchange between the water and conduit wall. Here, we demonstrate that the retardation and damping of a thermal pulse are simple functions of conduit properties, notably diameter. We derive analytical solutions for a sinusoidal input temperature, and use numerical simulations to demonstrate that these solutions can be used to estimate damping and retardation of single pulses with many of the underlying assumptions of the analytical solutions relaxed. These analytical relationships can be used as a simple means to extract rough information about conduit geometry using the retardation or damping of a thermal peak. We demonstrate how this technique can be used with a field example. Additionally, we use the analytical relation for retardation to provide constraints on the use of temperature as an indicator of flow-through time.