Mechanisms of heat exchange between water and rock in karst conduits M. D. Covington, 1 A. J. Luhmann, 2 F. Gabrov  sek, 1 M. O. Saar, 2 and C. M. Wicks 3 Received 18 March 2011 ; revised 19 July 2011 ; accepted 5 September 2011 ; published 15 October 2011. [1] Previous studies, motivated by understanding water quality, have explored the mechanisms for heat transport and heat exchange in surface streams. In karst aquifers, temperature signals play an additional important role since they carry information about internal aquifer structures. Models for heat transport in karst conduits have previously been developed ; however, these models make different, sometimes contradictory, assumptions. Additionally, previous models of heat transport in karst conduits have not been validated using field data from conduits with known geometries. Here we use analytical solutions of heat transfer to examine the relative importance of heat exchange mechanisms and the validity of the assumptions made by previous models. The relative importance of convection, conduction, and radiation is a function of time. Using a characteristic timescale, we show that models neglecting rock conduction produce spurious results in realistic cases. In contrast to the behavior of surface streams, where conduction is often negligible, conduction through the rock surrounding a conduit determines heat flux at timescales of weeks and longer. In open channel conduits, radiative heat flux can be significant. In contrast, convective heat exchange through the conduit air is often negligible. Using the rules derived from our analytical analysis, we develop a numerical model for heat transport in a karst conduit. Our model compares favorably to thermal responses observed in two different karst settings : a cave stream fed via autogenic recharge during a snowmelt event, and an allogenically recharged cave stream that experiences continuous temperature fluctuations on many timescales. Citation: Covington, M. D., A. J. Luhmann, F. Gabrov  sek, M. O. Saar, and C. M. Wicks (2011), Mechanisms of heat exchange between water and rock in karst conduits, Water Resour. Res., 47, W10514, doi:10.1029/2011WR010683. 1. Introduction [2] Water temperature is a crucial parameter in determin- ing water quality and can serve as a natural groundwater flow tracer [e.g., Anderson, 2005; Saar, 2011]. Temperature can be an indicator of anthropogenic influences on surface streams, and many aquatic species are sensitive to tempera- ture perturbations [Caissie, 2006]. Cave streams typically provide a more stable thermal environment than surface streams, though many cave streams also experience signifi- cant deviations in water temperature as a result of precipita- tion events, snow-melt, or seasonal changes in recharge temperatures [e.g., Luhmann et al., 2011]. Cave-adapted species may be sensitive to the magnitude, frequency, or pe- riodicity of these temperature changes [ Poulson and White, 1969; Jegla and Poulson, 1970]. Water and streambed temperatures are frequently used in surface streams to quan- tify surface water–groundwater interactions, and can also influence those interactions via the temperature-dependent viscosity of water [Silliman and Booth, 1993; Sinokrot and Stefan, 1993; Constantz, 1998, 2008; Hatch et al., 2006, 2010; Dogwiler et al., 2007 ; Vogt et al., 2010]. Similarly, it may be possible to quantify conduit–matrix exchange, or hyporheic exchange with sediments in cave streams using analysis of the longitudinal propagation of temperature pulses within the streams [Dogwiler and Wicks, 2005]. [3] Variations in spring temperature and chemistry play an important role in the field of karst hydrology as they are one of the few pieces of information that can be easily obtained from many karst aquifers, in hopes of constraining the properties of the conduit system. Lags between discharge responses and conductivity or temperature responses have been used to estimate the volume of conduit systems [Ashton, 1966; Atkinson, 1977; Sauter, 1992; Ryan and Meiman, 1996; Birk et al., 2004]. Thermal signals at karst springs have also been suggested to be a function of conduit geometry, recharge mode, aquifer depth, and conduit–matrix exchange flow [Benderitter et al., 1993; Bundschuh, 1993; Liedl et al., 1998; Liedl and Sauter, 2000; Birk et al., 2006; Long and Gilcrease, 2009; Luhmann et al., 2011]; however, the exact information content of thermal signals is not fully understood. [4] One barrier to an improved understanding of heat transport in cave streams is that a variety of models have been used to calculate heat exchange between the water in 1 Karst Research Institute, Znanstvenoraziskovalni Center Slovenske Akademije Znanosti in Umetnosti (ZRC SAZU), Postojna, Slovenia. 2 Department of Earth Sciences, University of Minnesota, Twin Cities, Minneapolis, Minnesota, USA. 3 Department of Geology and Geophysics, Louisiana State University, Baton Rouge, Louisiana, USA. Copyright 2011 by the American Geophysical Union. 0043-1397/11/2011WR010683 W10514 1 of 18 WATER RESOURCES RESEARCH, VOL. 47, W10514, doi:10.1029/2011WR010683, 2011