Reply to comment by A. Sahuquillo and J. Jaime Gómez‐Hernández on “Derivation of effective hydraulic parameters of a karst aquifer from discharge hydrograph analysis”

[1] In their comment, Sahuquillo and Gómez-Hernández [2003] (hereinafter referred to as S-GH) suggest that the approach we followed for deriving diffusivity values from spring flow hydrographs in a karstic aquifer [Baedke and Krothe, 2001] is flawed for two reasons. The first assertion is that groundwater flow toward springs is radial in karst aquifers. The second is that their theoretically based derivation of a spatially distributed eigenproblem solution to the groundwater flow equation suggests that the values of diffusivity obtained from our study ought to significantly underestimate the real values of diffusivity of the karst aquifer. [2] In regard to their first concern, groundwater flow toward springs is most definitely not necessarily radial in karst, or in other highly heterogeneous aquifers. Flow of water in and toward solutionally enlarged conduits is a fundamental characteristic of karst aquifers [White, 2002], and these conduits are not necessarily uniformly spaced nor radially configured. In particular, dye traces have empirically shown that at least one of the springs in our study area (Spring A) has a strongly-preferred north-south, not radially, oriented conduit system through which water is delivered to the spring orifice [Baedke and Krothe, 2000]. While it may be theoretically possible to model radial flow to the spring orifice in karst aquifers, this has been demonstrated to not be the case in our study area. Therefore this assertion by S-GH is wrong, at least in our study area. Fundamentally this is why, as we stated in our paper, traditional methods of establishing aquifer parameters that assume radial flow of water toward wells do not work for conduit-dominated karst systems. [3] Their second concern is that the values derived for diffusivity in our paper ought to significantly underestimate the real diffusivity values of the karstic aquifer. This supposition is precisely what our study attempts to address. Our study tested a simple conceptual model in which the karstic aquifer is a linear reservoir that is perfectly connected to a spring. Based upon this simple model, we followed a mathematical approach similar to Rorabaugh [1964] to derive diffusivity estimates for the hypothesized conduit, intermediate, and diffuse portions of the aquifer through hydrograph analysis. [4] To test and verify the diffusivity estimates derived with our technique, we compared our results to estimates obtained from other, more traditional methods (pump tests for estimates from the diffuse portion of the aquifer and dye traces for the conduit portion of the aquifer). These comparisons show that the values obtained from our hydrograph technique agreed favorably with those from the more traditional methods. Clearly, our model does not take into account the complexity of the real karst system, however, our study was unable to falsify this simple conceptual model. This indicates that regardless of its real complexity, the system behaves as the simple conceptual model says it should. This unavoidable reality, while not providing conclusive evidence in support of our method, strongly suggests that the technique is not so riddled with faults as S-GH would have us believe. We cannot, and neither can S-GH, discount our empirically supported technique on the basis that it does not agree with a theoretically-derived mathematical model. [5] We are also compelled to note that the approach proposed by S-GH in which diffusivity values are obtained through inverse modeling techniques [e.g., Estrela and Sahuquillo, 1997], does not allow us as karst researchers to address the fundamental problem of establishing real hydraulic parameters that are essential to understanding karst aquifers. As Taylor and Green [2001] explain “..in describing the hydraulic properties of the karst aquifer, four physical parameters must be described: T, the transmissivity of the solutional openings; S, the storativity of the solutional openings; Sf, the storativity of the network of diffuse fractures; and B, the rate of fluid exchange between the network of fractures and the solutional openings”. We prefer that these hydraulic parameters be determined and verified with field data, rather than having the field data be resolved on the basis of a groundwater flow model. [6] Finally, with the data that we have presented in Table 1 of Baedke and Krothe [2001], we are able to assess the validity of a conclusion drawn by S-GH in that “..it is only when the contrast between transmissivities is as large as three orders of magnitude [between the high conductivity and low conductivity zone] that two distinct slopes are clearly appreciated in the hydrograph.” Whether we reference our hydrograph derived transmissivities or those obtained by the more traditional approaches, we observe in our study area at least five orders of magnitude difference in the transmissivities of the conduit and diffuse portion of the karstic aquifer. In this regard, our work seems to agree with the theoretical model of S-GH.