Multivariate analyses with end-member mixing to characterize groundwater flow: Wind Cave and associated aquifers

Principal component analysis (PCA) applied to hydrochemical data has been used with end-member mixing to characterize groundwater flow to a limited extent, but aspects of this approach are unresolved. Previous similar approaches typically have assumed that the extreme-value samples identified by PCA represent end members. The method presented herein is different from previous work in that (1) end members were not assumed to have been sampled but rather were estimated and constrained by prior knowledge; (2) end-member mixing was quantified in relation to hydrogeologic domains, which focuses model results on major hydrologic processes; (3) a method to select an appropriate number of end members using a series of cluster analyses is presented; and (4) conservative tracers were weighted preferentially in model calibration, which distributed model errors of optimized values, or residuals, more appropriately than would otherwise be the case. The latter item also provides an estimate of the relative influence of geochemical evolution along flow paths in comparison to mixing. This method was applied to groundwater in Wind Cave and the associated karst aquifer in the Black Hills of South Dakota, USA. The end-member mixing model was used to test a hypothesis that five different end-member waters are mixed in the groundwater system comprising five hydrogeologic domains. The model estimated that Wind Cave received most of its groundwater inflow from local surface recharge with an additional 33% from an upgradient aquifer. Artesian springs in the vicinity of Wind Cave primarily received water from regional groundwater flow. Published by Elsevier B.V.