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Use of geochemical and mathematical models for the determination of mixing ratios in groundwater from municipal wells, Madison, Wisconsin, USA

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Geochemical and mathematical methods are presented, which include NETPATH model and the Moore-Penrose pseudo-inverse (MPPI) to quantify the contributions of water from distinct recharge areas and aquifers to public supply wells in the city of Madison, Wisconsin. Previous studies investigated the hydraulic connectivity between different aquifers in the study area and proved the impact of the shallower aquifers as well as the surface water on some of the deep wells, but did not address the percentages of the contributions of such sources. The MPPI, executed by MATLAB code, in conjunction with the inverse-based NETPATH model was used to estimate the mixing proportions of four end members (“initials”) in some of the deep groundwater wells. The quantitative estimation of the contribution of the different water resources (reference waters) on the water extracted from the deep municipal wells is considered as the main ultimate goal of this manuscript. Therefore, in this paper, many tools including WATEQ program, NETPATH and MPPI codes, were applied to verify the influence of such reference waters as well as to assess their ratios in the deep municipal wells. Datasets including major ion chemistry and stable isotopes (such as δ18O and δD) data were manipulated to determine similarities and differences between the samples and reference waters. These data provided a basis for selecting and grouping of the samples that are believed to be affected by mixing. The results showed that there are two groups of wells; one group was mainly affected by the deeper Mount Simon water (about 70%), while the second group showed a slight increase in the shallower Tunnel City water (up to 15%) and a significant increase in the Wonewoc Formation water (up to 40%) with a decrease in the ratio of the deeper Mount Simon water. The contribution of lake waters was almost around 20% in all of the studied groundwater wells. It is worth mentioning that it is not easy to choose the most appropriate models that express the mixing ratios if the necessary data are not available, as well as the appropriate programs used to adapt these data correctly. Therefore, the MPPI mathematical program was adapted along with other geochemical programs in order to constrain the models computed by such programs as well as to verify that the outputs of these programs will be as close to reality as possible. Generally, quantification of the contribution of different sources of recharge to ground-water sheds light on the vulnerability of a certain aquifer or well to pollution. Such analysis may also highlight the need for additional characterization of aquifer heterogeneity at a given location.

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Authors and Affiliations

  1. Hydrogeochemistry Department, Water Resources Division, Desert Reserch Center, PO Box 11753, Cairo, Egypt

    Hesham A. Ezzeldin

  2. University of Wisconsin, 1215 W. Dayton, St. Madison, WI, 53706, USA

    Jean M. Bahr

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  1. Hesham A. Ezzeldin
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Ezzeldin, H.A., Bahr, J.M. Use of geochemical and mathematical models for the determination of mixing ratios in groundwater from municipal wells, Madison, Wisconsin, USA. Geosci J 27, 367–383 (2023). https://doi.org/10.1007/s12303-023-0005-x

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