A New Approach to Conduct End-Member Mixing Analysis in Catchment Hydrology and Hydrogeology

End-member mixing analysis (EMMA) has been frequently applied to advance our understanding of hydrologic pathways, water sources, and surface water and groundwater interactions in catchment hydrology. Very recently, EMMA has been applied to hydrogeological systems to better understand groundwater recharge and movement. In conjunction with diagnostic tools of mixing models (DTMM), EMMA relies on eigenvectors extracted from coincident time series of geochemical and isotopic values measured at the same location to characterize the mixing space (numbers of end-members and conservative tracers), identify end-members, and quantify their contributions to streamflow and the groundwater system. However, this traditional approach limits the use of EMMA in many studies with small sample sets (short intervals). We hypothesize that EMMA can be extended to studies with infrequent sampling schemes if samples are collected from multiple scales or locations within a catchment by adding an additional mixing model assumption that end-members are consistent over varying scales. In other words, the underlying assumption means that only contributions of end-members vary with scales. This work uses two examples to demonstrate the success of EMMA for analyzing short-duration time series of water samples collected from multiple locations, one from a glacierized catchment in Bhutan and the other from a hydrogeological study in volcanic setting of El Salvador. The success was evaluated by independent tracers (not used in EMMA and also no direct connection with those used in EMMA) and semi-independent tracers (e.g., specific conductance (SC) and pH, which are chemically related to geochemical tracers used in EMMA). In the glacierized catchment, a three-end-member mixing model was developed using geochemical tracers for streamflow with contributions from glacier melt and direct precipitation, shallow groundwater (below and in front of glaciers), and catchment groundwater (base flow generated outside the glacierized area). The projections using the EMMA results and the measured values were very well correlated for independent and semi-independent variables, including SC (R² = 0.97, slope =0.98, p < 0.001), pH (R² = 0.70, slope =1.1, p < 0.001), stream temperature (R² = 0.77, slope =0.6, p < 0.001), and δ¹⁸O (R² = 0.90, slope =1.16, p < 0.001; not used in EMMA in this case). In the case of El Salvador study, three end-members were also identified for a number of groundwater wells, with direct precipitation and two types of groundwater from different geologic settings. The El Salvador model was validated using SC (R² = 1.00, slope =0.97, p < 0.001) and sulfur (R² = 0.87, slope =0.81, p < 0.01) that were not used in EMMA. The successful application of this new approach will significantly extend the application of EMMA to catchments that are difficult to access, or frequent sampling is impractical.