A geometrical method for quantifying endmembers' fractions in three-component groundwater mixing

We present a new geometrical method capable of quantifying and illustrating the outcomes of a three-component mixing dynamics. In a three-component mixing scenario, classical algebraic equations and endmember mixing analysis (EMMA) can be used to quantify the contributions from each fraction. Three-component mixing of natural waters, either in an element–element plot or by using the EMMA mixing subspace is described by a triangular shaped distribution of sample points where each endmember is placed on an apex, while each side corresponds to the mixing function of the two endmembers placed at the apex, considering the third endmembers' contribution equal to zero. Along each side, the theoretical mixing fractions can be computed using mass balance equations. Samples with contributions from three endmembers will plot inside the triangle, while the homogeneous barycentric coordinate projections can be projected onto the three sides. The geochemistry observed in the mineralized Ferrarelle aquifer system (southern Italy) results from three-component mixing of groundwater, each with diagnostic geochemical compositions. The defined boundary conditions allow us to parameterize and validate the procedures for modelling mixing, including selection of suitable geochemical tracers.