Multi-tracer assessment of seasonal water source changes in coastal water systems along the southeastern coast of Ivory Coast (West Africa)

Osemwegie, Isimemen; Stumpp, Christine; Barthélemy, Jean; Reichert, Barbara

doi:10.1080/02626667.2018.1558366

Cited by 6 publications

(2 citation statements)

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“…Following Osemwegie et al (2018) the theoretical endmembers can be defined as such:

U 1_{p} goodbreak= f_{D} U 1_{D} goodbreak+ f_{N} U 1_{N} goodbreak+ f_{F} U 1_{F}

U 2_{p} goodbreak= f_{D} U 2_{D} goodbreak+ f_{N} U 2_{N} goodbreak+ f_{F} U 2_{F}

f_{D} goodbreak+ f_{N} goodbreak+ f_{F} goodbreak= 1

where

U 1

and

U 2

are the two vectors defining the mixing subspace U ,

U 1_{p}

and

U 2_{p}

are the coordinates of p (generic sample point whose chemical composition is the produced by the three‐component mixing) and D , N and F subscripts detects the coordinates of the three endmembers. Combining Equations (), the mixing fractions can be obtained as follows:

f_{D} goodbreak= \frac{([], U 2_{p} ((), U 1_{N} goodbreak- U 1_{F})) - ([], U 1_{p} ((), U 2_{N} goodbreak- U 2_{F})) + ([], U 1_{F} ((), U 2_{N} goodbreak- U 2_{F})) - ([], U 2_{F} ((), U 1_{N} goodbreak- U 1_{F}))}{[(U 2_{D} - U 2_{F}) (U 1_{N} - U 1_{F}) - (U 1_{D} - U 1_{F}) (U 2_{N} -)]}

…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

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

Cuoco

Viaroli

Darrah

et al. 2021

Hydrological Processes

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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.

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“…Following Osemwegie et al (2018) the theoretical endmembers can be defined as such:

U 1_{p} goodbreak= f_{D} U 1_{D} goodbreak+ f_{N} U 1_{N} goodbreak+ f_{F} U 1_{F}

U 2_{p} goodbreak= f_{D} U 2_{D} goodbreak+ f_{N} U 2_{N} goodbreak+ f_{F} U 2_{F}

f_{D} goodbreak+ f_{N} goodbreak+ f_{F} goodbreak= 1

where

U 1

and

U 2

are the two vectors defining the mixing subspace U ,

U 1_{p}

and

U 2_{p}

f_{D} goodbreak= \frac{([], U 2_{p} ((), U 1_{N} goodbreak- U 1_{F})) - ([], U 1_{p} ((), U 2_{N} goodbreak- U 2_{F})) + ([], U 1_{F} ((), U 2_{N} goodbreak- U 2_{F})) - ([], U 2_{F} ((), U 1_{N} goodbreak- U 1_{F}))}{[(U 2_{D} - U 2_{F}) (U 1_{N} - U 1_{F}) - (U 1_{D} - U 1_{F}) (U 2_{N} -)]}

…”

Section: Resultsmentioning

confidence: 99%

“…The number of endmembers is given by m + 1, where m is the number of eigenvalues retained. In Following Osemwegie et al (2018) the theoretical endmembers can be defined as such:…”

Section: Fractions Quantification and Analytical Representationmentioning

confidence: 99%