What it does
A stream after rain is a blend of rainwater, water from the soil and groundwater. A sediment is a blend of material eroded from different rocks. If each source has its own fingerprint, such as chloride, sulfate or an isotope ratio, you can work backwards from a sample to how much of each source it holds. That is an end-member mixing model.
For simple tracers the mass balance is linear: the sample’s value is the fraction-weighted average of the sources. Isotope δ values are different. They mix in proportion to how much of the element each source carries, so a source rich in carbon pulls δ¹³C towards itself and the mixing line curves. This tool handles both kinds together.
How to use it
- Paste or open the sources: a header row of tracer names, then one row per source with its name and values. Use two or three sources.
- Paste or open the samples with the same tracer columns. Thousands of rows are fine.
- If you have δ columns (named like d18O, δ13C or delta2H), choose which concentration column they should be weighted by, or none. For δ¹⁸O and δ²H of the water itself, use none. For the δ¹³C of dissolved carbon, weight it by the carbon concentration.
- Pick two tracers for the plot.
What you get
- A table of fractions for each sample, as percentages that add up to 100.
- A misfit for each sample: the root mean square of the tracer errors, each divided by that tracer’s spread between the sources. With more tracers than strictly needed (for three sources you need two), the misfit tells you whether the sources really explain the sample.
- A note when a sample sits outside the sources’ triangle (or beyond the ends of a two-source line). The tool then gives the closest possible mix and shows the unbounded fractions, which go below zero. That usually means a missing source or a tracer that reacts rather than simply mixing.
- A plot of two tracers with the sources and the mixing lines between them, curved where δ weighting applies.
Worked example
All numbers are made up. The three sources are rain (Cl 1, SO₄ 2, δ¹⁸O −12 ‰), soil water (15, 40, −8 ‰) and groundwater (60, 10, −5 ‰).
Stream 1 has Cl 35, SO₄ 17 and δ¹⁸O −7.25 ‰. The tool gives 20.1 % rain, 28.8 % soil water and 51.1 % groundwater, with a misfit of 0.003. Three tracers for three sources leave one check, and this sample passes it easily.
Change Stream 1’s δ¹⁸O to −13 ‰, lighter than any source. The tool marks the sample as outside and gives the nearest mix it can.
Good to know
- Tracers must be conservative: they mix without being added or removed by reactions. Chloride and water isotopes usually are; nitrate and sulfate often are not.
- Sources vary in real life. If their values are uncertain, try the edges of their ranges to see how much the fractions move.
- With noisy data and nearly identical sources, fractions can swing a lot. Choose tracers that separate the sources well.
FAQ
Can I use four sources? This tool stops at three, which is where a single plot can still show the result. Four sources need at least three good tracers and a more careful statistical treatment.
Why do my fractions sum to exactly 100 %? That is built in: the mixture contains only the sources you listed.
Where the numbers come from
- End-member mixing analysis and isotope mass balance: standard hydrology and geochemistry methods, written from the mass-balance equations.
- Example data are made up by fibub for illustration.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-08.