WASR 8000 · Week 6
WASR 8000 · Environmental Tracers in Hydrology · Fall 2026

Whose Nitrate Is This?

An interactive primer on the two isotopic fingerprints a nitrate ion carries — δ¹⁵N of its nitrogen and δ¹⁸O of its oxygen — on the sources those fingerprints can name, on the one process (denitrification) that forges them along a predictable slope, and on the mixing models and co-tracers that keep a reading honest. Builds on Weeks 2 and 5; no tracer background needed.

Week 6 companion · read alongside the three readings ≈ 45–55 minutes 11 interactive demos · self-check quiz
1 · The opening question

A well reads +18‰. Is that the dairy?

A farm-supply well in a sandy aquifer returns 12 mg L⁻¹ of nitrate-N — above the 10 mg L⁻¹ drinking-water limit — and the nitrate's δ¹⁵N is +18‰. The consultant's report is one sentence long: "δ¹⁵N above +10‰ indicates animal waste; the source is the dairy upgradient." The dairy disputes it. You are asked whether the isotope settles the matter.

Kendall & Aravena state the trap in one sentence: denitrification of fertilizer nitrate "that originally had a distinctive δ¹⁵N value of +0‰ can yield residual nitrate with much higher δ¹⁵N values (e.g., +15 to +30‰) that are similar to the range of compositions expected for nitrate from a manure or septic-tank source … making source determination difficult." The consultant's rule of thumb is not wrong about the ranges. It is wrong about what a range can prove.

That is Week 6 in one example. A nitrate ion carries two isotopic fingerprints — δ¹⁵N on its nitrogen, δ¹⁸O on its oxygen — and each of the usual sources leaves a recognisable print. But the same microbial process that removes nitrate from an aquifer also re-inks both prints along a predictable slope, so a forged fertilizer signal can look exactly like an honest manure one. The week's craft is telling the two apart: with the concentration trend (Rayleigh vs mixing), with the second isotope (the 2:1 slope), with the product gas (excess N₂), with a third oxygen isotope (Δ¹⁷O), and with tracers that ride along but do not react (boron).

The three readings divide the labour: Xue et al. (2009) compile the source ranges and audit the method's limits; Kendall, Elliott & Wankel (2007) supply the process systematics, the cross-plot, and the "what works" verdicts; Kendall & Aravena (2000) supply the groundwater case studies — the Chalk, Abbotsford, the septic plumes, the Delmarva riparian zones. This page is a map to all three, not a substitute for reading them.

2 · Why nitrate, and why two numbers

One ion, two memories

Nitrate is the water-quality problem of agricultural landscapes — mobile, persistent under oxygen, and regulated at 10 mg L⁻¹ as N because of methemoglobinemia in infants — and it is also an unusually informative molecule. Its single nitrogen atom remembers the history of the nitrogen (was the ammonium it came from stripped of light ammonia in a manure pile?); its three oxygen atoms remember the birthplace of the ion (were they pulled from soil water and O₂ by microbes, from the air by a fertilizer plant, or from ozone in a polluted sky?). Pick a pathway and watch which atoms carry which stamp.

Typical δ¹⁵N of the resulting nitrate
relative to atmospheric N₂ (AIR)
Typical δ¹⁸O of the resulting nitrate
relative to VSMOW
O from water (H₂O)O from O₂ (air, δ¹⁸O ≈ +23.5‰)O touched by ozone (Δ¹⁷O > 0)N enriched by ammonia loss

The nitrogen axis: a memory of loss

Air is the reference (δ¹⁵N = 0‰; ¹⁵N/¹⁴N = 1/272, and 0.3663% of nitrogen is ¹⁵N). Fertilizers are fixed from air and stay near it. Soil organic N sits a few per mil above. Manure and sewage are heavy because ammonia volatilization — a strongly fractionating escape of ¹⁴N-rich NH₃ gas, about 25‰ overall — leaves the remaining ammonium enriched, and nitrification then hands that enrichment to the nitrate. The nitrogen atom, in other words, remembers whether the pool it came from was ever skimmed of its light isotope.

The oxygen axis: a memory of birth

Microbial nitrate takes two oxygens from water and one from O₂ (eq. 12.1 below), so it inherits the local water's δ¹⁸O and lands between roughly −10 and +10‰. A fertilizer plant takes all three from air, so synthetic nitrate reads +17 to +25‰. Atmospheric nitrate is built from ozone-oxidised NOₓ and carries very high δ¹⁸O (+63 to +94‰ across the U.S. NADP network by the current method) plus an ozone-only anomaly, Δ¹⁷O, that no terrestrial process can make. The oxygen atoms remember where the ion was assembled — and, crucially, that birthplace is independent of the nitrogen's history, which is why two numbers separate sources that one cannot.

The isotope notation is Week 2's: δ = (Rsample/Rstandard − 1) × 1000, with AIR for nitrogen and VSMOW for oxygen. Precision is about 0.1‰ for δ¹⁵N and 0.1–0.5‰ for δ¹⁸O of nitrate. Everything else this week is about what a difference of a few per mil can and cannot prove.
3 · The one equation behind every process

Products run light, leftovers run heavy

Every microbial step that consumes a nitrogen pool prefers the lighter isotope, so the product is depleted and the residue grows steadily enriched. Kendall & Aravena's Fig. 9.1 draws this for denitrification with the Rayleigh equation; the same curves, relabelled, describe nitrification eating an ammonium pool and volatilization skimming ammonia off a manure pile. Switch the process, set the enrichment factor ε, and drag the reaction along.

δ = δ₀ + ε · ln f Kendall & Aravena eq. 9.6 · Xue eq. 4

δ₀ is the substrate's starting composition, f the fraction of substrate remaining, and ε = 1000(α − 1) the enrichment factor, negative when the product is lighter. The instantaneous product sits ε below the current residue; the accumulated product starts at δ₀ + ε and climbs back to δ₀ when the reaction is complete — because mass balance guarantees that all of the product, taken together, must average the starting value.

−10‰
0‰
60%
Residual NO₃⁻
δ¹⁵N of what is left
Instantaneous N₂
the product being made right now
Accumulated N₂
all product so far, pooled

δ¹⁵N vs reaction progress

Fixed axes: −40 to +60‰. The dotted curves are the Fig. 9.1 family (ε = −5, −10, −20‰) for reference.

residual substrateinstantaneous productaccumulated product

Denitrification

The residue (nitrate) is what you sample, so it is the orange curve that matters: δ¹⁵N climbs without limit as nitrate disappears — "values >100‰ are not unusual" (Kendall et al.). Measured ε ranges from −40 to −5‰; lab cultures give −29.4 to −24.6‰ at 20–30 °C; field aquifers cluster at −5 to −8‰ (Mariotti et al. 1988), either because fast denitrification fractionates less or because diffusion into dead-end pores hides the fractionation. The Kalahari's −30 ± 6‰ is read as very slow denitrification over ~14,000 years.

Nitrification

Now the product (nitrate) is what you sample, so read the aqua curve: the first-formed nitrate is light by ε (−5 to −35‰ relative to the ammonium; the NH₄⁺→NO₂⁻ step in culture gives −38 to −14‰), and the pooled nitrate climbs back to the ammonium's value only when the pool is used up. This is Feigin et al.'s (1974) field record (Fig. 9.3): anhydrous ammonia applied near 0‰ yields nitrate at −10‰ in late May and +6 to +8‰ by September, while the dwindling ammonium climbs past +13‰. Hence the advice to sample beneath fields long after application, when the pool is spent and the nitrate reads its source.

Volatilization

Here the residue (ammonium) is what later becomes nitrate, so the orange curve is the one that matters again — but now it is a source being manufactured. An overall ε near −25‰ (Kendall et al.) lifts ammonium from +5‰ to +22‰ once half has escaped as NH₃, which is why manure-derived nitrate reads +10 to +20‰ and manure piles exceed +20‰. The lost ammonia, as low as −20‰, blows downwind and becomes someone else's light atmospheric ammonium.

Two readings of the same curve. A +20‰ nitrate might be manure ammonium that was volatilized before nitrification (a source signal, made before the nitrate existed) or fertilizer nitrate that was partly denitrified afterwards (a process signal, made in the aquifer). Both are Rayleigh residues; only the accompanying evidence — concentration, oxygen, redox, product gas — says which.
4 · The source atlas

What each source usually looks like — and how much the boxes overlap

Xue et al. compiled published δ¹⁵N values for twelve categories of nitrate source and sink (their Fig. 1) and δ¹⁸O values for three modes of formation (their Fig. 2). The box plots below are redrawn from those figures (25th–75th percentile boxes, 10th–90th whiskers, outliers as circles; values read to about ±1‰). Click a row or column to read its range and what produces it.

δ¹⁵N of nitrate by source and sink

After Xue et al. (2009), Fig. 1. Whiskers: 10th and 90th percentiles.

δ¹⁸O of nitrate by mode of formation

After Xue et al. (2009), Fig. 2.

Click any box to see its published range and the reason behind it.

What the atlas can separate

  • Fertilizer vs manure or sewage (−6 to +6‰ vs +5 to +25‰ / +4 to +19‰): usually, with δ¹⁵N alone — provided the groundwater is oxic and sandy so that denitrification "can be (more-or-less) ruled out."
  • Atmospheric vs microbial nitrate: not with δ¹⁵N (both straddle 0‰), easily with δ¹⁸O (+25 to +75‰ or higher vs −10 to +10‰).
  • Nitrate fertilizer vs everything microbial: with δ¹⁸O (+17 to +25‰ vs the nitrification band) — but only if the fertilizer really was nitrate; most applied fertilizer is ammonium or urea, which is nitrified in the soil and loses the distinction.

What it cannot

  • Soil N vs fertilizer: soil nitrate (0 to +8‰) overlaps fertilizer-derived nitrate (+4.7 ± 5.4‰ in Kendall's compilation) — "usually cannot be differentiated using δ¹⁵N alone."
  • Septic waste vs animal manure, or one farm animal vs another: "almost never" with δ¹⁵N alone; both are volatilization-enriched ammonium.
  • Any source, once denitrified: the residue drifts rightward into the manure box (Section 7).

Xue et al.'s effect-size meta-analysis puts a number on the second isotope: adding δ¹⁸O to δ¹⁵N helps on average (Hedges' d = 0.5, 95% CI 0.13–0.83) but the help is uneven — strongly positive for atmospheric and nitrate-fertilizer cases, negative for manure and sewage, whose δ¹⁸O is the same microbial value as everyone else's.

5 · The dual-isotope cross-plot

Reading a δ¹⁵N–δ¹⁸O diagram

Put the two memories on two axes and the sources spread into boxes: this is Kendall, Elliott & Wankel's Fig. 12.1, the figure every nitrate-isotope paper since has redrawn. The boxes below are traced from it (reading precision ±1‰); the two arrows are their denitrification vectors, starting from δ¹⁵N = +6‰, δ¹⁸O = −9‰, with slopes of 1:1 and 2:1. Drop a sample with the sliders or by clicking the plot, load a published data set, and — the important move — ask where the sample could have started if it has been denitrified.

δ¹⁸O vs δ¹⁵N of nitrate, with source boxes after Kendall et al. (2007) Fig. 12.1

Fixed axes: δ¹⁵N −20 to +35‰, δ¹⁸O −20 to +100‰. Click anywhere to place the sample.

+18‰
+4‰

How to read it

  • Vertical position is birthplace. Anything above ~+25‰ was assembled from atmospheric oxygen (nitrate fertilizer, +17 to +25‰; atmospheric nitrate, higher still). Anything in the nitrification band (drawn here as −16 to +15‰, after Fig. 12.1) was nitrified from ammonium in soil or water.
  • Horizontal position is history. Within the nitrification band, δ¹⁵N sorts fertilizer/rain ammonium (−10 to +4‰), soil (+2 to +8‰) and manure/septic (+5 to +25‰).
  • Diagonal trends are process. Denitrification moves a sample up and to the right along a slope of about 0.5 (δ¹⁸O:δ¹⁵N = 1:2) in most freshwater data sets, and 1:1 in pure cultures. Assimilation by algae does the same at 1:1.

Two atmospheric boxes?

The figure carries two: nitrate in precipitation analysed by the older silver-nitrate method (δ¹⁸O about +28 to +84‰; Kendall's 1998 survey gave +14 to +75‰) and by the denitrifier method (+60 to +98‰; across ~150 U.S. NADP sites, +63 to +94‰, mean +76.3‰). Kendall et al. suspect the older sealed-tube values suffered a "permil-scale contraction" from oxygen exchange with glass and O-bearing contaminants. The practical consequence: when you compare a new sample with an older paper's boxes, check which method drew the box (Section 13).

6 · Where microbial nitrate gets its oxygen

Two from water, one from air — in theory

Laboratory cultures show nitrifiers taking two of nitrate's three oxygens from water and one from dissolved O₂. If none of the steps fractionates and the microbes use bulk soil water and atmospheric O₂ (+23.5‰), the δ¹⁸O of new nitrate is a weighted average — and the whole "nitrification band" of the cross-plot follows from the range of meteoric water. Set the water, the O₂, and the mixing ratio.

δ¹⁸ONO₃ = ⅔ δ¹⁸OH₂O + ⅓ δ¹⁸OO₂ Kendall & Aravena eq. 9.8 · Kendall et al. eq. 12.1
−8‰
+23.5‰
1/3
Predicted δ¹⁸O of new nitrate
from the equation as set
Water's contribution
(1 − f) × δ¹⁸OH₂O
O₂'s contribution
f × δ¹⁸OO₂

Predicted nitrate δ¹⁸O against the water it formed in

Fixed axes. The line is the equation for the current O₂ and fraction; the marker is your water. Bands: theoretical −10 to +10‰; observed microbial −5 to +15‰; nitrate fertilizer +17 to +25‰.

Four assumptions, five explanations

The equation assumes (1) soils use the same 2:1 proportion as cultures, (2) no fractionation on incorporation, (3) the microbes' water is the bulk soil water, and (4) their O₂ is atmospheric O₂. Field nitrate often reads a few per mil — up to 5‰ — above the prediction. The candidate reasons, from Xue et al. and both Kendall chapters: evaporated (heavier) soil water; soil O₂ made heavy by respiration; fractionation during incorporation; more than one-third of the oxygen from O₂ when ammonium is limiting; and more than one nitrification pathway. Exchange of nitrate oxygen with water is ruled out as the cause — it would make the nitrate lighter, not heavier.

The Abbotsford check

Wassenaar's aquifer has groundwater at −10 to −12‰, so nitrified nitrate "was expected to have δ¹⁸O values from about −1 to +1‰." The observed nitrate ran +2 to +5‰, as high as +10‰ — attributed to summer nitrification in evaporatively enriched soil water, or minor denitrification under the manure piles. A 3‰ surplus is small on the cross-plot and large as a diagnostic: it is the difference between "the equation works" and "something else is happening." Kendall et al. add a useful test — plot δ¹⁸ONO₃ against δ¹⁸OH₂O: nitrification in contact with the local water gives a correlation; denitrification gives none.

7 · The forger and the informant

Denitrification moves a sample along a slope you can predict

Under oxygen below about 20 µM, facultative bacteria switch from breathing O₂ to breathing nitrate (4NO₃⁻ + 5CH₂O + 4H⁺ → 2N₂ + 5CO₂ + 7H₂O; with pyrite as donor, 14NO₃⁻ + 5FeS₂ + 4H⁺ → 7N₂ + 10SO₄²⁻ + 5Fe²⁺ + 2H₂O). Both atoms of the nitrate molecule fractionate together, so the residue climbs a straight line on the cross-plot — Böttcher et al.'s Fuhrberger Feld data gave ε¹⁵N = −15.9‰ and ε¹⁸O = −8.0‰ (a regression slope of 1:2.1), and most freshwater studies since fall between 0.5 and 0.7. Set the start, the enrichment factors and the fraction removed, and watch the forgery happen.

+3‰
+2‰
−15.9‰
2.0 : 1
60%
28 mg/L

The path on the cross-plot

Same frame as Section 5 (δ¹⁵N −20 to +35‰, δ¹⁸O −20 to +40‰ shown). Ticks mark 50%, 80%, 90% and 95% removal.

The same path against concentration

δ¹⁵N (orange) and δ¹⁸O (blue) vs nitrate-N on a log axis — Rayleigh residues are straight lines here. Fixed axes: 0.3–60 mg L⁻¹; −20 to +60‰.

Residual δ¹⁵N
Residual δ¹⁸O
ε¹⁸O =
NO₃⁻-N left
of the starting concentration

The forger

Start at fertilizer values and remove enough nitrate and the residue lands in the manure box. How much is "enough" depends entirely on ε: with the field-typical −5‰, a +15‰ shift requires losing 95% of the nitrate; with −20‰, 53%; with the Kalahari's −30‰, 39%. The same +15‰ can therefore mean a nearly exhausted plume or a half-consumed one — the isotope alone does not say which, and the concentration is the second witness.

The informant

Turned around, the same slope is evidence for denitrification and against dilution: a linear δ¹⁵N–δ¹⁸O trend with slope ~0.5, low nitrate paired with high δ, low dissolved oxygen, and a straight line against ln[NO₃⁻] (Section 8). Mengis et al. used exactly this in an Ontario riparian zone to show that nitrate loss was denitrification, not mixing of shallow high-nitrate and deep low-nitrate groundwater; Cey et al., with no clear δ¹⁵N–concentration trend at their site, needed the δ¹⁸O pairing (plus oxygen and Eh) to reach the same verdict.

The unsettled slope

Why ~0.5 in aquifers when pure denitrifier cultures give 1:1 (Granger 2006; Sigman et al. 2005)? Kendall et al. list the suspects: a "permil-scale contraction" in older δ¹⁸O data; co-occurring nitrate assimilation or anaerobic nitrification; enzyme-catalysed O exchange between nitrite and water with re-oxidation; and the NAP-enzyme "auxiliary denitrification" pathway, which gives 0.6. "Clearly, further work is needed" — and a critique of any 2007-era slope argument should say so.

8 · The three-plot test

Mixing bends one way, Rayleigh bends the other

A drop in nitrate along a flowpath with rising δ¹⁵N has two innocent explanations: microbes ate the nitrate (Rayleigh), or nitrate-free water diluted it while carrying a different δ¹⁵N (mixing). On a plot of δ against concentration both look like curves. Mariotti et al. (1988) supplied the discriminating trick, which Kendall et al. redraw as Fig. 12.6: mixing is a straight line against 1/[NO₃⁻] (eq. 9.11), Rayleigh is a straight line against ln[NO₃⁻] (eq. 9.6). Set the two processes side by side, then test yourself on a noisy data set.

δm = (Qaδa + Qbδb) / Qm, with Q = V × C Kendall & Aravena eq. 9.11

The explorer

Both processes start from the same water: 200 µM nitrate at δ¹⁵N = +5‰ (Kendall et al.'s Fig. 12.6). Mixing dilutes it with a second water; denitrification consumes it with enrichment factor ε.

1 µM
+40‰
−10‰
Look for the panel where a process is straight. Only a straight line lets you extrapolate: the slope of δ vs ln C is ε itself (the Chalk's regression, δ¹⁵N = 24.1 − 4.9 ln[N-NO₃⁻], r = 0.97, gives ε ≈ −4.9‰), and a straight δ vs 1/C line lets you extrapolate toward the end members. Fixed axes on all six panels: δ¹⁵N 0 to +45‰.

δ¹⁵N vs [NO₃⁻]

δ¹⁵N vs ln [NO₃⁻]

δ¹⁵N vs 1/[NO₃⁻]

mixingdenitrification (your ε)denitrification, ε = −5‰ and −10‰ (reference)

Test yourself: which process made these samples?

Twelve samples from a hidden process, with 1‰ of measurement noise and a random enrichment factor or end member. Decide from the three panels, then reveal.

δ¹⁵N vs [NO₃⁻]

δ¹⁵N vs ln [NO₃⁻]

δ¹⁵N vs 1/[NO₃⁻]

Score: 0 of 0. Hint: the straight panel is the honest one — and with only a modest range of concentrations, both can look straight everywhere.

The trap Kendall et al. flag with Fig. 12.6a: for nitrate between about 100 and 200 µM, all three curves are nearly linear, and "an incautious worker could try to interpret all three as mixing lines." The test needs a wide concentration range. Two wells do not make a curve.
9 · Auditing the product

Excess N₂: the denitrifier's receipt

Every nitrate ion that is denitrified becomes half a molecule of N₂, and that N₂ stays dissolved in the groundwater on top of the N₂ the water absorbed from air at recharge. Böhlke & Denver (1995) read the receipt on the Delmarva Peninsula: argon has no biological source, so a sample's Ar fixes its recharge temperature and the N₂ it should have; whatever N₂ is left over was made underground. When denitrification has run to completion, the δ¹⁵N of that excess N₂ recovers the δ¹⁵N of the nitrate that was destroyed — the source signal, before the forgery. Set the recharge conditions and the amount denitrified.

9 °C
0 cm³/L
270 µM
100%
+4‰

Argon against nitrogen, after Böhlke & Denver's Fig. 9.8a

The curve is air-saturated water from 0 to 25 °C (Weiss 1970 solubilities). Excess air pushes a sample along the air ratio (N₂/Ar = 83.5); denitrification pushes it horizontally. Fixed axes: 450–1000 µM N₂, 12–23 µM Ar.

shaded: Delmarva oxic waters, recharge at 9 ± 3 °Cexcess-air vectorexcess N₂

δ¹⁵N of dissolved N₂ against Ar/N₂, after Fig. 9.8b

Air-saturated water sits at the right (dissolution enriches N₂ by 0.7‰); excess N₂ pulls the point along the mixing line toward Ar/N₂ = 0, whose intercept is the δ¹⁵N of the excess N₂.

Dissolved N₂
air-equilibrated + excess air µM, plus excess N₂
Dissolved Ar
N₂/Ar =
Excess N₂
= of nitrate reduced
δ¹⁵N of excess N₂
accumulated product (ε = −15‰)
δ¹⁵N of total dissolved N₂
what the mass spectrometer sees
δ¹⁵N of the surviving nitrate
the forged number in the well

The Delmarva reading

Oxic waters plotted on the air-saturation line at 9 ± 3 °C; suboxic, nitrate-free waters carried up to 135 µM of excess N₂ — "equivalent to 270 µM reduced NO₃⁻" — and their excess N₂ had δ¹⁵N between +2 and +5‰, "indistinguishable from the range of δ¹⁵N of NO₃⁻ in oxic groundwaters from the same location where no denitrification has occurred." Complete denitrification returns N₂ with the initial nitrate's δ¹⁵N (Section 3's accumulated-product curve ends at δ₀), so the receipt names the source even when no nitrate survives to be measured. The trap: dissolved bubbles of trapped air (N₂/Ar = 83.5 against 37.3–38.3 for air-equilibrated water) also raise N₂/Ar, so recharge temperature and excess air must be fixed from Ar (or Ne) first — Week 5's noble-gas ledger, and Week 7's subject.

Why this is the strongest denitrification tool

Kendall et al. list it first among the "five most successful new isotopic approaches," and note that δ¹⁸ONO₃ "usually is not as useful for determining extent of denitrification as δ¹⁵NN₂." The nitrate isotopes describe the residue; the gas describes the loss itself, in moles. With groundwater ages from CFCs (Week 5) the two together turn a plume into a history: Böhlke & Denver's dated, denitrification-corrected recharge showed nitrate rising about fivefold between 1950 and 1990, in step with fertilizer use — a fertilizer record recovered from an aquifer where none was kept on paper.

10 · From reading to apportioning

Three sources, two isotopes, one honest answer per sample

Two measured numbers plus one constraint (fractions sum to one) fix exactly three unknown fractions — Xue et al.'s eqs. 6–8, the mass-balance model Deutsch et al. used to attribute a German river's nitrate 86% to drained agricultural soils, 11% to groundwater and 3% to atmospheric deposition. Drag the sample around the triangle of end members, then let denitrification act on it and watch the apportionment lie.

δ¹⁵NM = f₁δ¹⁵N₁ + f₂δ¹⁵N₂ + f₃δ¹⁵N₃  ·  δ¹⁸OM = f₁δ¹⁸O₁ + f₂δ¹⁸O₂ + f₃δ¹⁸O₃  ·  1 = f₁ + f₂ + f₃ Xue eqs. 6–8

End-member triangle on the cross-plot

Fixed axes: δ¹⁵N −10 to +30‰, δ¹⁸O −10 to +90‰. Click to place the sample (the filled marker); the hollow marker is where it sits after the denitrification you apply.

+4‰
+8‰
0%

End members (editable presets): fertilizer/soil ammonium-derived nitrate, manure/septic, atmospheric. Denitrification uses ε¹⁵N = −15‰ at 2:1.

Three ways the algebra lies

Moore & Semmens' objections, as Xue et al. relay them: the end members vary in time and space (a single value per source is a fiction); denitrification moves the sample after mixing (the fractions then describe a point that never existed); and real systems have more sources than the equations can hold (four sources, two isotopes: underdetermined). Kendall et al. put it bluntly — "the successful solution of the mixing algebra does not ensure that the source determinations are accurate" — and set the bar for a "quantitative" tool at fractions good to about ±20%.

What replaces the 3×3 solve

Bayesian mixing models — SIAR in Xue et al.'s outlook, built on a Dirichlet prior over the fractions — accept end members as distributions, carry a fractionation term per source and isotope, and return a probability distribution for each contribution rather than a single number. They do not repair a missing end member or an unrecognised process; they make the resulting uncertainty visible. The cheaper defence is the one Kendall & Aravena insist on: characterise the end members beneath where each source is applied, after nitrification, not from the bag of fertilizer or the manure pile.

11 · The unforgeable tag

Δ¹⁷O: a fingerprint no aquifer process can alter

Every ordinary fractionation moves ¹⁷O about half as far as ¹⁸O, so all terrestrial oxygen falls on one line, δ¹⁷O ≈ 0.52 δ¹⁸O. Ozone is the exception: its formation is mass-independent, it carries about +35‰ of excess ¹⁷O, and it passes that excess to the nitrate it helps make. Atmospheric nitrate therefore arrives with Δ¹⁷O of +20 to +30‰; nitrate made by microbes has Δ¹⁷O = 0; and — this is the point — denitrification, assimilation and every other mass-dependent process slide a sample along the line, leaving Δ¹⁷O untouched. Mix the two sources, then denitrify the mixture, and compare what δ¹⁸O and Δ¹⁷O each claim.

Δ¹⁷O = δ¹⁷O − 0.52 · δ¹⁸O Kendall et al., Fig. 12.4 (Michalski et al. 2002)
30%
+25‰
0%

End members: atmospheric nitrate δ¹⁸O = +76‰ (the NADP mean), microbial nitrate δ¹⁸O = +3‰, Δ¹⁷O = 0. Denitrification uses ε¹⁸O = −8‰.

Triple-oxygen plot, after Kendall et al. Fig. 12.4

Fixed axes: δ¹⁸O −10 to +100‰, δ¹⁷O −10 to +70‰. Mass-dependent line in grey; mixing line dashed; the vertical bracket is Δ¹⁷O.

δ¹⁸O of the sample
after mixing and loss
Δ¹⁷O of the sample
unchanged by loss
Atmospheric fraction, from δ¹⁸O alone
(δ¹⁸O − 3) / (76 − 3)
Atmospheric fraction, from Δ¹⁷O
Δ¹⁷O / Δ¹⁷Oatm

What the anomaly buys

With 0.1‰ resolution on Δ¹⁷O, atmospheric nitrate is detectable at 0.5% of total nitrate (Michalski et al. 2004) — "in the absence of any recycling of atmospheric nitrate in the watershed (admittedly a large caveat)." In the two storm studies that measured both, δ¹⁸O "significantly underestimated" the atmospheric contribution to runoff, and in the Neuse River watershed the Δ¹⁷O peaks were sharp and on the falling limb while δ¹⁸O showed only a broad hump (Fig. 12.7). The anomaly can also be run backwards: since Δ¹⁷O fixes the atmospheric fraction, the original δ¹⁸O can be reconstructed and the shift attributed to consumption.

What it cannot

Nitrification erases it. Atmospheric nitrate that is taken up, mineralised and re-nitrified comes back with the terrestrial Δ¹⁷O of zero — which is how Loch Vale's stream nitrate during snowmelt turned out to be half or more microbial, "probably originally of atmospheric origin but had lost its atmospheric signature during microbial recycling in the talus." A zero anomaly means no unrecycled atmospheric nitrate, not no atmospheric nitrogen. Its seasonality is a second subtlety: Δ¹⁷O runs about +20‰ in summer rain and +30‰ in winter, tracking the shift from OH-driven to N₂O₅-driven nitric-acid formation (Fig. 12.5), so the atmospheric end member is a moving target.

12 · Tracers that ride along without reacting

What works, what doesn't, and what to add

Kendall, Elliott & Wankel close their chapter with a plain-language ledger of which source pairs the nitrate isotopes can separate, and under what conditions; Xue et al. add the co-migrating discriminator that rescues the hardest case. Click a row for the conditions and the tracer that helps. The verdicts are theirs; the conditions are the fine print that a critique should quote.

Source pairδ¹⁵N aloneAdding δ¹⁸OWhat settles it

Select a row.

Boron beside nitrogen: δ¹¹B vs δ¹⁵N of the usual suspects

Ranges from Xue et al. (δ¹¹B) and their Fig. 1 (δ¹⁵N). Hover a box.

Why boron

Boron is in nearly every water, is not touched by nitrification or denitrification, and its two isotopes (¹¹B ≈ 80%, ¹⁰B ≈ 20%) span about 90‰ in nature. Sewage carries the boron of perborate laundry bleach and reads δ¹¹B from −7.7 to +12.9‰; manure runs +6.9 to +42.1‰; fertilizers +8 to +17‰. So the pair that δ¹⁵N "almost never" separates — sewage from animal waste — comes apart on a δ¹¹B axis, which is exactly how Widory et al. (2004, 2005) sorted fertilizer, greenhouse discharge, sewage and hog, cattle and poultry manure in French aquifers, and how Seiler (2005) split domestic wastewater from fertilizer in Nevada. The caveat, in both readings: boron is fractionated by adsorption on clays and oxides, so the tracer is conservative in the sense that matters (no redox reaction) and not in every sense.

The wider toolkit in Kendall et al.: ⁸⁷Sr/⁸⁶Sr (fertilizer distinctive, animals not, and water–rock exchange often overprints it), δ³⁴S of sulfate, δ⁷Li (industrial lithium at +200 to +400‰), δ¹⁸O of phosphate, water δ¹⁸O and δ²H, chloride, potassium, caffeine and pharmaceuticals, DNA — and, humbler than any of them, a good hydrogeological model.

13 · How the numbers are made

Three ways to turn a litre of water into two δ values

The method matters more here than in most tracer work, because the δ¹⁸O of nitrate is a hard measurement and the field's reference boxes were drawn with different techniques. Xue et al. describe the three routes; Kendall et al. explain why the oldest one may have compressed the δ¹⁸O scale.

Ion exchange ("AgNO₃ method")

Chang et al. 1999; Silva et al. 2000. Concentrate nitrate on anion resin (can be done in the field), elute with HCl, neutralise with Ag₂O, strip other O-bearing anions with BaCl₂, freeze-dry to AgNO₃; combust to N₂ (850 °C) and CO₂, or pyrolyse to N₂ + CO (1400 °C, TC/EA).

Preparation3–5 days
Consumablesup to 60 € per sample
Nitrate needed100–200 µmol
Weak spotCl⁻, SO₄²⁻, DOC interfere; large volumes for dilute water

Bacterial denitrifier method

Sigman et al. 2001; Casciotti et al. 2002. Denitrifying bacteria that lack N₂O reductase convert the sample's nitrate to N₂O overnight; the gas is purified and measured for both isotopes. Now the standard; every atmospheric nitrate it has measured reads above +60‰.

Preparation2–3 days (plus 10–12 days of culture growth)
Consumablesup to 5 € per sample
Nitrate needed~100 nmol — a thousandth of the resin method
Weak spottoxic samples stall the culture; NO₂⁻ biases N₂O; δ¹⁸O needs corrections for O loss and exchange

Cadmium–azide chemical reduction

McIlvin & Altabet 2005. Spongy cadmium reduces nitrate to nitrite overnight (or in minutes on a copperised column); sodium azide in acetic acid reduces nitrite to N₂O; measure as above.

Preparationwithin a day
Consumablescheap; cadmium reusable
Nitrate neededworks at 0.5 µmol L⁻¹
Weak spotcadmium, azide and HN₃ are toxic; same O-exchange corrections; still "requires further demonstration" (2009)
The permil-scale contraction. Kendall et al. suspect that sealed-tube combustion of silver nitrate let oxygen exchange with the glass and picked up O from contaminants in the AgNO₃, especially below the recommended 100–200 µmol of CO₂ — squeezing the δ¹⁸O scale toward the middle. Three consequences worth carrying into the readings: the two atmospheric boxes on Fig. 12.1; the possibility that some published denitrification slopes of ~0.5 would steepen on an uncontracted scale; and a rule for the term paper — when quoting a pre-2002 δ¹⁸ONO₃ value, quote the method with it.
14 · Reading the three sources

Three readings, three blocks, one molecule

Xue et al. supply the ranges and the audit; Kendall, Elliott & Wankel supply the process systematics and the verdicts; Kendall & Aravena supply the aquifers. The guides below are maps, not substitutes: what each asks, where its load-bearing figures live, which equations to recognize, which numbers to be able to quote, and where a careful reader might press. The notes and the critique are yours to write.

Block 1 · Core reading

Xue, D., Botte, J., De Baets, B., Accoe, F., Nestler, A., Taylor, P., Van Cleemput, O., Berglund, M., & Boeckx, P. (2009). Present limitations and future prospects of stable isotope methods for nitrate source identification in surface- and groundwater. Water Research, 43(5), 1159–1170.

Twelve pages that compile the source boxes, weigh the second isotope statistically, name the two ways the boxes fail (mixing and fractionation), and propose the fixes: co-migrating tracers, Bayesian mixing, and cheaper analysis. doi:10.1016/j.watres.2008.12.048

Block 2 · Supplementary reading

Kendall, C., Elliott, E. M., & Wankel, S. D. (2007). Tracing anthropogenic inputs of nitrogen to ecosystems. In R. Michener & K. Lajtha (eds.), Stable Isotopes in Ecology and Environmental Science (2nd ed., pp. 375–449). Blackwell.

The long-form chapter: the Kohl–Hauck controversy that stalled the field, the isotopic composition of every major N reservoir, each process in turn, mixing vs cycling, applications by setting, and a "what works" ledger. doi:10.1002/9780470691854.ch12

Block 3 · Supplementary reading

Kendall, C., & Aravena, R. (2000). Nitrate isotopes in groundwater systems. In P. G. Cook & A. L. Herczeg (eds.), Environmental Tracers in Subsurface Hydrology (pp. 261–297). Kluwer.

The groundwater chapter of the book that supplied Weeks 3 and 5: fundamentals, the nitrogen cycle process by process, the reservoirs, and then the case studies — Runnels County, Grand Cayman, Abbotsford, the septic plumes, the Chalk, Fuhrberger Feld, Delmarva, the Boyne River. doi:10.1007/978-1-4615-4557-6_9

Cross-paper synthesis, in one line: Xue et al. show how much the source boxes overlap and how a process can move a sample between them; Kendall, Elliott & Wankel explain the processes and rule on which pairs of sources the isotopes can actually separate; Kendall & Aravena show the method working — and needing help — in real aquifers. The question that carries forward: for the nitrate your proposal cares about, which pair of sources must you separate, which process could forge the difference, and which measurement would catch the forgery?
15 · Practice

Four situations to reason through

Each scenario gives the kind of evidence a Week 6 reader should now be able to interrogate. Choose the reading you would defend first, then compare with the debrief.

Habit to keep: before naming a nitrate source, say aloud which two boxes you are choosing between, what the dissolved oxygen was, which way the concentration moved with δ, and which measurement would expose a denitrified impostor. A source assignment that cannot survive those four questions is a box plot wearing a lab coat.
16 · Self-check

Ten questions before the meeting

Immediate feedback, no grade, no record. If you miss one, the linked section is the fix.

17 · Vocabulary

Glossary

The Week 6 working vocabulary, with a few terms you will meet again in Weeks 7 and 11. Search or browse.

18 · Where to go next

The Week 6 readings — and one optional companion

Papers are not posted for this course: retrieving them from the citation and DOI — via the UGA Libraries, GALILEO, or the publisher — is part of the training. All three are chapters or articles behind publisher walls; the library holds each.

CORE

Xue, D., et al. (2009). Present limitations and future prospects of stable isotope methods for nitrate source identification in surface- and groundwater. Water Research, 43(5), 1159–1170.

Source ranges (Figs. 1–2); the effect-size audit (Fig. 3); the fractionating processes; hydrochemistry and land use; boron; the mixing model and SIAR; three analytical methods compared. doi:10.1016/j.watres.2008.12.048

CHAPTER

Kendall, C., Elliott, E. M., & Wankel, S. D. (2007). Tracing anthropogenic inputs of nitrogen to ecosystems. In Michener & Lajtha (eds.), Stable Isotopes in Ecology and Environmental Science (2nd ed., pp. 375–449). Blackwell.

The Kohl–Hauck controversy; sources (Fig. 12.1) including NADP precipitation; processes; Δ¹⁷O (Figs. 12.4–12.5); mixing vs cycling (Fig. 12.6); settings from forests to estuaries; the "what works" ledger; the multi-tracer toolkit. doi:10.1002/9780470691854.ch12

CHAPTER

Kendall, C., & Aravena, R. (2000). Nitrate isotopes in groundwater systems. In Cook & Herczeg (eds.), Environmental Tracers in Subsurface Hydrology (pp. 261–297). Kluwer.

Fundamentals and the Rayleigh equation (Fig. 9.1); the nitrogen cycle (Figs. 9.2–9.4); sources and case studies — soil N, septic plumes (Fig. 9.5), Abbotsford (Fig. 9.6), the Chalk (Fig. 9.7), excess N₂ (Fig. 9.8), Delmarva (Fig. 9.9), the Boyne riparian zone (Fig. 9.10). doi:10.1007/978-1-4615-4557-6_9

OPTIONAL

Aravena, R., & Robertson, W. D. (1998). Use of multiple isotope tracers to evaluate denitrification in ground water: study of nitrate from a large-flux septic system plume. Ground Water, 36(6), 975–982.

The septic-plume study behind Fig. 9.5: δ¹⁵N and δ¹⁸O of nitrate together with δ³⁴S and δ¹⁸O of sulfate, showing reduced sulfur as well as carbon acting as electron donor. Not discussed in a block.

Next week — contaminant source identification II: noble gases

The excess air that complicated Section 9's N₂/Ar ledger, and the recharge temperature that set Week 5's gas clocks, get their own week: dissolved Ne, Ar, Kr and Xe as thermometers of recharge, the closed-system-equilibration model of excess air, and what noble-gas records say about contamination histories and past climate. Everything this week said about a reactive tracer's fingerprint now meets a family of tracers that do not react at all.

Carry-forward question, for your proposal one-pager: if your question involves a solute rather than the water itself, which two sources must you separate, and which process between source and sample could move the tracer from one box into the other — and what is the cheapest measurement that would tell you it had?