The Gases That Do Nothing
An interactive primer on the five gases that never react — and therefore remember only physics: the temperature at the water table when rain became groundwater, the air that was trapped and squeezed into solution on the way down, and the helium that the rock has been adding ever since. Recharge thermometry, excess air and its three models, the inverse fit that lets the data choose among them, and what the records say about past climate and contamination histories. Builds on Weeks 3, 5 and 6; no tracer background needed.
Five degrees colder — or an artifact of a bubble?
In 1995 a group led by Martin Stute measured the noble gases dissolved in old groundwater from a semi-arid aquifer in tropical Brazil and reported that the last glacial maximum had been about 5 °C cooler there than today — a number that landed in the middle of an argument about how much the tropics cooled. Four years later two other noble-gas specialists argued that the cooling was an artifact: the "excess air" in the samples was fractionated, the fractionation had been modelled inadequately, and the temperature had absorbed the error. A year after that, a new model of excess air was applied to the same data and the 5 °C came back. Same samples, three verdicts. Where would you stand?
Kipfer and colleagues tell the story in two sentences: the Brazilian result "was challenged on grounds of insufficient modelling of the excess air fractionation by Ballentine and Hall (1999), but later confirmed by using the CE-model for excess air (Aeschbach-Hertig et al. 2000)." Other tropical records then fell into line, "suggesting that the tropics and subtropics … cooled rather uniformly by around 5°C during the LGM." The number survived — but only because the bubble finally got a physical description that could be tested.
The three readings divide the labour: Kipfer, Aeschbach-Hertig, Peeters & Stute (2002) is the full review — components, solubilities, the three excess-air models, the inverse method, lakes, dating and paleoclimate; Aeschbach-Hertig, Peeters, Beyerle & Kipfer (1999) is the method paper that turned "correct for excess air, then read the temperature" into a least-squares fit with honest error bars (note: it predates the CE model, which arrived in 2000); White (2015, Ch. 12) supplies the geochemical backdrop — where the noble gases came from, why helium has three parents, and what the isotope ratios say about crust, mantle and air. This page is a map to all three, not a substitute for reading them.
A tracer that does nothing tells you the most
Every tracer so far in this course carried a chemical liability. Nitrate is eaten; CFC-11 is degraded under anoxia; carbon exchanges with the aquifer; even water's own isotopes exchange with the rock in the hot crust. Helium, neon, argon, krypton and xenon have full outer electron shells; helium's first ionization potential, 2373 kJ mol⁻¹, is the highest of any element, and although the potential falls steeply down the group (xenon's, 1170 kJ mol⁻¹, sits below hydrogen's), none of the five forms compounds or joins reactions in nature (the heavier ones, xenon in particular, can be adsorbed on mineral surfaces, but they are never chemically bound). Once dissolved, their concentrations can change only for physical reasons. That is the whole method. Kipfer et al. write the measured concentration of gas i as a sum of parts:
The four parts, in the order the water acquires them
- Equilibrium (eq) — what Henry's law dissolves from moist air at the water's temperature, salinity and atmospheric pressure. This is the thermometer, and the salinometer and altimeter.
- Excess air (ex) — the surplus, ubiquitous in groundwater, from air bubbles trapped in the pores and pushed into solution by the pressure of the rising water table. Typically 10–50 % supersaturation. This is the confounder — and, read the right way, a rain gauge.
- Radiogenic (rad) — produced by decay inside the aquifer: ⁴He from U and Th, ³He from tritium (the "tritiogenic" clock of Week 5), rarely ⁴⁰Ar from ⁴⁰K and ²¹Ne from (α,n) reactions.
- Terrigenic (ter) — gases that flow in from outside the aquifer: crustal helium from deeper rock, or mantle helium with its distinctive ³He/⁴He.
Only ⁴Herad, ³He (radiogenic and tritiogenic), occasionally ⁴⁰Arrad and very rarely ²¹Nerad are produced in amounts that show up in natural waters. Neon (mostly), argon, krypton and xenon in groundwater are therefore atmospheric gases only — which is why they can carry the recharge signal cleanly, and why helium needs special handling (Section 10).
Five gases, five different characters
Pick a gas. Solubility in water increases with atomic mass (White pp. 418–419; helium the least soluble, xenon the most — the reverse of their order in magma); diffusivity decreases with mass; atmospheric abundance is wildly uneven (argon is nearly 1 % of air, xenon 87 parts per billion). Those three facts set which gas responds to which process.
Henry's law is the thermometer
Water in contact with air dissolves each gas until the dissolved concentration is proportional to the gas's partial pressure. The proportionality constant depends on temperature (cold water holds more gas, and holds proportionally much more of the heavy gases) and on salinity (salt water holds less). The partial pressure depends on the gas's mixing ratio in dry air and on the total pressure minus the water-vapour pressure — which is how altitude enters. Kipfer et al. write all of it into one equilibrium concentration, Ci,eq(T, S, P), using the moist-air solubilities of Weiss (He, Ne, Ar, Kr) and Clever (Xe):
Solubility explorer — five gases on fixed axes
Each panel is drawn in absolute units (cm³ STP per gram of water) on its own fixed axis, 0–30 °C. Move temperature and watch where the marker sits on each curve; add salt or altitude and watch the whole curve sink. The percentages in the tiles are the local slopes of the equilibrium curves — how much each gas's equilibrium concentration changes per degree at your temperature (the next section's Table 2 quotes the change of a sample's total concentration, excess air included, over a one-degree step, hence its slightly smaller numbers). Computed from the parameterizations in Kipfer et al.'s Table 1B; the values reproduce their Table 1 (S = 0.1 ‰, 1 atm) to within 0.3 %.
Check against Kipfer et al. Table 1 (fresh water, 1 atm)
| T | He ×10⁻⁸ | Ne ×10⁻⁷ | Ar ×10⁻⁴ | Kr ×10⁻⁸ | Xe ×10⁻⁸ |
|---|
Table rows: Kipfer et al. (2002) Table 1, S = 0.1 ‰; page values computed at S = 0.1 ‰ for the comparison.
Why temperature and excess air can be told apart — and salinity and pressure cannot
Aeschbach-Hertig et al. built a synthetic sample (10 °C, fresh, 1 atm, with 3 × 10⁻³ cm³ STP g⁻¹ of dissolved air) and nudged one parameter at a time. The chart is their Table 2: how much each gas's concentration moves for a one-degree warming, a one-per-mil salting, a 0.01 atm rise in pressure, a small extra dose of air, and a small diffusive loss of the excess (the "R" of the partial re-equilibration model). Hover the bars.
Percent change in each dissolved gas for a unit change in one parameter
Transcribed from Aeschbach-Hertig et al. (1999), Table 2. Base state: T = 10 °C, S = 0 ‰, P = 1 atm, A = 3 × 10⁻³ cm³ STP g⁻¹, R = 0.
Read the shapes, not the numbers
- Temperature bites hardest on the heavy gases: xenon −3.35 % per °C, helium only −0.32 %. The fingerprint is a steep ramp from He to Xe.
- Excess air is the mirror image: it fattens helium and neon (the least soluble gases, so a little air is a large fraction of what was dissolved) and barely touches xenon. A ramp the other way.
- Pressure and salinity both ramp gently with mass — pressure because, with excess air present, it "is relatively more important for the heavy noble gases"; salinity because its effect "increase[s] with molar mass". The two ramps are so alike, and so like a combination of temperature and excess air, that "especially the effects of P and S are very similar".
- Re-equilibration (diffusive loss of the excess) strips helium and neon most, because they diffuse fastest and because most of their excess was excess air to begin with.
The consequence
Two parameters with different fingerprints can be separated from one sample; two with the same fingerprint cannot. Temperature and excess air are opposite ramps — "readily identifiable", in Kipfer et al.'s words. Salinity and pressure are nearly the same gentle ramp — "hard to separate", and the errors explode if you try (Section 9's ladder: fitting T and P together costs ±0.62 °C; T, S and P together, ±7.6 °C). This is why a noble-gas study fixes salinity (fresh recharge, S ≈ 0) and pressure (from the altitude of the recharge area) before it fits temperature and air.
The ramp for excess air also explains a rule of thumb you will meet in every paper: excess air is measured by neon. Neon has no significant radiogenic or terrigenic source, so any neon above equilibrium is trapped air — and the relative neon excess, ΔNe, becomes the currency in which excess air is quoted.
Excess air: the ubiquitous surplus
Groundwater almost always holds more dissolved air than a lake would at the same temperature. Heaton and Vogel named it "excess air" (1979, 1981) after finding it in several South African aquifers of different lithology, hydrology and climate, and it has turned up in "virtually all noble gas studies of ground water" since. The mechanism is in the name of the zone where it forms: just above and below a rising water table, up to 10–20 % of the pore space is occupied by immobile bubbles of trapped soil air. The rising water loads them hydrostatically; pressure forces gas into solution; and because the bubbles cannot escape, the surplus stays. Excess air is quoted as the relative neon excess:
The arithmetic of a bubble
- How much air? Unfractionated excess air of Ad cm³ STP per gram adds Ad·zi of each gas. A dose of 10⁻³ cm³ STP g⁻¹ raises neon by about 9 % at 10 °C and 10 % at 22 °C (Aeschbach-Hertig et al.: 1 % ΔNe per 10⁻⁴ cm³ STP g⁻¹, "exact for T = 22.4 °C, P = 1 atm, and S = 0 ‰"); Kipfer et al.'s rule of thumb is 10 % ΔNe per 10⁻³ cm³ STP g⁻¹, "requiring at least 0.05 atm overpressure".
- How much pressure? To hold 2 × 10⁻³ cm³ STP g⁻¹ of air permanently in solution at 13 °C takes an excess pressure of about 0.1 atm — roughly a 1 m column of water on top of the bubble, or the surface tension of a bubble about 30 µm across (Kipfer et al., eq. 14 and the discussion after it).
- Is that plausible? "Water table fluctuations of the order of 1 m probably occur in most recharge areas." Oxygen consumption in soil air could raise the other gases' partial pressures by up to 25 % if the O₂ were entirely removed, but it is usually not, so that route "is questionable" as a 0.1 atm source.
- Where does the excess sit? In the light gases. The stack on the right shows a real sample from southern France read with unfractionated excess air — the neon is 29 % above equilibrium as published (27 % when recomputed here at sea level), the xenon barely 2 %.
Component stack — after Kipfer et al. Fig. 4
Each bar is the measured concentration as a percentage of equilibrium at the recharge temperature (100 % line). Set the temperature, the excess air, the radiogenic ⁴He and the tritiogenic ³He, and watch which gases the bubble and the rock reach.
The neon–xenon diagram: reading temperature and air off one plot
Because neon answers to excess air and xenon to temperature, a plot of one against the other separates the two by geometry. Air-saturated water (ASW) traces a curve as temperature changes; adding plain air moves a sample off that curve along a straight line whose slope is the atmospheric Xe/Ne ratio. Read a sample back along the line to the curve and you have its recharge temperature; the length of the line is its excess air. Kipfer et al.'s Fig. 8 does exactly this for an alluvial aquifer in Switzerland: shallow winter samples land at 7.4 °C, shallow summer and autumn samples at 9.4 °C, deep samples at 8.7 °C.
Ne versus Xe, absolute units, fixed axes
ASW curve for 0–30 °C at your altitude; thin line = addition of unfractionated air to the sample; dashed = the same sample if its excess air were fractionated (CE model, F = 0.5). Hover the curve for temperatures.
The three presets place samples at the three group temperatures of Fig. 8 with illustrative excess-air amounts; the figure's scatter along each line is the range of excess air among the wells. The mean temperatures from Ne and Xe alone (winter 7.4, summer 9.4, deep 8.7 °C) "lie close to the mean temperatures calculated from all noble gases (7.4, 9.2, and 8.6 °C, respectively)".
Unfractionated air, partial re-equilibration, closed-system equilibration
The excess is rarely plain air. "There is increasing evidence that excess air tends to be fractionated relative to atmospheric air, with an enrichment of the heavy gases," and any model of recharge conditions must say how. Kipfer et al.'s Table 2 lists the candidates. Each is a story about what a trapped bubble does; each has one or two parameters; and, disconcertingly, "in many cases all of them provide a reasonable fit to the measured concentrations of Ne, Ar, Kr, and Xe." Where they differ is in what they predict for helium, for the isotope ratios, and for the physical plausibility of their own parameters.
| Model | What the bubble does | Excess of gas i | Parameters | Reference |
|---|---|---|---|---|
| UA · unfractionated excess air | Bubbles dissolve completely. The excess has the composition of air. | Ad · zi | Ad: dissolved air (cm³ STP g⁻¹) | Heaton & Vogel (1981) |
| PR · partial re-equilibration | Bubbles dissolve completely, then part of the excess diffuses back out across the water table; light, fast gases leave first. | Ad · zi · e−R·Di/DNe | Ad: initial dissolved air; R: degree of re-equilibration | Stute et al. (1995b) |
| MR · multi-step partial re-equilibration | The same, in n repeated dissolve-and-degas steps. | Ad · zi · e−Ri (1 − e−nRi)/(1 − e−Ri) | Ad, R per step; n steps | Kipfer et al. (2002) |
| CE · closed-system equilibration | Bubbles dissolve only partly; water and the remaining trapped air reach a new equilibrium at elevated pressure. No diffusion. | (1 − F) Ae zi / (1 + F Ae zi/Ci,eq) | Ae: entrapped air; F: reduction of its volume by dissolution and compression | Aeschbach-Hertig et al. (2000) |
The UA model is the special case R = 0 or F = 0 of the others, so "the problem of model choice essentially reduces to the PR / MR and CE models." The 1999 paper you are reading works with UA and PR; CE was published the following year and is the subject of Section 8.
Model lab — what each story does to the excess
Left: the elemental pattern of the excess relative to air, normalised to neon (a value of 1 means "the same proportion as in air"; UA is flat at 1 by definition). Right: the He/Ne ratio of the excess, Lex, against the model's fractionation parameter — a reproduction of Kipfer et al.'s Fig. 7 at 10 °C, with your setting marked. The atmospheric ratio Lair = 0.288 is the ceiling for every model; the ratio in air-saturated water, Leq, is the floor for CE but not for PR.
Excess pattern relative to air (Ne = 1)
Lex = (He/Ne)ex against F (CE) or R (PR) — after Fig. 7
A bubble that dissolves only as far as the pressure lets it
The CE model's idea is simple enough to draw. Start with air-saturated water and a finite volume of trapped air per gram of water, Ae. Raise the water table; the bubble is now under a total pressure Ptot greater than atmospheric. Gas dissolves until the water is in a new equilibrium with what is left of the bubble — in a closed system, with nothing escaping. The excess of each gas is then:
v is the fraction of the trapped gas left in the bubble, q the pressure on it relative to the atmosphere; "any pair of the parameters Ae, F, q, and v fully determines the amount and composition of excess air, the most intuitive choice being Ae (≈ air / water volume ratio) and q (≈ pressure exerted on the entrapped air)." The three are coupled by one physical requirement: the partial pressures in what is left of the bubble must add up to Ptot. Given Ae, q and the temperature, that requirement fixes F — which is what the lab below solves, using the solubilities of N₂, O₂ and Ar, the gases that make up the bubble.
CE lab — set the bubble and the pressure, read the excess
Excess of each gas relative to its equilibrium concentration
Fixed 0–200 % axis. Coloured = the CE result; grey = unfractionated air with the same neon excess (what a UA reading of this sample would assume for the other gases).
ΔNe against trapped air at your q — the pressure, not the reservoir, sets the scale
Press hard here — the assumptions the CE model carries
The course plan asks Block 2 to lean on the excess-air models. Here is where the weight goes; each item is drawn from the readings' own caveats.
Four numbers, three unknowns, one statistic
The old way was iterative: subtract a guessed amount of atmospheric excess air from each gas, compute a temperature from each corrected concentration, and adjust the guess until the four temperatures agree. It works, and the scatter of the four temperatures is a rough error bar. Aeschbach-Hertig et al. (1999) replaced it with an inverse fit: treat T, S, P and the excess-air parameters as unknowns, fix the ones you know (fresh recharge, S ≈ 0; altitude gives P), and find the rest by minimising the weighted misfit
The weights are the measurement errors, which buys three things: every gas counts in proportion to how well it was measured; the covariance of the fit gives honest parameter errors (and their correlations); and the minimum χ² itself is a test of the model. With n measured gases and m fitted parameters, a correct model gives χ² ≈ ν = n − m on average. If the probability of a χ² that large is below a cut-off — "pc = 0.01 proved to be appropriate", in Kipfer et al.'s later practice; the 1999 paper itself rejected at p < 0.05 — the model is rejected for that sample. Apply the same model to N samples and the summed χ² tests it against the whole data set, "with a much larger number of degrees of freedom": a model can fail a data set while passing every sample in it.
χ² lab — synthetic samples with a hidden truth
Choose the world that made the sample (its true temperature and excess-air story are hidden until you fit), add 1 % measurement noise to Ne, Ar, Kr and Xe, and fit each of the three models. Watch χ², the degrees of freedom, the p-value, the verdict at pc = 0.01 — and what the wrong model does to the temperature. New noise draws give the sampling spread; Aeschbach-Hertig et al.'s Monte Carlo of 1,000 such draws returned T = 10.007 ± 0.216 °C and A = (2.995 ± 0.147) × 10⁻³ for a UA world at 10 °C.
The sample: measured concentrations relative to ASW at the fitted temperature
Bars: measured ÷ equilibrium at the currently fitted T (100 % = equilibrium). Error bars: ±1 % (1σ). Hollow markers: the fitted model's prediction.
Fit history for this sample
| Model | T (°C) | Excess air | χ² | ν | p | Verdict |
|---|
The uncertainty ladder — what each extra unknown costs
Kipfer et al.'s Table 3: the 1σ error of the fitted parameters for a synthetic sample at 10 °C, S = 0, 1 atm, Ad = 3 × 10⁻³, with 1 % errors on all four concentrations, as the set of free parameters grows. Choose which error to display.
The gas with three parents
Neon through xenon in groundwater are atmospheric; helium is not. Its ⁴He has an atmospheric part (equilibrium plus excess air), a terrigenic part from the rock (crustal or mantle), and its ³He has all of those plus the decay product of tritium — the Week 5 clock. Separating them is bookkeeping with three equations (Kipfer et al. eqs. 29a–c), and the bookkeeping hinges on two assumptions: the He/Ne ratio of the excess air, Lex, and the ³He/⁴He ratio of the terrigenic helium, Rter.
Helium separator
A sample at the chosen temperature, with the neon excess, total ⁴He and ³He/⁴He you set. Change the two assumptions and watch ⁴Heter, ³Hetri and the ³H–³He age move.
Where the ⁴He and ³He come from — measured totals split into parts
What accumulates, and what decays
Once the atmospheric parts are separated, what remains is time. Tritiogenic ³He grows as tritium decays, from the moment the water is cut off from the air; radiogenic ⁴He accumulates from the rock for as long as the water stays underground; and five radioactive noble-gas isotopes, made in the atmosphere or by industry, decay on schedules from days to hundreds of thousands of years. Between them they cover, in Kipfer et al.'s summary, "months to about 50 years" (³H–³He, ⁸⁵Kr, with ²²²Rn for the first 20 days), "thousands to millions of years" (⁴He, ⁴⁰Ar, ⁸¹Kr), and the awkward 100–1,000 years in between (³⁹Ar).
Half-lives and windows from Kipfer et al. (2002). Sample volumes are the ones they quote for the rare isotopes: about 500 L of water for ³⁹Ar and about 15,000 L for ⁸¹Kr, whose atmospheric abundances are near 10⁻¹⁵ of their element; ⁸⁵Kr/Kr is near 10⁻¹¹.
The ³H–³He clock, from isolation onward
Kipfer et al.'s Fig. 9, computed: while the water is open to the air, its tritiogenic ³He escapes and stays at zero; once isolated, ³Hetri grows exactly as ³H decays. Their ratio is a unique function of the time since isolation — the ³H–³He age — and, unlike either concentration alone, needs no input history.
Two cautions from the text. For τ ≪ 1/λ the age is linear in the ratio (eq. 34) but "not of ³H", so a mixture's apparent age "is always biased towards the component with the higher ³H concentration." And in the unsaturated zone the ³He escapes: the clock starts at the water table, not at the ground surface — which is why deep unsaturated zones lag the input functions of ⁸⁵Kr, CFCs and SF₆ as well.
The ⁴He accumulation age — and its two rate constants
If ⁴He accumulates at a constant rate JHe, the residence time is simply τ = ⁴Herad/JHe (eq. 35). "The problem is to determine the accumulation rate." In situ production from the aquifer's own uranium and thorium (eq. 36, Andrews & Lee 1979) is calculable; a flux from the whole crust below (Torgersen & Clarke 1985) is not — and the two can differ by orders of magnitude. Set both and compare the ages.
From a noble-gas temperature to a climate
The equilibrium component records the temperature at which the water last exchanged with air. For groundwater that is not the rain's temperature but the ground's: percolating water "equilibrates continuously with ground air until it reaches the capillary fringe and the quasi-saturated zone", so the noble-gas temperature (NGT) is, after the excess-air correction, the mean ground temperature at the water table. From there to a climate statement is a chain of local relationships — and the chain, not the thermometer, carries most of the uncertainty.
The instruction that follows in the text: convert NGT to air temperature "based on local relationships between ground and air temperature or calibrated locally by analysing young ground water that infiltrated under known climate conditions." Mixing in the aquifer and along long well screens smooths the record, so "the noble gas method cannot be used to study short-term climate fluctuations, but it is well-suited to derive quantitative estimates of mean temperatures during major climate states" — above all the difference between the last glacial maximum (about 21 kyr ago) and the Holocene.
Three records
Charts are redrawn from Kipfer et al.'s Figs. 21–23 at reading precision (about ±0.3 °C, ±1 kyr, ±10 % ΔNe); the numbers quoted in the panels are the authors' own. Where a panel is marked schematic, only the trend is shown.
The nuisance that became a proxy
For twenty years excess air was "a disturbance for which the measured data had to be corrected." Heaton and Vogel had suggested in 1981 that it might record recharge conditions — sporadic, heavy rainfall in semi-arid climates should trap and dissolve more air — and Heaton et al. (1983) found peaks of excess air in the Kalahari at ages of about 10 and 30 kyr, "coinciding with independently reconstructed periods of more humid climate and flooding." Then the temperate aquifers showed no systematic variation at all, and the idea went quiet. The CE model revived it, because it gave the signal a physical meaning: ΔNe measures pressure, pressure means water-table rise, and water-table rise means recharge — its intensity and variability more than its mean.
ΔNe against noble-gas temperature in three semi-arid aquifers — after Kipfer et al. Fig. 24 (trends only)
Niger (solid), Brazil (dotted), Australia (dashed): "all three aquifers show strong and very similar decreasing trends of ΔNe with temperature (about −10 % per °C)", r = 0.71, 0.83 and 0.63. In the Brazilian aquifer, glacial water carried roughly two to three times the ΔNe of Holocene water (Stute et al. 1995b).
What can be said, and what cannot
- Five semi-arid aquifer systems — Stampriet Auob (Namibia), Serra Grande and Cabeças (Brazil), the Continental Intercalaire (Niger), the Continental Terminal (Niger), and the Great Artesian Basin (Australia) — show past periods of strongly increased excess air, "in several of these studies … correlated to known periods of more humid climate." Hence the hypothesis "that excess air is a proxy for infiltration conditions, in particular the intensity and variability of recharge in semi-arid regions."
- Temperate, humid aquifers show "little evidence for systematic variations of excess air."
- Lithology matters less than it once seemed: Wilson and McNeill (1997) found the Ne excess increasing from granites through sandstones to limestones, but the CE model "argues against a major influence of lithology, unless very fine pores cause the surface tension to become a major source of excess pressure on the trapped bubbles, or very low porosity severely limits air entrapment."
- The missing link: "A verification of a direct link between water table fluctuations and ΔNe or q under field conditions is still missing." Sand columns (Holocher et al. 2002) support the q–amplitude correlation, and show that fluctuations of less than 1 m can generate excess air. That is a laboratory, not an aquifer.
A diagnosis board
Each row is a symptom you might meet in a noble-gas data set, the physical cause the readings offer, and the test or fix. Click a row for the detail.
Three readings, three blocks, one bubble
Kipfer et al. supply the whole apparatus and the case studies; Aeschbach-Hertig et al. supply the statistical method and its first field tests; White supplies the geochemical backdrop. The guides below are maps, not substitutes: what each asks, where its load-bearing figures live, which equations to recognise, which numbers to be able to quote, and where a careful reader might press. The notes and the critique are yours to write.
Kipfer, R., Aeschbach-Hertig, W., Peeters, F., & Stute, M. (2002). Noble gases in lakes and ground waters. Reviews in Mineralogy and Geochemistry, 47, 615–700.
Eighty-six pages: the components, the solubilities and the analytics; the four excess-air models and how to separate components by hand or by inverse fit; lakes (mixing, ³H–³He, helium fluxes, mantle gases); groundwater (young-water dating, old-water dating, the noble-gas thermometer, excess air as a climate proxy); and a coda on noble gases in ice. doi:10.2138/rmg.2002.47.14
Aeschbach-Hertig, W., Peeters, F., Beyerle, U., & Kipfer, R. (1999). Interpretation of dissolved atmospheric noble gases in natural waters. Water Resources Research, 35(9), 2779–2792.
The method paper: a general, error-weighted least-squares inversion of Ne, Ar, Kr and Xe (and He where it can be trusted) for temperature, salinity, pressure, excess air and re-equilibration — with Monte Carlo error analysis, then tested on air-equilibrated water, lakes, rivers, springs and aquifers. It works with the UA and PR models; the CE model came a year later. doi:10.1029/1999WR900130
White, W. M. (2015). Noble gas isotope geochemistry. Ch. 12 in Isotope Geochemistry (pp. 418–452). Wiley.
The textbook chapter: what noble gases are and where they came from (solar and planetary patterns), then helium, neon, argon, krypton and xenon in turn — production, isotope ratios, the crust–mantle–atmosphere story — and the origin and evolution of Earth's noble-gas inventory. Hydrology gets a few paragraphs; the rest is the context that makes those paragraphs intelligible.
Four situations to reason through
Each scenario gives the kind of evidence a Week 7 reader should now be able to interrogate. Choose the reading you would defend first, then compare with the debrief.
Ten questions before the meeting
Immediate feedback, no grade, no record. If you miss one, the linked section is the fix.
Glossary
The Week 7 working vocabulary, with a few terms you will meet again in Weeks 9 and 10. Search or browse.
The Week 7 readings — and what follows
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. The review and the article are behind publisher walls; the chapter is in the library's e-book collection.
Kipfer, R., Aeschbach-Hertig, W., Peeters, F., & Stute, M. (2002). Noble gases in lakes and ground waters. Reviews in Mineralogy and Geochemistry, 47, 615–700.
Components and solubilities (Table 1, Figs. 1–4); the excess-air models (Fig. 5, Table 2, eqs. 13–28); component separation and the inverse method (eqs. 29–32, Figs. 7–8, Table 3); lakes (Figs. 9–16, Tables 4–5); dating young and old groundwater (Figs. 17–20); the noble-gas thermometer and its records (Figs. 21–24); ice. doi:10.2138/rmg.2002.47.14
Aeschbach-Hertig, W., Peeters, F., Beyerle, U., & Kipfer, R. (1999). Interpretation of dissolved atmospheric noble gases in natural waters. Water Resources Research, 35(9), 2779–2792.
The model (eqs. 1–11); the inverse method and its errors (eqs. 12–13, Tables 1–2, Fig. 1); air-equilibrated water, lakes, the Caspian Sea, glacier ponds, rivers, groundwater of the Töss valley and Botswana, altitude in the Alps (Figs. 2–6). doi:10.1029/1999WR900130
White, W. M. (2015). Noble gas isotope geochemistry. In Isotope Geochemistry (Ch. 12, pp. 418–452). Wiley-Blackwell.
Chemistry and abundances (Tables 12.1–12.3, Fig. 12.1); helium in atmosphere, crust, oceans and mantle (Figs. 12.2–12.5); neon (Figs. 12.6–12.7); argon (Fig. 12.8); krypton and xenon (Figs. 12.9–12.12); mantle–atmosphere evolution and the xenon paradox (Figs. 12.13–12.16); problems.
Next week — the Picarro laboratory
Week 8 leaves the desk for the bench: laser spectroscopy of water isotopes in practice — standards and the VSMOW–SLAP scale, memory and carry-over, organic contamination, and the QA/QC that makes a data set defensible. The lesson of this week travels with you: a measurement's precision (1 % on a noble gas; 0.1 ‰ on δ¹⁸O) is only the beginning of its uncertainty, and the assumptions in the reduction — the excess-air model here, the calibration and drift correction there — usually dominate.
Carry-forward question, for your proposal: if your question turns on when or under what conditions water was recharged, which of this week's quantities would answer it — the noble-gas temperature, the excess air, the tritiogenic helium, the radiogenic helium — and which assumption in its derivation would a hostile reviewer attack first?