WASR 8000 · Week 3
WASR 8000 · Environmental Tracers in Hydrology · Fall 2026

How Old Is This Water?

An interactive primer on groundwater age — what the word can and cannot mean, how the radiometric clocks (¹⁴C, ³⁹Ar, ⁸¹Kr) work and where they fail, and why a residence time is a distribution rather than a number, from confined aquifers down to the water inside a tree. Builds on the decay law of Week 2; no dating background needed.

Week 3 companion · read alongside the four papers ≈ 40–50 minutes 11 interactive demos · self-check quiz
1 · The opening question

One water sample. Three careful methods. Three wildly different ages.

A well taps a shallow confined aquifer. Darcy's law, applied to the measured head gradient and a reasonable hydraulic conductivity, says the water took hundreds of thousands of years to arrive from the recharge area. Its radiocarbon activity is about a tenth of the pre-bomb recharge value — by the decay law you met in Week 2, less than 20,000 years. Its helium-4 content implies millions of years. (The situation is real; it is the worked example in Bethke & Johnson, 2008.)

Seen the new way, the sample is water that flowed along the aquifer and mixed with modern water recharging from the surface and with ancient water discharging from below. The Darcy estimate describes the flow path; the radiocarbon clock is dominated by the young fraction (a decaying tracer barely notices dead water, as Section 7 shows); the helium clock is dominated by the old fraction. Three honest instruments, three different questions answered. The disagreement is not an error to be explained away — it is information about the flow regime, and reactive transport modeling (Section 8) is how the field has learned to read it.

That is the whole of Week 3 in one example. "How old is this water?" is the first question a hydrogeologist asks — of sustainability, of contamination risk, of a proposed waste repository. The week's work is to replace the question's naive form (one number) with its usable form: what is the distribution of ages in this water, and what can each tracer tell me about it?

Cook & Böhlke call the enterprise "hydrochronology," by analogy with geochronology. The analogy is honest about the ambition — dating water as geologists date rock — and, as this week's papers show, honest ambition runs into an interesting problem: rocks mostly stay put, and water mixes.

2 · The word itself

"Age" is easy to define and easy to break

The definition sounds innocent: the age of groundwater at a point is the time that has elapsed since it entered the subsurface. Bethke & Johnson note, a little mischievously, that almost no textbook states even this — the texts jump straight to isotope formulas. Start slower, because the definition is where the trouble lives.

The packet picture (piston flow)

  • A parcel of rain infiltrates, becomes a closed packet, and rides a flow line from recharge to well. Nothing enters or leaves it.
  • Age then grows along the path at the pace of the flow: the age gradient is the reciprocal of velocity. Water moving 10 m yr⁻¹ is 100 years older every kilometre.
  • Every classical dating formula in Section 3 quietly assumes this picture. One sample, one age, one equation.

The molecule picture (the "new thinking")

  • Water molecules diffuse into and out of neighbouring aquitards, disperse along and across the flow, and leak between formations. There are no closed packets.
  • So a sample is a crowd: each molecule has its own residence time. The sample's age is defined as the average over the crowd — and the crowd has a shape.
  • Two samples with the same average can be utterly different waters. The shape, not the mean, decides what a well is telling you.
dτ/dℓ = 1/v piston flow: age gradient = 1 / velocity (Bethke & Johnson, eq. 1)

Same mean age, four different waters

Each panel below is a possible age distribution for a sample whose mean age is identical — the four sketches of Bethke & Johnson's Figure 2. Click through them. The x-axis is the age of individual water molecules; the curve is how much of the sample is that old.

Keep the course's frame in view: rates and dates are the same question in different clothes. A date across a known distance is a rate (¹⁴C ages down the Carrizo aquifer gave 2.4 m yr⁻¹ at 15 km from the outcrop — Pearson & White, 1967, the early study Bethke & Johnson cite as promising). A known rate predicts the dates. When the two disagree — as at the Great Artesian Basin, or the Milk River aquifer, famously — one of the assumptions connecting them has failed, and finding which one is where the science is.
3 · The clock shop

Three ways a tracer can tell time

Water molecules carry no age information of their own. Every dating method therefore rides on a marker dissolved in, or part of, the water — and every marker keeps time in one of three ways (Cook & Böhlke §1.2; Bethke & Johnson's three classes). Click each clock.

Click a clock to see how it keeps time, what it needs to be trusted, and how it fails.

t = −(1/λ) · ln(C / C₀) the draining clock (Cook & Böhlke eq. 1.1; λ = ln 2 / t½)

The ruler of time — and the holes in it

Each bar is the range of ages a tracer can usefully date; the axis is logarithmic, from one year to ten million. Hover or tap a bar for the tracer's story. Notice what Cook & Böhlke noticed: the widely available methods cluster in two windows — younger than ~50 years and roughly 2,000 to 40,000 years — leaving a gap between decades and millennia that only the hard-to-measure ³⁹Ar spans, and another beyond radiocarbon where ⁸¹Kr, ³⁶Cl and ⁴He take over.

The numbers behind the bars
TracerHalf-lifeClock typeUsable window (approx.)
³H (with ³He)12.3 yrdraining / calendar< ~50 yr
⁸⁵Kr10.76 yrcalendar (rising)< ~50 yr
CFCs, SF₆calendar (rising)< ~50–70 yr
³²Si152 yrdraining~30–1,000 yr; sorbs, unreliable to date
³⁹Ar269 yrdraining~50–1,000 yr
¹⁴C5,730 yrdraining~2,000–40,000 (to ~50,000) yr
⁸¹Kr229,000 yrdraining~5×10⁴–1×10⁶ yr
³⁶Cl~301,000 yrdraining / pulse~10⁵–10⁶⁺ yr
⁴Hestablefilling~10⁴–10⁸ yr, semi-quantitative

Half-lives as quoted in Bethke & Johnson (2008); windows as characterized in Cook & Böhlke (2000), Bethke & Johnson (2008), and Lehmann et al. (1993) — the ⁸¹Kr window is Lehmann et al.'s; the ³⁹Ar and ³²Si spans are the ranges conventional in the dating literature, implied by their half-lives. "Usable" assumes the initial condition and subsurface sources are under control, which is precisely what Sections 4 and 7 complicate.

Two cautions before you trust any bar. First, the input must be known: the draining clock needs C₀ at recharge, the filling clock needs the accumulation rate, the calendar clock needs the atmospheric history — and CFCs, whose atmospheric concentrations have stopped rising and begun to fall since international restrictions, now return two possible dates for one measurement (Cook & Böhlke §1.2.3). Second, the subsurface makes tracers too: given uranium- and thorium-bearing rock and enough isolation time, in-situ production of ³H, ⁴He, ³⁶Cl, ³⁷Ar, ³⁹Ar, ⁴⁰Ar, ⁸⁵Kr and others can overshadow the atmospheric signal entirely (Lehmann et al., 1993). A concentration is only a clock after the sources are audited.
4 · The workhorse and its rivals

¹⁴C, ³⁹Ar, ⁸¹Kr: dating old water

The week's title methods are the draining clocks for water older than living memory. Radiocarbon is the workhorse — cosmic rays make ¹⁴C in the atmosphere, it dissolves into recharge as CO₂, and its 5,730-year half-life spans the last ice age. The demo turns the crank on the decay law, then shows the two ways the answer lies to you.

The decay-clock calculator

Choose a nuclide, then set the measured concentration as a fraction of the initial (for ¹⁴C, think "percent modern carbon"). The curve is the decay law; the shaded band is the clock's comfortable range — roughly a tenth of a half-life to five half-lives. Outside it, the measurement drowns in precision limits (too young) or in background (too old).

25%
piston-flow age
half-lives elapsed
t / t½
if C measured ±2% (abs.)
age uncertainty from precision alone

Thief 1: dead carbon

The decay law needs C₀ — the ¹⁴C content the water started with. But groundwater dissolves calcite and oxidizes ancient organic matter along the way, and both add carbon with no ¹⁴C at all. The activity per gram of carbon drops, and the clock reads old without a single year passing. Drag the slider: q is the fraction of the dissolved carbon that actually came from recharge.

0.85
apparent extra age
added to every sample, young or old
the correction industry
δ¹³C & mass-balance models
Wigley et al. (1978); Fontes & Garnier (1979) — cited in Bethke & Johnson

³⁹Ar — the gap-bridger

A noble-gas radionuclide (t½ = 269 yr) made by cosmic rays; chemically inert, so nothing sorbs it or dissolves extra into the water — theoretically the cleanest clock for the 50–1,000 year gap that ³H and ¹⁴C both miss. Two catches: measuring it has historically demanded heroic low-level counting on large samples (Loosli et al., 2000, in the Cook & Herczeg volume), and it has a subsurface source — neutrons from U and Th decay make ³⁹Ar from potassium via ³⁹K(n,p)³⁹Ar, so in U-rich rock the "atmospheric" signal needs auditing (Lehmann et al., 1993).

⁸¹Kr — the deep-time noble gas

Also inert, with t½ = 229,000 yr: the right decay constant for water tens of thousands to a million years old, where ¹⁴C is dead and ³⁶Cl is haunted by subsurface production and dead-chloride dilution. Lehmann et al. (1993) single out ⁸¹Kr (with ³H/³He at the young end) as the dating method with the least interpretive complication — its subsurface production is negligible — and its historical obstacle as purely analytical: counting a handful of atoms. Their conclusion aged well; atom-counting techniques have since turned both ⁸¹Kr and ³⁹Ar from theoretical into practical tools, which is why your reading list keeps them in the title of Week 3.

Where is ³⁶Cl? It works like radiocarbon with a 301,000-year half-life — Bentley et al. (1986) used it to date Great Artesian Basin water to around a million years — but it carries every complication at once: an initial ratio that varies with climate and distance from the coast, dilution by dead chloride from halite and upward-diffusing brines, and its own subsurface production by neutron capture on ³⁵Cl. Bethke & Johnson use it as their running example precisely because it is complicated; Section 8 shows what they do with it.
5 · One aquifer, ideal case

Where the ages live: groundwater stratigraphy

Before distributions, get the ideal geometry into your hands. In an unconfined aquifer of constant thickness receiving uniform recharge — Vogel's classic 1967 model, the backbone of Cook & Böhlke's §1.3 — age is stratified like sediment: youngest at the water table, oldest at the base, with the isochrons crowding together logarithmically at depth. Cook & Böhlke call reading this record "groundwater stratigraphy," and it is how single wells become recharge gauges.

The Vogel aquifer

Drag the sliders; the cross-section recolours by age and the profile replots. Hover either panel to probe a depth. The age at depth z is independent of where you drill horizontally — one of the model's quiet surprises.

33 m
0.35
— mm yr⁻¹

Cross-section, coloured by age

Age–depth profile at a well

vertical velocity at the water table (R/ε)
what a shallow tracer profile measures
mean age of full-depth discharge (Hε/R)
the exponential model's τ — Section 6
age at probed depth
hover a panel
t(z) = (Hε / R) · ln[ H / (H − z) ] age below the water table (Cook & Böhlke eq. 1.3, after Vogel 1967)

What people actually do with this

  • Recharge from a dated profile. Fit the age–depth curve from multi-level samplers and R falls out. At Cape Cod, ³H and ³He peaks ~27 m below the water table gave a water-table velocity R/ε of 3.3 m yr⁻¹ (Solomon et al., 1995, in Cook & Böhlke §1.4.1); with ¹⁴C, recharge rates as small as 0.1–0.2 mm yr⁻¹ have been extracted (Murray Group, Leaney & Allison, 1986). Across methods, ³H/³He and CFCs have mapped recharge of 100–1,200 mm yr⁻¹; ¹⁴C covers 2–100 mm yr⁻¹.
  • Velocity from ages along a confined aquifer. Carrizo Sand: ¹⁴C ages rise downgradient from <4,000 to >28,000 yr, giving 2.4 m yr⁻¹ at 15 km and 1.6 m yr⁻¹ at 50 km — agreeing with the hydraulics (Pearson & White, 1967). Age differences between wells dodge the initial-condition problem entirely (Phillips et al., 1989).
  • The unsaturated zone is part of the story. The tracer's total residence time is root zone + unsaturated zone + groundwater (Cook & Böhlke Fig. 1.3). A ³H peak parked 4 m deep in the English Chalk in 1968 — rainfall's 1963–64 bomb peak, four to five years on — gave 0.9 m yr⁻¹ of downward crawl (Smith et al., 1970); at Cape Cod the unsaturated lag was 14 years. Forgetting this lag shifts every "recharge date" you infer.
  • Groundwater as archive. Date the water, then read its passengers against the calendar: nitrate loading beneath Maryland farmland rising three- to six-fold from 1950 to 1990, tracking fertilizer use, with ~30% of applied N reaching the water table (Böhlke & Denver, 1995); sulphate recharge peaking with 1960s–70s acid deposition; a halocarbon history of the Danube reconstructed from a riverside aquifer (Böhlke et al., 1997). And with age in hand, slow chemistry gets rate constants no laboratory could measure: denitrification with a ~5,000-year half-life in the Kalahari (Vogel et al., 1981), dedolomitization at tenths of a µmol L⁻¹ yr⁻¹ over 30,000 years in the Madison aquifer (Plummer et al., 1990).
6 · From a number to a distribution

What a well actually samples

Wells are rarely points. A screen spanning the aquifer, a spring, a stream — each collects flow lines of every age at once, and the sample's tracer content is set by the whole age frequency distribution g(t), not by any single age. The classical "lumped-parameter models" are a small zoo of g(t) shapes, each the exact consequence of an idealized geometry you have already seen (Cook & Böhlke Table 1.1, Fig. 1.4; Maloszewski & Zuber's framework).

The distribution explorer

Pick a model and a mean transit time τ. The main panel is g(t) — the fraction of discharge in each age band; the dashed curve is the cumulative version. The readouts answer the question a distribution is for: how much of this water is young? Two axis views: in years, dragging τ stretches the whole family; in multiples of τ — the convention of Cook & Böhlke's Fig. 1.4 — every τ collapses onto one universal shape, so that view deliberately sits still as τ moves (and "older than 2τ", a property of shape alone, never moves in either view).

10 yr
mean age
first moment of g(t)
median age
half the water is younger
younger than 1 yr
the contamination-relevant fraction
older than 2τ
the tail the mean hides
Cout(ti) = ∫₀ Cin(ti − t) · g(t) · e−λt dt the convolution integral (Cook & Böhlke eq. 1.6)

This is the machine that connects a distribution to a measurement: feed the tracer's input history through g(t), decay it, and out comes what the well should read today. Fitting measured concentrations of tracers with different input histories — ³H and CFC-12 and SF₆ together — can pin down both τ and the shape of g(t), because each tracer averages the distribution differently (Cook & Böhlke Fig. 1.5, computed for 1998 sampling; the same logic runs TracerLPM in Week 5).

Check yourself against the chapter: for the exponential model with τ = 10 yr, Cook & Böhlke read off that a bit under 10% of the discharge is less than a year old, and about 4% is between 9 and 10 years old (Fig. 1.4). Set the explorer to those settings and confirm both numbers — then set τ = 100 yr and notice that even century-old water delivers ~1% of modern recharge to the well every year. A mean age of a century does not mean safety from last year's spill; that single sentence is most of groundwater-vulnerability science.
7 · Why the clocks disagree

The apparent age of a mixture

Now run the dating formulas of Section 3 on water that is honestly a mixture — and watch each class of clock fail in its own characteristic direction. This is Bethke & Johnson's Figure 3 made adjustable, and it is the single most useful diagram in the week.

Two waters, one sample

Blend a younger water A with an older water B and read the sample three ways. The true mean age is the flow-weighted average (the "age mass" rule of Section 8). Each method's apparent age is what its formula returns for the blended concentration.

50%
true mean age
age-mass weighted
draining clock (¹⁴C-style)
biased young
filling clock (⁴He-style)
exact for a uniform source
calendar clock (SF₆-style)

Why decay clocks read young

  • Concentration decays along a curve; mixtures sit on the straight chord between the end-members — and the chord lies on the young side of the curve, always.
  • The bias is mild for similar ages (longitudinal dispersion) and extreme for young + very old: half modern water, half radiocarbon-dead water reads as one ¹⁴C half-life — 5,730 years — however ancient the old half is.
  • The same geometry afflicts calendar clocks whenever part of the blend pre-dates the marker's history.

Why the filling clock doesn't

  • ⁴He grows linearly with time, and a straight line is its own chord: mixing preserves the mean exactly (when the source rate is uniform).
  • The catch is the premise. Aquitards often out-produce aquifers, the deep crust leaks ⁴He upward, and an unnoticed uranium deposit reads as stagnant water (Bethke & Johnson's error analysis).
  • So the honest clock has the dirty source, and the clean-sourced clocks lie about mixtures. Every dating study lives somewhere on that trade.
Re-read the hook with new eyes: Darcy hundreds of thousands of years, ¹⁴C under twenty thousand, ⁴He millions. A mostly-old blend with a thread of modern recharge does exactly this — the ¹⁴C rides the young thread, the ⁴He weights the ancient fraction (and its crustal source), and the flow calculation describes the aquifer rather than the blend. Three answers, one consistent water. The reconciliation is quantitative, not rhetorical, and it is the subject of the next section.
8 · The new thinking

Age mass: making "age" something that can be transported

If a sample's age is an average over molecules, age must be carried, mixed and diluted like a solute. Ages themselves don't add — mixing 20-year and 40-year water does not make 60-year water — so Goode (1996) found the quantity that does: age mass, the product of water mass and age. One kilogram of ten-year-old water holds ten kilogram-years. Age mass mixes linearly (the equal blend above is 30 years old), obeys a transport equation, and turns age from an isotope formula into a field you can model.

∂τ/∂t = ∇·D·∇τ − ∇·(vτ) + 1 age transport (Bethke & Johnson eq. 15)

Read the terms: age disperses, age advects, and the "+1" says every kilogram of water everywhere grows one year older per year — a uniform, zero-order source that no real tracer quite matches. Age behaves like a reacting solute with the simplest source law in the world, which is exactly why real tracers (each with its own source law) are imperfect proxies for it.

Aquitards age aquifers simply by existing

Solve the steady transport equation across an aquitard sandwiched between two aquifers (Bethke & Johnson eqs. 19–24, their Figure 4). With no cross-flow the excess-age profile is a parabola peaking at b²/2D*. Axes are absolute — depth in metres inside a fixed ±100 m frame, excess age in years — so both sliders reshape the curve: b widens the aquitard and grows the peak as b²; D* stretches or shrinks it horizontally. Then note the readout the sliders cannot change.

50 m
10⁻¹⁰ m² s⁻¹

Excess age across the aquitard

peak excess age b²/2D*
at the aquitard centreline
age-mass flux to the aquifers
ρφb — fixed
one kilogram-year per year, per kilogram of aquitard water: independent of D* and of cross-flow

The efflux result is the section's punchline: every kilogram of water stored in an aquitard exports one kilogram-year of age per year, whatever the diffusion coefficient and whatever the leakage rate. Slow exchange sends a few very old molecules; fast exchange sends many slightly-old ones; the aging shipment is the same. Piston-flow dating along an aquifer is therefore correct only when b = 0 — no aquitards at all — and the velocity implied by two well ages must be corrected by the stored-water ratio: v = (1 + φaqtb / φaqfB) · Δx/Δτ (their eqs. 25–26). Wells 10 km and 10,000 ¹⁴C-years apart under an equal-water aquitard flow at 2 m yr⁻¹, not 1.

Reactive transport modeling: inverting the tracers together

The alternative to dating samples one formula at a time: build a 2-D flow model of the whole regime, transport each marker with its true source law (decay, in-situ production, basal flux), and adjust permeabilities until the simulated concentrations match every observation at once — heads, salinity and temperature included. The age field then falls out of the same model via the +1 equation. Three worked cases from Bethke & Johnson:

9 · The same idea in days

Age distributions in the soil–plant system

Everything so far scales down. Replace "aquifer" with a three-metre soil profile, "recharge" with sprinkler rainfall, "well" with a tree — and the age of water becomes a days-to-months question with the same mathematics. Block 3's paired papers do exactly this at Biosphere 2's enclosed rainforest, where the boundary conditions of a real catchment's problem are, for once, actually known.

The experiment (Evaristo et al., 2019)

The Biosphere 2 Tropical Rainforest: a 1,936 m² glass-enclosed mesocosm near Tucson, ~27 m tall, soils 1–3.5 m deep over a drained basement — so everything that leaves the bottom ("deep percolation," the stand-in for groundwater recharge) is collected and measured. The team switched the rain off for 68 days, then rewet the system with 66 mm of deuterium-labelled rainfall at +152‰ δ²H over four events — screamingly distinct from the −60‰ background — followed by 87 mm of ordinary rain over 13 events. For months afterward they tracked the label through bulk soil water at seven depths, the basement seepage, and weekly xylem water from five canopy species, sampled by clipping from a bosun's chair.

seepage ("recharge") MTT
≈ 9 days
215 hr [205, 250]
soil water at 0.25 m
≈ 14 days
330 hr — older than the seepage below it
transpired water MTT
17–62 days
by species: ~17, ~21, ~62 d

Read those three tiles together and the paper's two findings appear. Separation in time: water leaving as recharge moved 2–7× faster than water leaving through trees. Separation in space: the Bayesian mixing model says trees drew 89 ± 6% of their water from bulk soil-matrix storage rather than the freely draining "mobile" water — even though soil at 25 cm is older on average than the seepage collected at 3 m, which only makes sense if much of the seepage bypassed the soil matrix through preferential flowpaths. The old phrase "tightly bound water" earns a correction here: the matrix water trees used was not bound at all, merely slow to drain — the authors adopt Brantley et al.'s term "matrix water," and the two-water-worlds offset of Week 2 acquires a transport mechanism.

Gamma-shaped ages: the explorer

The 2019 analysis fits each breakthrough with a gamma transit-time distribution — the two-knob family (shape α, scale β; mean = αβ) that catchment hydrology reaches for first. α is the shape's whole personality: α < 1 gives an L-shaped, young-dominated distribution with a long tail; α ≈ 1 is exponential (the well-mixed reservoir of Section 6); α > 1 rises to a delayed hump. Load each fitted preset and read its story.

0.25
9 d
scale β
time per "compartment"
median
vs mean
younger than 7 d
one week's worth
skewness 2/√α
the tail-heaviness index
The seepage α of ~0.25 sits below the 0.3–0.7 range reported for real catchments — an extremely young-water-dominated outflow — while the tree fits (0.57, 0.70) land squarely inside that catchment range, and H. crepitans (α 3.7, a six-week hump) behaves like a piston with dispersion. Two species never showed the label at all: one apparently living on the mesocosm's "stream," the other on stored water — a free lesson that a tracer you never see constrains a source you cannot otherwise reject. And the modelled mass recoveries (~60% seepage, ~45% transpiration) remind you the accounting was closed enough to mean something. "Trees are not straws": species, not just soil physics, set the age of transpired water.
10 · Two ways to read a curve

The breakthrough curve, parametric and phenomenological

The 2026 Comment reopens the same Biosphere 2 dataset with a teaching agenda: strip transit-time analysis down to two approaches simple enough for any lab group to run, apply both to every breakthrough curve (BTC), and be honest about what neither can promise. It is the shortest path in this course from "I have tracer data" to "I have a defensible timescale."

Parametric (mechanistic)

  • Fit the BTC with a theoretical TTD and interpret the parameters. Two candidate shapes, two hypotheses about plumbing: gamma = serial (water queues through compartments in series — the sum of exponential steps), lognormal = parallel (many simultaneous pathways whose effects multiply).
  • Selection by a six-criteria vote (AIC, BIC, R², RMSE, KS, Anderson–Darling): gamma won 7 of 8 soil curves; lognormal won 4 of 5 xylem curves. Serial soils, parallel trees — as a hypothesis, not a verdict; the paper is explicit that the fits are descriptive, and several are near-ties.

Phenomenological (data-based)

  • No assumed shape. Read three numbers straight off the curve: tz, when the peak arrives; tμ, the concentration-weighted mean time; and Δt = tμ − tz, a tailing metric — how far dispersion and retention drag the mean past the peak.
  • Plus a velocity: flowpath length over tμ — 2–14 cm d⁻¹ through the soils, 18 cm d⁻¹ to deep percolation, and 52–193 cm d⁻¹ up the trees.
  • The cost of assumption-freedom: the numbers only integrate over the observed window, so where the tail is unfinished (the trees, above all) tμ is a lower bound.

Anatomy of a breakthrough curve

A synthetic BTC with two knobs: when the peak comes, and how heavy the tail is. Watch the three phenomenological metrics respond — then truncate the record and watch tμ quietly shrink, which is precisely why the Comment reports its empirical means as lower bounds.

7 d
0.35
240 d
tz (peak)
the fast pathway's vote
tμ (mean, within window)
every pathway's vote
Δt (tailing)
dispersion + retention

What the reanalysis found — and proposed

  • Preferential flow, quantified. In one soil pit the tracer peaked at 2 days at every depth from 15 to 130 cm — vertically coherent bypass channels — while the neighbouring pit's peaks walked down (2 → 20 days). Two pits a few metres apart, two different plumbing diagrams: a warning against single-profile generalization.
  • "Xylem bias," a named hypothesis. Tracer velocities up the five trees spanned 0.52–1.93 m d⁻¹, and the fraction of labelled water at the xylem peak averaged only ~20% — roughly 80% of what trees transpired was older, stored water. The Comment proposes that stands route a disproportionate share of transpiration through hydraulically "advantaged" individuals — preferential flow's canopy-level analogue — offered explicitly as something to test, with sap-flux and storage measurements named as the test.
  • Method matters at the tree scale. Parametric and data-based means nearly agree in soils (14 ± 2 vs 12 ± 2 days) but split two-fold in plants (59 ± 13 vs 29 ± 6 days) — the unfinished tails again. And a concentration BTC is not a TTD: without coupling concentrations to water fluxes, all such timescales are comparative metrics, not absolute means. The Comment says so of its own numbers, repeatedly — model that candour.
  • The stakes. A table of ten climate and terrestrial-biosphere models (CLM, JULES, ORCHIDEE, …) shows none representing the weeks-to-months lag between infiltration and transpiration, or tree-internal storage, that both papers document. The "call for broader dialogue" of the title is aimed there — at ecophysiology, soil physics and catchment hydrology jointly instrumenting the next experiment.
2019 vs 2026: the same trees, different numbers — a discussion point, not an erratum
Outflux2019 MTT (flow-weighted gamma)2026 MTT (parametric BTC fit)2026 tμ (data-based)
Seepage / recharge≈ 9 d22 d19 d
C. racemosa≈ 17 d53 d
H. elatus≈ 21 d45 d
H. crepitans≈ 62 d109 d47 d
P. indicusexcluded (no label uptake)18 d15 d

Per-species tμ is quoted in the Comment's text only for the fastest and slowest trees; across species tμ spans 15–47 days. Same dataset, defensible choices at every step, materially different numbers. The 2019 study convolved the input in flow-weighted time and required tracer-mass accounting; the 2026 Comment fits concentration curves directly and says its timescales are experiment-specific comparisons. Nothing here is hidden — the Comment cites the 2019 uncertainty analysis as the fuller treatment. For the seminar: which choices moved the numbers, and which number would you put in a model? (Notice the pattern of Section 7 returning at days-scale: methods weight the same mixture differently.)

11 · Reading the four papers

Four papers, three blocks, one argument

Cook & Böhlke supply the working machinery of groundwater dating; Bethke & Johnson dismantle its central assumption; the Block 3 pair rebuilds the same ideas at the scale of a soil profile and a tree. The guides below are maps, not substitutes: what each paper asks, where its load-bearing figures live, which equations to recognize, and where a careful reader might press. The notes and the critique are yours to write.

Block 1 · Core reading

Cook, P. G., & Böhlke, J.-K. (2000). Determining timescales for groundwater flow and solute transport. Ch. 1 of Cook & Herczeg (eds.), Environmental Tracers in Subsurface Hydrology. Kluwer.

Thirty pages that set up the whole enterprise: tracer types, the transport models, and what age data are used for. The reading list cites the volume by its editors (Cook & Herczeg); the chapter itself is by Cook and Böhlke. doi:10.1007/978-1-4615-4557-6 (volume)

Block 2 · Supplementary reading

Bethke, C. M., & Johnson, T. M. (2008). Groundwater age and groundwater age dating. Annu. Rev. Earth Planet. Sci., 36, 121–152.

The conceptual reset: age as a property of molecules, samples as mixtures, and reactive transport modeling as the way forward. Thirty-two pages, generously illustrated, no field data of its own — every example is a model with a purpose. doi:10.1146/annurev.earth.36.031207.124210

Block 3a · Paired reading

Evaristo, J., Kim, M., van Haren, J., Pangle, L. A., Harman, C. J., Troch, P. A., & McDonnell, J. J. (2019). Characterizing the fluxes and age distribution of soil water, plant water, and deep percolation in a model tropical ecosystem. Water Resour. Res., 55(4), 3307–3327.

The controlled experiment: a drought, a deuterium-labelled rewetting, and transit-time distributions for seepage, soil and transpiration in one closed system. Open access (CC BY-NC-ND). doi:10.1029/2018WR023265

Block 3b · Paired reading

Evaristo, J., Wright, C., Bauser, H. H., Knighton, J., Johnson, D. M., & Kim, M. (2026). Tracer labelling and transit time modelling in soil–plant systems: perspectives and a call for broader dialogue in ecohydrology. Ecohydrology, 19(1), e70182.

A Commentary that reuses the 2019 dataset as a teaching testbed: two accessible modelling routes, a named hypothesis (xylem bias), and an argument about what land-surface models are missing. Open access, with code and data links. doi:10.1002/eco.70182

Cross-paper synthesis, in one line: Cook & Böhlke teach you to compute an age, Bethke & Johnson teach you not to trust one, and the Biosphere 2 pair shows both lessons operating in a system small enough to audit. The question that carries forward: when your proposal says "we will date the water," which of this week's four meanings of that sentence will it mean — and would the other three give the same answer?
12 · Practice

Four situations to reason through

Each scenario gives the kind of evidence a Week 3 reader should now be able to interrogate. Choose the reading you would defend first, then compare with the debrief.

Habit to keep: before quoting any water age, say aloud which age it is — a piston-flow sample age, a mean of a distribution you have argued for, or a comparative timescale from one experiment — and what the same measurement would read if the sample were a mixture. Most published "ages" survive the first question and stumble on the second.
13 · Self-check

Ten questions before the meeting

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

14 · Vocabulary

Glossary

The Week 3 working vocabulary, plus a few terms you will meet again in Weeks 5 and 11. Search or browse.

15 · Where to go next

The Week 3 readings — and two optional companions

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. Two of this week's four are open access.

CORE

Cook, P. G., & Herczeg, A. L. (eds.) (2000). Environmental Tracers in Subsurface Hydrology, Ch. 1 — Determining timescales for groundwater flow and solute transport (Cook & Böhlke).

Tracer types and time windows; Vogel-type age models and the lumped-parameter zoo; recharge, velocity, archive and reaction-rate applications. The week's machinery. doi:10.1007/978-1-4615-4557-6

RESET

Bethke, C. M., & Johnson, T. M. (2008). Groundwater age and groundwater age dating. Annu. Rev. Earth Planet. Sci., 36, 121–152.

Age as a mixture property; the three clock classes and their mixing biases; age mass, aquitards, and reactive transport inversion. The week's argument. doi:10.1146/annurev.earth.36.031207.124210

TEST

Evaristo, J., et al. (2019). Characterizing the fluxes and age distribution of soil water, plant water, and deep percolation in a model tropical ecosystem. Water Resour. Res., 55(4), 3307–3327.

A drought–rewetting D₂O experiment at Biosphere 2: transit times for seepage (~9 d) versus transpiration (17–62 d), and matrix-water use by trees. Open access. doi:10.1029/2018WR023265

DIALOGUE

Evaristo, J., et al. (2026). Tracer labelling and transit time modelling in soil–plant systems. Ecohydrology, 19(1), e70182.

The 2019 dataset reread two ways — parametric (gamma/lognormal) and phenomenological (tz, tμ, Δt) — plus the xylem-bias hypothesis and the case to the land-surface-modelling community. Open access. doi:10.1002/eco.70182

OPTIONAL

Suckow, A. (2014). The age of groundwater — definitions, models and why we do not need this term. Appl. Geochem., 50, 222–230. · Lehmann, B. E., Davis, S. N., & Fabryka-Martin, J. T. (1993). Atmospheric and subsurface sources of stable and radioactive nuclides used for groundwater dating. Water Resour. Res., 29(7), 2027–2040.

Suckow pushes this week's logic to its provocative conclusion — retire the word "age" altogether in favour of tracer-specific statements. Lehmann and colleagues audit every nuclide's atmospheric and in-situ sources, and conclude ³H/³He and ⁸¹Kr carry the least interpretive baggage. Not discussed in a block.

Coming after the holiday — Groundwater dating II: young water

The under-50-year window gets its own meeting: ³H/³He as a self-starting clock, CFCs and SF₆ as calendar clocks with atmospheric complications, and the lumped-parameter models of Section 6 turned into a working tool (the TracerLPM workbook). Everything this week said about mixtures applies with the signs filled in.

Carry-forward question, for your proposal topic: for the water your question cares about, what age range do you expect — and does a tracer exist whose window, source terms, and mixing behaviour could actually resolve it? If the answer is "not cleanly," that is not a dead end; it is a proposal rationale.