Clocks That Fall With the Rain

Ten years earlier, yet closer to the surface

Between 1982 and 1985 Fred Phillips and his colleagues sampled three desert soils in New Mexico and measured, at two of them, both of the radioactive tracers that the weapons tests had dropped onto the ground: chlorine-36, whose fallout peaked around 1955, and tritium, whose fallout peaked in 1963–64. Chloride is an anion, and in laboratory soil columns anion exclusion pushes it into the faster-moving water so that it travels ahead of the water itself. So the ³⁶Cl — with a ten-year head start and, if anything, a chemical advantage — should have been the deeper of the two. It was not. At both sites where both tracers were measured, the tritium peak sat 1–3 m down while much of the bomb ³⁶Cl was still near the surface. Which explanation would you defend?

This is the week's whole argument in miniature. A tracer is a physical object that must actually travel through the soil, and the rules it travels by — solute, gas, or part of the water molecule — decide what its clock is reading. Section 4 draws the two fallout pulses, Section 5 the profiles, and Section 6 the explanation the authors settled on, with its own uncertainties named.

Cosmic rays as an isotope factory, bombs as a calendar

The cosmogenic tracers of this week's readings were made in the atmosphere. Cosmic rays smash into nitrogen and argon nuclei and leave fragments behind: tritium and radiocarbon from nitrogen; sulfur-35, chlorine-36, argon-39 and silicon-32 from argon; krypton-81 from krypton. Each is rained or dusted out onto the land surface, and its arrival rate through time — its input function — is what makes it a clock. Cosmogenic production is roughly steady, so a cosmogenic isotope keeps time by decay. The weapons tests added something different: sharp pulses. Neutron activation of chloride in seawater during the Pacific atoll tests made a ³⁶Cl spike that peaked around 1955; the later tests, fired in the stratosphere at high northern latitudes after the first test moratorium lapsed, made the tritium and ¹⁴C spikes that peaked in 1963–64. A pulse is not a decay clock but a dated marker: find it in a soil or an aquifer and you know where a particular year's water has got to. Click a card.

The half-life sets the window

A radioactive tracer is useful while enough of it is left to measure and little enough has decayed that the remaining fraction still changes with time. Five half-lives leave about 3 % — a workable rule of thumb for the far end of the window, subject to how well the laboratory can count. For ³⁵S that is 1.2 years; for tritium about 60; for ³⁶Cl a million and a half. Drag the elapsed time and watch what survives of each. The axis is logarithmic because the half-lives span six orders of magnitude; the curves are the same function, e^−λt, with λ = ln 2 / t_½.

Two pulses, two chemistries, one calendar

The thermonuclear tests of the 1950s fired on Pacific atolls, and their neutrons activated the ³⁵Cl in seawater into ³⁶Cl, which the atmosphere washed out within a few years: a global-mean fallout that Bentley et al. modelled with a peak around 1955, hundreds of times the natural fallout rate. The later, larger tests, after the first moratorium lapsed, fired in the stratosphere at high northern latitudes; they activated no seawater but made tritium and ¹⁴C, whose fallout peaked in 1963–64 — about 6,000 TU at the peak in Ottawa (3,278 TU as the 1963 annual mean in the GNIP record, the value the Week 5 primer used), 60 TU in Melbourne. The two pulses are ten years apart, and only one of them decays on a human timescale. Slide the sampling year to see what is left of each by the time a profile is cored.

The ³⁶Cl curve is redrawn at reading precision from Phillips et al.'s Fig. 1 (the Bentley et al. 1982 box-model fallout, with the Dye 3 ice-core points of Elmore et al. 1982 as circles); the tritium and ¹⁴C curves are smoothed annual reconstructions anchored to the published records summarised in Cartwright et al.'s Fig. 4 and the Ottawa values used in the Week 5 primer. They are teaching curves, not station data. The 'natural fallout' line is implied by the paper's own inputs rather than stated: 0.375 mg L⁻¹ of input chloride × 20 cm yr⁻¹ of rain × a natural ratio of 700 × 10⁻¹⁵ is about 28 atoms m⁻² s⁻¹, or 0.03 on the chart's scale, so the 1955 peak was some three hundred times natural. Phillips et al. add a caution that applies to all three: actual fallout "was highly variable, both seasonally and as a function of location", so a local input history is always better than a global one.

Three New Mexico profiles

Two sites on the Sevilleta National Wildlife Refuge north of Socorro (20 cm of rain a year against 178 cm of lake evaporation) and one on the New Mexico State University Ranch 200 km to the south (23 cm against 239 cm of pan evaporation). SNWR 1 is a uniform fine sand on an old floodplain of the Rio Salado, with the water table at about 5 m; SNWR 2 a sandy loam on a Pleistocene terrace with a carbonate horizon at 1–2 m; NMSUR a sandy loam to sandy clay loam with 12–24 % clay. Chloride was leached from several kilograms of soil, precipitated as AgCl, and counted by accelerator mass spectrometry; samples for tritium were sealed in the field and their water extracted by nitrogen-gas evaporation–condensation or azeotropic distillation. Pick a site and read the four profiles together.

Why the anion lost the race

Three explanations were on the table. Adsorption fails on chemistry: anions generally sorb only at pH below about 5, and these soils, like virtually all soils of this desert region, are basic — the anion-exclusion regime, where chloride should run ahead. Salt sieving — water films thinner than the anion-exclusion layer — is documented in compressed clays but uncertain in unsaturated soils, and a laboratory experiment in which chloride was redistributed through the Sevilleta sand at 2–11 % volumetric water content under constant vapour pressure showed no chloride retardation at all; if anything chloride led the water. That left vapour. Tritiated water can cross an air-filled pore as vapour; a chloride ion cannot. In a soil this dry, some liquid flow paths dead-end at such vapor gaps: the water continues, the solute is stranded, and only diffusion back against the flow can free it. A steady input like stable chloride reaches equilibrium with the traps; a transient pulse like bomb ³⁶Cl is retarded. Switch between the laboratory and the field, then fit the authors' one-parameter model to the SNWR 1 data.

Five ways to a number, and why they disagree

The profiles, and the soil-physics record at Sevilleta 1, yield recharge rates by five methods — not every method at every site. Darcy's law from years of moisture and tension data (a geometric-mean conductivity gives 3.7 cm yr⁻¹, a harmonic mean 0.70). The tritium-peak method: the water stored above the bomb tritium peak divided by the 20 years since the peak fell. A tritium mass balance (Allison's method): the soil tritium inventory against a decay-corrected input, times effective precipitation. The ³⁶Cl-peak method: the same arithmetic with the ³⁶Cl peak and 30 years. And the chloride mass balance from the stable-chloride profile. The chloride-based numbers come out two to six times lower than the tritium-based ones — which is exactly what Section 6 predicts if chloride lags the water. Click a method; then try the peak arithmetic yourself.

The peak method, step by step

A dated marker at depth d, Δt years after it fell, gives a mean pore-water velocity v = d/Δt and — with the mean volumetric water content θ̄ of the column above it — a water flux R = θ̄·v. Phillips et al. divided the cumulative water above the peak by 20 or 30 years, which is the same thing done interval by interval; Tao et al. report the velocity alone (their eq. 1), with n = 57 years for cores averaged over 2017 and 2020. The presets set d and Δt from the papers and choose θ̄ so that the result reproduces the reported figure (Table 1's own water contents give somewhat higher values — a point taken up in the Phillips guide); the sliders are yours.

Two velocities in one soil

On the Changwu Tableland of China's Loess Plateau (585 mm of rain a year, 897 mm of potential evapotranspiration, a water table below 30 m), Tao, Evaristo and colleagues cored to 13.6–27 m under four apple orchards planted in 2008, 2005, 1998 and 1994, and under the cropland the orchards replaced. Between July 2016 and October 2020 — wet years — new water recharged the upper 5.4–7.6 m under every orchard, some 300 mm of storage in three orchards and 483 mm in the oldest; below that, the deep soil lost water — 109 to 392 mm — where the roots reach. And the 1963 tritium peak? After 57 years it sits at 7.25 m under cropland and only 5.7–7.15 m under the orchards. New water moved more than five metres in four years; the tritium-tagged water moved six or seven in fifty-seven. Same soil, two speeds. Choose a profile.

How old is the water the trees are drinking?

If the profile moves as a piston, the water at depth z fell as rain z/υ years ago, and the depleted zone's depth range maps directly onto an age range. The authors weight each depth's age by its water loss (their eq. 3) and use υ = 0.13 m yr⁻¹ for all orchards; the readout here uses the simpler midpoint age of the zone, so it differs a little from the reported values, which are shown for comparison. Slide the velocity down toward the orchard values and watch the ages climb.

A clock that runs out in a year

Sulfur-35 is made by cosmic-ray spallation of argon above the troposphere, oxidises to sulfate, and comes down in rain and snow as ³⁵SO₄²⁻ — at 5–12 mBq L⁻¹ in the Sagehen snowpack, which works out to roughly one ³⁵S atom per 10¹³–10¹⁴ sulfur atoms in snow holding a few tenths of a milligram of sulfate per litre. Its half-life of 87.5 days is what makes it interesting: after five half-lives, 1.2 years, 3 % is left. So a groundwater or stream sample containing measurable ³⁵S must contain water that fell within the last year or so, and the ratio of the sample's activity to the snow's, corrected for the decay of the snow since melt began, is the percent new snowmelt. Urióstegui et al. define new snowmelt as the current water year's, take the pulse to start on the day after peak snow water equivalent (t₀), and write PNS = A_GW,SW/A_SNOW(t) × 100 (their eq. 2). Three things move the answer: the snow end-member, its decay by the sampling date, and the counting error on an activity that is often a few tenths of a millibecquerel. Set them.

How much of the creek is this winter's snow?

Sagehen Creek drains 27 km² of Tertiary volcanics on the eastern slope of the Sierra Nevada, 1,940–2,600 m, about 80 cm of precipitation a year of which 80 % is snow. Sampled every other month from February 2010 to August 2011, the creek never carried more than 14 % new snowmelt — 14.0 ± 3.4 % soon after melt began in April 2010, 4.8 % in May as discharge kept rising, 8.4 % at August baseflow, 0.2 ± 6.6 % in August 2011 — even though water year 2011 brought 82 % more precipitation and nearly twice the peak snow water equivalent (0.47 → 0.89 m) of 2010. A perennial spring held 0.8–6.2 %. Over the April–July melt season, which carries 79–84 % of the year's flow, new snowmelt was 8.0 ± 0.3 % of discharge in 2010 and 9.9 ± 0.5 % in 2011. The rest was groundwater recharged in earlier winters: the creek is a spring in a river's clothing.

From a percentage to a recharge budget

Hydrograph separation turns PNS into a volume: the new-snowmelt discharge during April–July, S_AMJJ. The authors then write groundwater recharge as R = T_p − S_AMJJ − ET (Table 5, footnote b), with T_p the year's precipitation over the basin and ET an annual rate from two published models (1.8 mm d⁻¹, or 1.4 in the dry year), and convert R to a change in head with a specific yield of 0.08–0.15. The presets reproduce Table 5; the sliders show how much of the answer is the evapotranspiration you assume.

Wells that remember the spring, then forget it

Martis Valley Groundwater Basin is five times larger than Sagehen (148 km²), with wells screened from 15 to 415 m below ground. In December 2011–January 2012 and again in June 2012, every well sampled carried measurable ³⁵S — 8 to 28 % new snowmelt, across the whole range of screen depths. By September 2012 only the shallowest well (I, 15–61 m, next to Donner Creek) and one other (N) still had detectable activity; seven were at or below background. New snowmelt had reached the aquifer within months and then, the authors suggest, been pumped from an age-stratified aquifer, discharged through shallow flowpaths, or mixed away within a season — the same season in which ³H/³He ages at the same wells drifted older. Click a bar for the well.

A recharge rate is an average over a residence-time distribution

Cartwright et al.'s review makes one argument from many tracers: because groundwater sampled from a well is a mixture of water that followed flow paths of different lengths, a tracer concentration reflects a distribution of residence times, and any recharge rate derived from it is averaged over that distribution — years to decades for ³H, CFCs, SF₆ and ⁸⁵Kr; millennia for ¹⁴C; hundreds of thousands of years for ³⁶Cl and ⁸¹Kr. Their eq. 1 is Week 5's convolution integral; their eqs. 2–4 turn a mean residence time into a rate (R = φ v_z for near-vertical flow; R = φ H ln[H/(H − z)]/τ_z for the exponential model); and their eq. 5 is a simpler bookkeeping applied in Niger, the Murray Basin, Korea and France — the renewal rate, the fraction of the upper aquifer's water replaced each year: C_g(t) = (1 − R_N) C_g(t − 1) e^−λ + R_N C_i(t), with R = R_N φ H_b. Run it against the bomb pulses.

The ¹⁴C input is the atmospheric curve of Section 4 (pre-bomb value near 98 pMC); Cartwright et al. point out that the input that matters is soil CO₂, which rose only from about 95 to 115–130 pMC in the early 1990s and was 110–115 by the mid–late 2000s — later and flatter than the air — so the ¹⁴C axis here overstates the bomb excursion. Their Fig. 5 is drawn for Southern Hemisphere waters on a linear 0–4.5 TU axis; the log axis here lets the Ottawa input fit on the same panel. The point survives: with no mixing, tritium falls to near background before there has been substantial decay of ¹⁴C, and a sample with more tritium than its ¹⁴C allows is a mixture.

Eqs. 2 and 4: from a residence time to a rate

For a sample z metres below the water table with mean residence time τ_z. The piston version assumes vertical flow; the exponential version (Cook & Böhlke's, for a homogeneous unconfined aquifer of thickness H under uniform recharge) accounts for the flow lines converging toward the base. A well screened over the lower part of that aquifer sees Week 5's partial-exponential distribution — Cartwright et al.'s Fig. 3 and text give its 5th–95th percentiles as 6–18 years for a 10-year mean, and about 3,000–9,000 years for a 5,000-year mean.

The mixing bias: why the calculated age is too young

Because radioisotope activity falls off exponentially with age, a mixture of young and old water does not have the activity of its mean age: it has more, because the young fraction contributes disproportionately. Read that activity as a single age and you underestimate the true mean residence time — Cartwright et al.'s Fig. 6, and the same trap Weeks 3 and 5 set for ¹⁴C and the ³H/³He clock. Mixing happens in the aquifer (heterogeneous hydraulic conductivity, macroscopic dispersion, exchange with aquitards), at the well (long screens that draw several flow paths), and under pumping that redirects flow paths. Choose a tracer and mix two waters.

Which clock for which question

The week's third learning goal: match the tracer to the timescale the question actually asks about. Start with the question, never the isotope. Pick one.

A diagnosis board

Each row is a symptom you might meet in a cosmogenic or bomb-pulse data set, the cause the readings offer, and the test or fix. Click a row for the detail.

Four readings, three blocks, one habit of mind

Cartwright et al. supply the map of the whole toolkit and its limits; Phillips et al. and Tao et al. are the paired Block 2 readings — the same bomb-pulse method, thirty-five years and two continents apart, and both find a soil moving at two speeds; Urióstegui et al. take the shortest clock in the box to a mountain basin. 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.

Four situations to reason through

Each scenario gives the kind of evidence a Week 9 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 9 working vocabulary, with a few terms you will meet again in Weeks 10 and 11. Search or browse.

The Week 9 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 Catena paper is open access under a CC BY licence; the reading list notes a green open-access copy of the review; check the two Wiley articles through the library.