Introduction: measuring the age of the stagnant zone
In #12 (fluoride) and #13 (arsenic), the high concentrations both clustered in the long-residence stagnant zone — water that had lingered for decades, reacting with rock. But how do we measure those “decades”?
Groundwater records two things about itself: where it was born (recharge source) and when it was born (age). The former is told by the stable isotopes of the water molecule (δ¹⁸O, δD); the latter by environmental tracers whose atmospheric concentrations have changed over time (³H, CFCs, SF₆, ⁸⁵Kr). This article reviews these tools for reading “the time of water,” from textbook basics to field cases.
Where #11–13 were about water gaining its chemistry by reacting with rock, #14 measures the time that governs those reactions.
A water’s fingerprint: stable isotopes
This section reviews isotope basics in some depth. Readers already familiar may skip to “Where was it born.”
What isotopes are
Isotopes are atoms with the same number of protons (i.e., the same element) but different numbers of neutrons. Each of water’s two elements has stable isotopes:
- Oxygen: ¹⁶O (99.76%), ¹⁷O (0.04%), ¹⁸O (0.20%)
- Hydrogen: ¹H (99.985%), ²H = deuterium D (0.015%) (plus radioactive ³H = tritium, below)
So most water molecules are the light ¹H₂¹⁶O, but a tiny fraction are heavy ¹H₂¹⁸O or ¹HD¹⁶O. The slight difference in these ratios is the fingerprint of a water’s history.
Why δ notation — a relative value against VSMOW
The absolute ¹⁸O/¹⁶O ratio is about 0.0020, and differences between samples are a thousandth of that. Rather than absolute values, we express the deviation from a standard in per mil (‰) — the δ notation:
\[\delta = \left(\frac{R_{\text{sample}}}{R_{\text{standard}}} - 1\right) \times 1000\ (‰), \qquad R = \frac{^{18}\mathrm{O}}{^{16}\mathrm{O}}\ \text{or}\ \frac{\mathrm{D}}{\mathrm{H}}\]
- The standard is VSMOW (Vienna Standard Mean Ocean Water); by definition δ¹⁸O = δD = 0‰.
- Negative δ = lighter than the standard (depleted in the heavy isotope). Continental precipitation and groundwater are usually negative.
- Example: δ¹⁸O = −8‰ means “8‰ (0.8%) less ¹⁸O/¹⁶O than VSMOW.”
Isotope fractionation — heavy and light water behave differently
During phase changes (evaporation, condensation), heavy and light molecules move slightly differently — fractionation.
- Equilibrium fractionation: heavy isotopes (¹⁸O, D) bond more strongly and stay in the liquid (condensate), resisting the vapor. The effect is larger at lower temperature.
- Kinetic (non-equilibrium) fractionation: extra fractionation during rapid evaporation into dry air — larger when humidity is low. It is the source of d-excess (below).
- As a result,
- vapor evaporated from the sea is lighter than seawater (enriched in ¹⁶O, ¹H);
- as rain condenses and falls, the heavy water leaves first, so the remaining vapor becomes progressively lighter (Rayleigh distillation);
- hence the more the vapor is carried inland, higher, or to colder latitudes, raining out along the way, the lighter (more negative) the later rain becomes.
The meteoric water line (GMWL)
Craig (1961) found that precipitation worldwide falls on a single line when δ¹⁸O and δD are plotted — the Global Meteoric Water Line (GMWL):
\[\delta \mathrm{D} = 8\,\delta^{18}\mathrm{O} + 10\]
- Slope 8 reflects the ratio of equilibrium fractionation for H and O (D fractionates about 8× more than ¹⁸O). As long as evaporation/condensation is near-equilibrium, the two move together at this slope.
- Intercept 10 = d-excess (Dansgaard 1964), defined \(d = \delta \mathrm{D} - 8\,\delta^{18}\mathrm{O}\), reflecting the relative humidity of the vapor source — larger for water evaporated from dry seas.
- Each region forms a Local Meteoric Water Line (LMWL) close to the GMWL. Groundwater keeps the δ of the precipitation that recharged it (little evaporation underground), so it plots on this line — the basis for tracing recharge.
The “effects” that shift δ (Dansgaard 1964)
Precipitation δ varies systematically, all understandable via Rayleigh distillation:
- Latitude effect: lighter at higher latitude.
- Altitude effect: lighter at higher elevation (about −0.15 to −0.5‰/100 m in δ¹⁸O) → used to estimate recharge elevation.
- Continental effect: lighter farther inland.
- Amount effect: lighter for heavier rainfall (marked in the tropics).
- Seasonal effect: winter precipitation is lighter than summer.
Where was it born — reading recharge (the altitude effect)
Of these effects, the altitude effect is the one most used for groundwater. Since precipitation δ is lighter at higher elevation, the δ of groundwater can be back-calculated to the elevation at which it recharged.
Figure 1 shows the relationship. Groundwater (red) plots on the meteoric water line and moves toward the lower-left (lighter) the higher the recharge elevation. Water that has evaporated, in contrast, leaves the line along an evaporation line of slope 4–5. Seawater sits at δ ≈ 0 (upper right); a fresh–seawater mixture falls on the line joining them (well suited to the freshwater lens of #7).
In the Kirishima case (Ide et al. 2016), spring δD correlated clearly with mean catchment elevation, indicating recharge mainly at 700–1000 m. The δ value is a label for “at what elevation the water was born.”
When was it born — dating groundwater
Once the source is known, we turn to age. Young groundwater (within decades) can be timed with substances whose atmospheric concentration has changed over time. Each has a distinct atmospheric history, as in Figure 2.
- Tritium ³H (half-life 12.3 yr): the radioactive hydrogen isotope; nuclear testing left a large peak (bomb tritium) in 1960s precipitation. Age follows from decay and input history.
- CFCs: rose monotonically through the late 20th century, then plateaued after the Montreal Protocol. The atmospheric level at recharge gives the recharge year.
- SF₆: a similarly rising anthropogenic tracer.
- ⁸⁵Kr (krypton-85) (half-life 10.8 yr): risen from nuclear-fuel reprocessing; strong for young water (< 50 yr) and less affected by local contamination.
What these give is not a single absolute date but a “model age” that includes flow mixing. Water pumped from a well is a mixture of many paths and ages. So a lumped parameter model (LPM: piston flow PFM, exponential mixing EMM, etc.) is assumed to estimate a mean residence time. The resulting age is an “apparent/model age” resting on that assumption — to be read honestly as such.
The Kumamoto case — dating with ⁸⁵Kr (Kagabu et al. 2017)
Kumamoto depends on groundwater for nearly 100% of its drinking water. Kagabu et al. (2017) measured ⁸⁵Kr, CFCs, SF₆ and ³H together to map the time structure of the regional flow system.
Here ⁸⁵Kr was decisive. Where CFCs and SF₆ were anthropogenically contaminated in urban areas and could not yield ages, ⁸⁵Kr — little affected — made dating possible (the core of this study).
The result was clear: along the main flow line A–A′, the ⁸⁵Kr apparent age increased from ≈16 yr (recharge) → ≈36 yr (discharge) → ≥55 yr (stagnant zone) (Figure 3), consistent with an LPM analysis using a ³H time series.
The striking point: this “stagnant zone ≥55 yr” is exactly where the fluoride of #12 and the arsenic of #13 concentrated. An independent tracer, ⁸⁵Kr, gave the answer of time — “because the water is old” — to why they accumulate there.
The Kirishima case — the distribution of residence time (Ide et al. 2016)
The same idea works in volcanic terrain. Ide et al. (2016) measured CFCs in 25 springs of the Kirishima volcanic group and, assuming exponential-mixing plus piston flow (EMM+PFM) in an LPM, estimated mean residence times of 1–58 years:
- under 10 years near the summits (young water);
- 10–40 years around the foot;
- 50–60 years at the longest, where piston flow dominated (note: the system as a whole is dominated by mixing flow (EMM); piston-flow dominance is limited to this longest flow path — the end of the Takachihonomine lava).
Residence time is set by topography and flow style. Combined with the altitude effect (recharge elevation), one can map “where the water was born and how many years it travelled.”
Age as a time axis — back to water quality
Isotopes and age are not ends in themselves. Their value is in giving a time axis to water quality.
- Water quality is a function of age. The fluoride of #12 and the arsenic of #13 both concentrated in the long-residence stagnant zone (≥55 yr). Age answers why there with time.
- A bridge to the next article: Ide et al. (2018) showed at Kirishima that dissolved silica saturates and secondary minerals shift from kaolinite to Ca-smectite about 20 years after recharge. Residence time (this article) × water–rock “maturation” is followed with PHREEQC in #15.
Summary
- Groundwater records both where it was born (δ¹⁸O, δD = recharge source, altitude effect) and when (³H, CFCs, SF₆, ⁸⁵Kr = age).
- On the meteoric water line δD = 8δ¹⁸O + 10, groundwater preserves its recharge fingerprint; the altitude effect gives recharge elevation, the evaporation line records evaporation.
- Age is not a single value but a model age assuming a flow style (LPM) — read honestly as such.
- In Kumamoto, ⁸⁵Kr traced 16 → 36 → ≥55 yr, tying the stagnant, old water to the concentration zones of #12/#13. In Kirishima, residence times of 1–58 yr followed topography.
- And age gives water-quality concentration its time axis, leading to the “maturation” of #15.
At Kirishima, we combine residence time (this article) × water–rock reaction (PHREEQC). Ide et al. (2018)’s finding — “silica saturation and a kaolinite→Ca-smectite shift about 20 years after recharge” — is retraced along a PHREEQC reaction path. The article where PHREEQC shines most.
References
- Kagabu, M., Matsunaga, M., Ide, K., Momoshima, N., Shimada, J. (2017) Groundwater age determination using ⁸⁵Kr and multiple age tracers (SF₆, CFCs, and ³H) to elucidate regional groundwater flow systems. Journal of Hydrology: Regional Studies, 12, 165–180.
- Ide, K. et al. (2016) Estimation of spring water residence time in the Kirishima volcanic area using CFCs from repeated sampling (in Japanese). Journal of Japanese Association of Hydrological Sciences, 46(3), 213–231.
- Ide, K., Hosono, T., Hossain, S., Shimada, J. (2018) Estimating silicate weathering timescales from geochemical modeling and spring water residence time in the Kirishima volcanic area, southern Japan. Chemical Geology, 488, 44–55.
- Craig, H. (1961) Isotopic variations in meteoric waters. Science, 133, 1702–1703.
- Dansgaard, W. (1964) Stable isotopes in precipitation. Tellus, 16, 436–468.
- Clark, I. & Fritz, P. (1997) Environmental Isotopes in Hydrogeology. Lewis Publishers.
- Cook, P.G. & Herczeg, A.L. (eds., 2000) Environmental Tracers in Subsurface Hydrology. Kluwer.