Data are collected with six Mirion (formerly Canberra) Broad Energy intrinsic germanium detectors (BEGe) with carbon fiber endcaps and ultra-low background cryostats which are cooled with liquid nitrogen. The detectors are shielded with 10 cm of ultra-low background lead. Data acquisition is performed with Mirion DSA-1000 or Lynx digital signal processors running with Genie 2K software v.3. The specific BEGe detector design is important because it provides excellent efficiency at low gamma energies for ²¹⁰Pb acquisition without sacrificing efficiencies at high energies. Carbon fiber provides good transmission of the low energy ²¹⁰Pb emission which is otherwise attenuated by an aluminum endcap. Samples are typically run using a standardized four-day count time. Of two detector models, BEGe 3830 (38 cm² detector active area, 30 mm thickness) and larger BEGe 5030 (50 cm², 30 mm), the latter saves one day of counting and accomplishes in three days what the 3830 accomplishes in four.

Foliage, litter, and soil samples are oven dried at 60°. Bulk soils are sieved or hand-picked to remove clasts and debris > 2 mm in diameter. Fine roots > 1 mm diameter or > 2 cm in length are removed by hand. Foliage and leaf litter (Oi and Oe horizon) are typically milled to <1 mm using a Wiley mill with stainless steel blades. Soil samples are loosely disaggregated as necessary by agate mortar and pestle and packed into 110 cm³ polyethylene petri dishes with snap closures. The petris are sealed with common electrical tape and rested for >2 weeks to allow for ²²²Rn ingrowth, although we will show that this approach does not quantitatively retain Rn (see also Murray et al., 1987, 2018). Our handling of the problem of Rn emanation from both laboratory samples and soils in situ is discussed below.

Gamma detector calibration is based on geometric efficiency, which is the proportion of photons emitted by the sample that are recorded by the detector, absent sample self-absorption of photons. Net efficiency includes self-absorption, which is dependent on each sample's specific elemental composition. We measure net efficiency directly by using a series of soils/sediment doped 1 % by weight with either uranium ore BL5 or thorium ore OKA2 which are available from Natural Resources Canada Certified Reference Material Project. Geometric efficiency for the standards is then calculated as the quotient of net efficiency and the standard self-absorption coefficient at each photopeak energy (described below). Geometric efficiencies are representative of the detector-sample geometric relationship and applicable to all sample unknown measurements. Efficiencies for photopeaks not represented in the standards are estimated by regression from adjacent photopeaks in the U or Th standards (e.g., ⁷Be, ²⁴¹Am, or ¹³⁷Cs; these are not known to have coincidence summing effects). Reported uncertainties on the standard activities is 0.2 % for U and 1.0 % for Th, and secular equilibrium is assumed for both.

Net efficiency for individual samples is calculated as the product of geometric efficiency determined from standards and the sample self-absorption at each energy of interest (Landis et al., 2012). To do this, self-absorption for each sample is measured using a planar uranium ore source (same diameter as sample) placed directly on top of the sample. This is performed as a second data acquisition following the sample “long count” which does not use the point source. Self-absorption at all energies is calculated using the method of (Cutshall et al., 1983), or in the case of non-uranium series radionuclides, is estimated by linear regression from the U-series photopeaks.

Calibration uncertainty estimated from geometric efficiencies of 6 standards of bulk density ranging from 0.5 to 200 g cm⁻³ is less than 2 % relative standard deviation for each of our detectors. Uncertainty of sample self-absorption derived from peak integration (below) contributes <1 %. Thus, our net efficiency calibration uncertainties are ∼2 % at the 1σ level.

A semi-automated peak integration routine is implemented in Excel worksheets (Fig. 2) (Landis et al., 2012). For each detector, peak shape parameters are measured across all energies either within the collected sample spectrum using peaks > 10 000 counts or using prior collection of a high-activity point source spectrum, by least-squares fitting of peaks using the Solver tool and unknowns μ, σ, L, H as below, where x is the channel energy, μ is the peak centroid, σ is Gaussian peak width, and L and H are low and high energy transitions of peak tails to logarithmic rather than Gaussian form. 1p(xi)=∫-∞LeL2x-2μ+L2σ2+∫LHe-x-μ22σ2∫H∞eH2μ-2x+H2σ2/∫-∞∞p The peak shape model is then used to estimate the partial area of analyte peaks that are integrated digitally by summation of peak channel count rates. Partial peak integration reduces measurement uncertainty by avoiding peak tails which contribute disproportionately to integration error. 2A=Rf⋅ε⋅p⋅γ⋅m Finally, radionuclide activity A [Bq kg⁻¹] is calculated following Eq. (2), where R is the integrated count rate (gross minus off-peak background count rate), f is the measured attenuation coefficient, ε* is detector geometric efficiency, p is the partial peak integration area, γ is photopeak yield constant, and m is the sample mass [kg⁻¹] (Fig. 2).

In addition to off-peak background subtraction, all radionuclide peaks are also corrected for on-peak background contributions which are measured with composite background spectra totaling hundreds of days of count time. Backgrounds for each peak may variously include impurities in the detector housing and shielding, ambient Rn in the laboratory, artifacts of the gamma spectrum, and ambient construction materials in the laboratory facility.

Environmental gamma spectrometry is capable of producing percent-level precision on par with other capital analytical platforms such as ICP-MS. Precision in gamma spectrometry measures of radionuclide activity is easily documented because many radionuclides emit photons at multiple energies. These typically have variable coincidence summing effects that require correction at each energy, as well as sample self-absorption factors that also require correction at each energy. Concordance among measures of multiple photopeaks spanning the energy spectrum thus provides a robust estimate of precision.

For quality control measures we recommend reporting multi-line means and uncertainties for three radionuclides: ²²²Rn measured at ²¹⁴Pb (295, 352 keV) and ²¹⁴Bi (609 keV); ²²⁸Ra measured with up to four emission lines from ²²⁸Ac (209, 338, 463, 911 keV); and ²²⁸Th measured by ²¹²Pb (238 keV), ²⁰⁸Tl (538 keV), and possibly ²²⁴Ra (241 keV) (Fig. 3).

The coefficient of variance (CV) or relative standard deviation (RSD) for multiple emission peaks for each of ²²²Rn, ²²⁸Th, and ²²⁸Ra provides an assessment of measurement accuracy and precision in the gamma spectrum (Fig. 4). These are in the 1 %–5 % range for typical crustal activity concentrations of 20 Bq kg⁻¹. ²²²Rn is important because it is often used as an indirect measure of ²²⁶Ra, with integration uncertainties 5–10 times lower (Fig. 4a), but also with this important caveat, that the actual values of the two measures may differ substantially due to geochemical disequilibrium caused by Rn leakage (Sect. 3.5).

Multiple important radionuclides in the gamma spectrum suffer significant peak-peak overlap that requires deconvolution. Most notable are ⁷Be which has interference from both ²²⁸Ac (478 keV) and ²¹⁴Pb (280 keV) (Landis et al., 2012), and ²²⁶Ra which has interference from ²³⁵U at 185 keV and which approximately doubles its analytical uncertainty (Zhang et al., 2009). Our ⁷Be deconvolution regime is verified elsewhere using repeat measures of a single natural sample, since the known half-life of ⁷Be can be exploited to predict its change in concentration over monthly timescales (Landis et al., 2012). The ²²⁶Ra deconvolution regime can be tested against certified reference materials; however, the reported uncertainties for ²²⁶Ra in available standards typically exceeds 10 % and are therefore of limited use in verifying robust measurement of this radionuclide (more below in Sect. 8).

Deconvolution can also be tested using the measure of ²²⁴Ra (half-life 3.6 d, 241 keV) as a proxy for its parent radionuclide ²²⁸Th because of its photopeak overlap with ²¹⁴Pb at 242 keV. The peak deconvolution procedure is evaluated with the expectation that radioactive equilibrium is maintained, i.e., with a slope of 1 in correlation between the parent and daughter (Fig. 5). Here the slope = 0.985 ± 0.006 which shows a systematic error of just 1.5 ± 0.6 %.

The defining limitation in LRC age model development is the problem of ⁷Be detection. The combination of low natural abundance, low photon yield (10.5 %), and short half-life (54 d) requires extraordinary efforts in both the logistics of sample collection and availability of instrument time to make these measurements possible. Samples should be measured within 1 month of collection and must be counted for 4 d or more per sample to define the ⁷Be soil depth profile (Fig. 6). Following these protocols ⁷Be may be detected to soil depths of 10 or more centimeters in humid or moist climates, which has important implications both for how soils are perceived to function and how age models are applied to soils (Landis et al., 2016).

Demonstrating accuracy of LRC requires concordance with independent chronometers, and bomb-pulse ²⁴¹Am is the prime candidate due to its long half-life, limited solubility or bioavailability (in contrast to ¹³⁷Cs), and potential for its concurrent measurement in the gamma spectrum. The bomb-pulse has a well-known history of activity in the atmosphere (Appleby et al., 1991; Health and Safety Laboratory, 1977). Abundance of ²⁴¹Am is low, however, rarely exceeding 1 Bq kg⁻¹ in temperate soils, and is altogether undetectable in equatorial soils where fallout deposition was 10-times lower than mid-latitudes (Chaboche et al., 2021). Alternate measurement of Pu isotopes by ICPMS or AMS is becoming routine and may offer an alternative where ²⁴¹Am cannot be measured (e.g. Alewell et al., 2017).

In contrast to ²⁴¹Am, ¹³⁷Cs is easily measured in the gamma spectrum. However, it can be subject to biological cycling as a K analog especially where soil K may be deficient (Kaste et al., 2021). As a result, the shape of Am and Cs profiles can diverge remarkably (Fig. 7). ²⁴¹Am is always the preferred measure of bomb pulse. Still, where ²⁴¹Am and ¹³⁷Cs profiles appear consistent, ¹³⁷Cs may provide constraints on shape of the ²⁴¹Am profile when the latter is detection limited if it can be shown, e.g. by regression, that there is no systematic bias between the ²⁴¹Am and ¹³⁷Cs depth profiles or mass distributions.

Total ²¹⁰Pb is the sum of both atmospheric (excess) and geogenic (supported) sources and is easily measured in gamma spectrum with BEGe detectors. The strongest source of error is self-absorption since this can vary by a factor of 2–3 through the soil profile. However, the low photon yield (4 %) can make measurement of supported ²¹⁰Pb challenging in soils with typical crustal uranium abundance. The four-day count time is thus important for providing adequate precision for defining ²¹⁰Pb_ex at the tail of its depth distribution (where ²¹⁰Pb_ex is calculated as ²¹⁰Pb_total minus ²²²Rn; see below).

The measure of ²²⁶Ra is important, in principle, for defining the activity of ²¹⁰Pb that is supported in soil by secular equilibrium with U-bearing minerals and organic matter (discussed in detail in Sect. 4). However, here we show that, due to endemic radioactive disequilibrium in soils, indirect measure of ²²²Rn should be preferred over direct measure of ²²⁶Ra for estimating supported ²¹⁰Pb. Secular equilibrium requires that radionuclides in a decay chain have equal activities, and we should observe this in the abbreviated chain ²²⁶Ra > ²²²Rn ≫ ²¹⁴Bi > ²¹⁴Pb ≫ ²¹⁰Pb provided that gaseous Rn can be retained within the sample (≫ indicates omitted radionuclide). Instead, we observe that ²¹⁴Pb and ²¹⁴Bi (indirect measures of ²²²Rn) underestimate ²²⁶Ra even in samples that are sealed and rested for the ingrowth period required for Rn to achieve equilibrium (5 half-lives or about 20 d) (Fig. 8). The obvious conclusion is that Rn emanates from packed soil samples during routine measure. Disequilibrium between ²²²Rn and ²²⁶Ra is difficult to assess in a single sample, because of high uncertainties on the ²²⁶Ra measure due in part to significant overlap from the primary ²³⁵U emission at 185.7 keV (Zhang et al., 2009).

In this dataset we quantify disequilibrium between ²²²Rn and ²²⁶Ra as fRn, or fraction Rn, which is simply the ratio of the two measures. (We acknowledge that the problem is somewhat more complicated because the effective volume of Rn in the detector shield will be greater than volume of the sample itself, due to its diffusion from the sample container into surrounding air). Among all soil pits the mean measured fRn = 79±1 % (± RSE, n=30) (Fig. 8). Importantly, the variance of fRn within a single pit is much smaller than among pits [p<0.0001], which means that fRn is a property of the geochemistry of individual soils (with respect to hosting of Ra in primary vs. secondary minerals, grain size, susceptibility to chemical weathering, geologic age, etc.).

Affirming the accuracy of ²²⁶Ra measurements is foundational for understanding Rn emanation, and therefore for interpreting ²¹⁰Pb in the soil profile. Here we confirm the accuracy of direct ²²⁶Ra measurements (186 keV) against certified reference materials (CRMs) (Fig. 9). Performance is excellent with standard 4 d count times (Fig. 9a). We note that analytical uncertainties thus achieved are typically far better than those of the certification process itself. This reflects the difficulties in robust measure of ²²⁶Ra which requires long count times and corrections for self-absorption and deconvolution (Tasker et al., 2019).

The IAEA-385 material is the most rigorously-calibrated soil standard available to date and is critical to our ability to validate high-quality gamma spectrometry (International Atomic Energy Agency, 2013; Pham et al., 2008). Even so, the original recommended ²²⁶Ra activity of 22.7 ± 0.7 Bq kg⁻¹ (Pham et al., 2005) is 3.6 % higher than the eventual certification value of 21.9 Bq kg⁻¹. The lower value derives from the averaging of direct ²²⁶Ra measurements with lower estimates from ²¹⁴Pb (352 keV) and ²¹⁴Bi (609 keV) (Fig. 9b–e). The latter should be viewed as suspect since both Rn emanation and coincidence summing losses can bias the ²²²Rn daughters too low. FRNA measurements appear to confirm a systematic ²²²Rn loss of 3.4 % as the difference between ²²⁶Ra activities (22.7 ± 0.3) and ²²²Rn (21.98 ± 0.07) [p=0.0186].

For analysis of sample unknowns we sought to confirm the accuracy of our ²²⁶Ra measures and therefore that Rn disequilibrium is due to Rn loss and not an analytical artifact (Syam et al., 2020). We performed an experiment with NIST-traceable ²²⁶Ra standard solution (Eckert and Ziegler; certified uncertainty <2 %). which is important to verify that ²²⁶Ra is measured accurately and with high enough activity to measure it with percent-level precision (here approximately 360 Bq kg⁻¹). A second calibrated ²²⁸Ra solution was prepared by dissolution of thorium ore OKA-2. Accuracy of both Ra source calibrations was previously confirmed by isotope-dilution thermal ionization mass spectrometry (Landis et al., 2018). Briefly, both the ²²⁶Ra and ²²⁸Ra standard solutions were co-precipitated in a wet synthesis of MnO₂ from KMnO₄ and MnCl₂ at pH ∼ 9. To replicate a typical soil sample in 110 cm³ petri geometry, the synthesized Ra-MnO₂ was air dried onto a bed of quartz sand. The Ra-Mn-sand thus produced represents a worst-case scenario for Rn emanation because all Ra is contained in amorphous or microcrystalline secondary mineral.

Samples were packed into our standard polypropylene petri as for a soil sample. The petri was first closed with electrical tape and measured serially to observe Rn ingrowth. Yields of both ²²⁶Ra and ²²⁸Ra are within error of 100 % of certified or expected values (Fig. 10). Short-lived ²²⁰Rn (aka thoron, half-life = 56 s) is fully retained by the sample, but grows in following the half-life of intermediary ²²⁴Ra (3.6 d) which is expelled from the initial suspension of MnO₂ by alpha recoil.

In contrast, for long-lived ²²²Rn we observed an equilibrium fRn of just 55 % after approximately thirty days. The sample was then resealed using hot glue, but this reduced Rn retention, presumably due to porosity in the glue that visibly forms upon cooling. Finally, the sample was encased in 2 mm of paraffin wax. This final step increased fRn to 85 %, but the impracticality of the method coupled with imperfect Rn retention is a fatal strike against its routine use in our laboratory.

Our subsequent efforts to seal samples under vacuum in aluminized Mylar bags improve Rn retention up to 90 %–95 % for our 110 cm³ petri (Mauring and Gäfvert, 2013), but we have not standardized this approach due to remaining uncertainty in precise quantification of retention, the creation of additional laboratory waste and, in the face of these problems, the uncertain value of improving the indirect measure of ²²⁶Ra to defining ²¹⁰Pb_ex (see below).

The accuracy of reported integration uncertainties can be assessed using multiple emission lines for a single radionuclide, since each must conform to the same true mean activity value. We show this by means of Z-score, which is the difference between emission line activities, normalized by the propagated uncertainty for the difference. The standard deviation of Z should be equal to 1 if the estimated integration uncertainties accurately represent the true distribution of random error in the measurements (Fig. 13). We observe standard deviations in Z of 0.8, 1.2, and 1.4 for ²²²Rn, ²²⁸Th, and ²²⁸Ra, respectively. These are close to 1 which implies that the integration uncertainties are robust. In the case of ²²⁸Th and ²²⁸Ra the real uncertainties are somewhat underestimated which means that uncertainties in calibration contribute an additional error, and one that is similar in scale to uncertainties in integration, i.e., if similar errors are propagated the result is a 40 % higher than either, √(12+12)=1.4.

On the other hand, our prior assessment suggests that integration uncertainties are overestimated by on the order of 30 %, based on the unique experiment of measuring radioactive decay of ⁷Be since the true value of the sample is known based on its rate of decay, and estimated uncertainties can be evaluated against the observed dispersion of measurements around this known value (Landis et al., 2012). Overestimation of integration errors is consistent with our observed Z<1 for the ²²²Rn lines comparison above. That uncertainties for ²²⁸Th and ²²⁸Ra are greater than for ²²²Rn suggests that the interaction of coincidence-summing and self-absorption effects yields higher error in calibration, since these are not handled independently in our calibration routine, i.e., by using a Th point source instead of U for Th-series photopeaks. Future work is required to determine whether one ²²⁸Ra measurement may be preferred over others (e.g., among the ²²⁸Ac photopeaks at 209, 338, and 911 keV).