Apparent Water Ages Research Articles

Combining 14CDOC and 81Kr with hydrochemical data to identify recharge processes in the South German Molasse Basin

• Combination of 14 C DOC and 81 Kr provides new insight of recharge dynamics in the UJA. • Groundwater dating with 14 C DOC and 81 Kr proves to be useful for deep aquifers. • Groundwater dating revealed high spatial heterogeneity in groundwater ages. • The main recharge area of the UJA may be located at the southern border of the SGMB. • Glaciations may be the driving force for groundwater recharge. To face the challenges of ongoing climate change, renewable energy sources are needed to reduce CO 2 emissions to the atmosphere. The South German Molasse Basin (SGMB) contains an important geothermal aquifer in Germany; however, an enhanced understanding of the flow regime at the basin scale remains a fundamental limiting factor in assessing a long-term and sustainable strategy for using this green energy source. Here we report 14 C DOC and 81 Kr groundwater dating results together with hydrochemical data, stable water isotopes, noble gases and out-diffusion experiments that indicate that the thermal groundwater consists of at least two groundwater sources: a formerly unknown young groundwater component with apparent water ages between 9,800 and 18,700 a and an old groundwater component, which shows an apparent water age of up to approximately 300 ka. The results of the out-diffusion experiments with core material from the Upper Jurassic aquifer (UJA) suggest that diffusion processes between rock-matrix water and more mobile fracture water represent a controlling mechanism for groundwater flow and the observed extended apparent groundwater ages within the UJA. The observed elevated 14 C DOC activities and the high spatial heterogeneity in groundwater ages close to the southern margin of the SGMB were interpreted as a recharge zone of the system. The combination of the 14 C DOC and 81 Kr methods shows the potential as a powerful groundwater dating tool for deep aquifers.

Radium isotope assessment of submarine groundwater discharge and associated nutrient inputs in Eastern Liaodong Bay, China

The accurate assessment of submarine groundwater discharge (SGD) and associated nutrient fluxes plays a significant role in water resources management and ecological environment protection in the coastal area. Currently, Liaodong Bay has become one of the most polluted marine areas in China. However, the nutrient fluxes carried by the SGD and its environmental effects have not yet been thoroughly reported in eastern Liaodong Bay, China. In this study, the distribution of 224Ra/223Ra activity ratio and its influencing factors under the geochemical conditions were explored. The activity of radium was affected by the water type and the geochemical factors. The radium isotopes in seawater were positively correlated with the ratios of Mg2+/Na+ and Ca2+/Na+ but negatively correlated with salinity and SO42−. The average apparent water age was evaluated to be 13.0 days. Furthermore, based on the radium mass balance model, the total average SGD flux was calculated to be 1.31 × 108 m3 day–1. The nutrient fluxes carried by the SGD were 7.16 × 107, 1.01 × 106, 1.61 × 107, 0.92 × 106, and 5.41 × 107 mol day−1 for DIN, DIP, NH4+, NO2−, and NO3−, respectively. The nutrient inputs through the SGD have an average DIN : DIP ratio of 70, which was able to seriously affect the ecological environment. The SGD-derived nutrient fluxes were higher than the local river input, which demonstrated that the SGD was a major source of nutrients affecting regional marine ecosystems.

Estimation of apparent water age and mixing process of water in the creek ecosystem of Mumbai Harbour Bay

Short-lived Ra isotopes (224Ra and 223Ra) were used to estimate the apparent water age and mixing process, in the creek ecosystem of Mumbai Harbour Bay. The apparent water age was estimated using the Radium Age Model and the Radium Balance Approach. The apparent water age for three different sampling trips in the creek varies from 3.65 ± 1.22 to 4.51 ± 1.51 days using the Radium age model. Whereas using the Radium Balance Approach in the creek, the apparent water age was estimated to be 6.51 ± 1.67 days. Similar apparent water age from both approaches was found for the creek ecosystem under steady state. The longitudinal variation of the 224Ra and 223Ra activity ratio from the middle of the creek indicated net water mass movement towards the open sea. The flushing rate of the creek water towards the open sea was estimated to be 6.67 ± 0.89 km day−1. The horizontal mixing coefficient (Kh) of the creek water was estimated to be 800 ± 107 m2s−1 indicating rapid dispersion of the tracer.

Explicit Modeling of Radon-222 in HydroGeoSphere During Steady State and Dynamic Transient Storage.

Transient storage zones (TSZs) are located at the interface of rivers and their abutting aquifers and play an important role in hydrological and biogeochemical functioning of rivers. The natural radioactive tracer 222 Rn is a particularly well-suited tracer for studying TSZ water exchange and age. Although 222 Rn measurement techniques have developed rapidly, there has been less progress in modeling 222 Rn activities. Here, we combine field measurements with the numerical model HydroGeoSphere (HGS) to simulate 222 Rn emanation, decay and transport during steady state (riffle-pool sequence) and transient (bank storage) conditions. Comparing the HGS mean water ages with the conventional 222 Rn apparent ages during steady state showed a systemic underestimation of apparent age with increasing dispersion and especially where large concentration gradients exist within the subsurface. A large underestimation of apparent water age was also observed at the advective front during bank storage where regional high 222 Rn groundwater mixes with newly infiltrated surface water. The explicit modeling of radiogenic tracers such as 222 Rn offers a physical interpretation of this data as well as a useful way to test simplified apparent age models.

Nutrient input through submarine groundwater discharge in two major Chinese estuaries: the Pearl River Estuary and the Changjiang River Estuary

In this study, we used a 224Ra mass balance model to evaluate the importance of submarine groundwater discharge (SGD) for the budgets of biogenic elements in two major Chinese estuaries: the Pearl River Estuary (PRE) and the Changjiang River Estuary (CRE). The apparent water age in the PRE was estimated to be 4.8 ± 1.1 days in the dry season and 1.8 ± 0.6 days in the wet season using a physical model based on the tidal prism. In the dry season, the water age in the CRE was estimated to be 11.7 ± 3.0 days using the 224Ra/223Ra activities ratios apparent age model. By applying the 224Ra mass balance model, we obtained calculations of the SGD flow in the PRE of (4.5–10) × 108 m3 d−1 (0.23–0.50 m3 m−2 d−1) and (1.2–2.7) × 108 m3 d−1 (0.06–0.14 m3 m−2 d−1) in the dry season and wet season, respectively, and the estimated SGD flux was (4.6–11) × 109 m3 d−1 (0.18–0.45 m3 m−2 d−1) in the dry season of the CRE. In comparison with the nutrient fluxes from the rivers, the SGD-derived nutrient fluxes may play a vital role in controlling the nutrient budgets and stoichiometry in the study areas. The large amount of dissolved inorganic nitrogen and phosphorus fluxes together with high N: P ratios into the PRE and CRE would potentially contribute to eutrophication and the occurrence of red tides along the adjacent waters.

Significance of Submarine Groundwater Discharge in Nutrient Budgets in Tropical Sanya Bay, China

To quantify the contribution of submarine groundwater discharge (SGD) to the nutrient budget in tropical embayments, naturally occurring radium isotopes (223Ra, 224Ra, 226Ra, and 228Ra) were investigated as SGD tracers in Sanya Bay, China. Higher activities of radium were present along the north coast and near the Sanya River estuary. Using the activity ratio of 224Ra/228Ra, the apparent water age in Sanya Bay was estimated to be 0–13.2 days, with an average of 7.2 ± 3.2 days. Based on the mass balance of 226Ra and 228Ra, SGD was calculated to be 2.79 ± 1.39–5.07 ± 2.67 × 106 m3 d−1 (or 4.3 ± 2.1–7.8 ± 4.1 cm d−1). SGD associated dissolved inorganic nutrient fluxes into Sanya Bay were estimated to be 3.94 ± 2.00–7.15 ± 3.85 × 105 mol d−1 for oxidized inorganic nitrogen, 4.64 ± 2.74–8.42 ± 5.19 × 103 mol d−1 for phosphate, and 6.63 ± 3.29–12.0 ± 6.34 × 105 mol d−1 for silicate. The estuarine nutrient flux from the Sanya River was a few times smaller than the phosphate flux via SGD and at least an order of magnitude smaller than the oxidized inorganic nitrogen and silicate fluxes carried by SGD. SGD was also more important than atmospheric deposition and nitrogen fixation in the nutrient budget. Our results demonstrate that SGD compensated for at least 15% phosphate, 90% oxidized inorganic nitrogen, and 60% silicate of the nutrients sink in Sanya Bay.

Age Constraints on Gulf of Mexico Deep Water Ventilation as Determined by14C Measurements

AbstractWhile the exchange of water through Yucatan Strait is reasonably well known, the age of the deep water in both the Caribbean Sea and Gulf of Mexico is not. We recently measured the radiocarbon (14C) concentrations in deep water in the Gulf of Mexico from a line of stations along 90°30′W. The mean apparent age of water below 900 m, the depth of the Florida Strait sill, was found to be about 740 yr relative to the 195014C standard. Depending on how the corrections for biological activity in the upper water are applied, this converts to a “true” age of between 231 ± 28 and 293 ± 74 yr. These ages agree with a previous estimate of the age of the deep water in the Gulf of Mexico based on heat flows, put upper limits on the age of the deep water in the Caribbean Sea, and provide constraints on modelers for the return of deep water from the Gulf of Mexico to the Caribbean. This might be important in the event of a future deep water oil or other chemical spill in the region.

Submarine groundwater discharge and nutrient addition to the coastal zone of the Godavari estuary

Submarine groundwater discharge (SGD) represents a significant pathway of materials between land and sea, especially as it supplies nutrients, carbon and trace metals to coastal waters. To estimate SGD fluxes to the Godavari estuary, India, we used multiple tracers: salinity, Si, 223Ra, 224Ra, 228Ra and 226Ra. Tracer abundances were elevated in groundwater from the unconfined coastal aquifer and in surface water from the near shore zone; these enrichments decreased to low levels offshore, indicative of groundwater discharge. A model based on the decay of 224Ra relative to 228Ra was used to determine apparent water ages of various bays within the estuary. These ages ranged from 2.6 to 4.8d during November 2011. Knowing the water age, the distribution of radium in the estuary, and the radium isotopic composition of groundwater enabled us to calculate SGD fluxes to the estuary. These fluxes (in units of 106m3d−1) were on the order of 5 in the Gautami Godavari estuary, 20–43 in the Vasishta Godavari estuary, and about 300 in Kakinada bay, where enhanced ion exchange processes and redox-controlled cycling in the mangrove ecosystem may contribute to higher fluxes. These estimates of water fluxes allowed us to determine the magnitude and seasonal variability in the nutrient fluxes to the estuary associated with SGD. These nutrient fluxes (in units of mmolm−2d−1) ranged from 1–19 (N), 0.6–2.6 (P), and 5–40 (Si) in Gautami Godavari; 19–40 (N), 2.6–5.5 (P), and 200 (Si) in Vasishta Godavari; and 120–140 (N), 10 (P), and 220 (Si) in Kakinada bay. The high SGD fluxes to Kakinada bay contribute significant nutrients to this bay; considerably lower SGD fluxes to Vasishta Godavari still contribute significant nutrients to this estuary. Thus SGD represents a major source of new nutrients to these coastal ecosystems. For the entire Godavari estuarine system, SGD fluxes contribute (48–88)×109molDICy−1 and (51–94)×109molTAy−1. These fluxes represent ~54 and ~62% of the riverine DIC and TA fluxes to the Godavari estuarine system. This study provides baseline data against which future changes in nutrient and carbon fluxes due to urbanization and economic growth over this region can be compared.

Hydrodynamics in the Yellow River Estuary via radium isotopes: Ecological perspectives

We used radium isotopes as tracers to characterize coastal hydrodynamics and submarine groundwater discharge (SGD) in the Yellow River Estuary in order to assess the ecological effects in one of the most turbid estuaries in the world. Based on apparent water ages calculated by 224Ra/223Ra activity ratios, we found that the river plume flowed mainly southeast at a flow rate of 5–7kmd−1, while a small portion of the river plume was diverted northeast to the central Bohai Sea at a flow rate of less than 2kmd−1. We estimate that with this flow regime, nutrients would be consumed within about two weeks mostly by microplankton and nanoplankton near shore, and picoplankton further offshore to support an average primary production of 0.14gCm−2d−1. We then used a 226Ra mass balance model to quantify the SGD flux in the study area. The estimated SGD flux was 1.3×109m3d−1 with a range of 2.8×108–3.0×109m3d−1. Even the minimum SGD value was about 3 times higher than the Yellow River discharge at that time. The SGD input of dissolved nutrients was shown to be very important to the estuarine nutrient budget, at least 5 times higher than river input. Sediment regeneration of nutrients proved to be very small relative to the SGD flux in this region.

Occurrence of pesticides in transboundary aquifers of North-eastern Greece

A five-year groundwater monitoring program undertaken in Evros (north-east Greece), showed a diversification in the levels of pesticide residues detected in adjacent transboundary aquifers. During the first two years 37 wells, including irrigation, drinking water and artesian wells were monitored while the next three years the survey was focused on the 11 most contaminated wells. The presence of pesticide residues was also monitored in the phreatic horizon (shallow groundwater) of four experimental boreholes drilled in the respective margins of four fields. Among the compounds found alachlor, metolachlor, atrazine, desethylatrazine (DEA), desisopropylatrazine (DIA) and caffeine were constantly detected. Pesticide concentrations were much lower (up to 1.54μg/L) in the water of the monitored drinking water wells (deep groundwater aquifers) compared to those found in the phreatic horizon (experimental boreholes) of the respective areas (up to 5.20μg/L). DEA to atrazine concentration ratios (DAR) determined for the phreatic horizon of the three boreholes and respective wells were lower than 1, indicating that preferential flow was the cause of the fast downward movement of atrazine to the phreatic horizon. In contrast the DAR for the fourth borehole and the adjacent well were greater than 1 indicating the absence of preferential flow of atrazine. Catabolic processes of the soil converted atrazine to DEA which is more mobile than atrazine itself through chromatographic (darcian) flow.This differential behavior of pesticides in adjacent aquifers (3km) was further investigated by determining the apparent age of water in the two wells. The apparent age of the water present in the first aquifer was 21.7years whereas the apparent age of that in the second aquifer was approximately 1.2years. The faster replenishing rate of the latter is an indication that this aquifer is very vulnerable to contamination with pollutants present in the infiltrated soil water.

Investigation of residence time and groundwater flux in Venice Lagoon: comparing radium isotope and hydrodynamical models

The four naturally-occurring isotopes of radium were coupled with a previously evaluated hydrodynamic model to determine the apparent age of surface waters and to quantify submarine groundwater discharge (SGD) into the Venice Lagoon, Italy. Mean apparent age of water in the Venice Lagoon was calculated using the ratio of 224Ra to 228Ra determined from 30 monitoring stations and a mean pore water endmember. Average apparent age was calculated to be 6.0 d using Ra ratios. This calculated age was very similar to average residence time calculated for the same period using a hydrodynamic model (5.8 d). A mass balance of Ra was accomplished by quantifying each of the sources and sinks of Ra in the lagoon, with the unknown variable being attributed to SGD. Total SGD were calculated to be 4.1 ± 1.5, 3.8 ± 0.7, 3.0 ± 1.3, and 3.5 ± 1.0 × 10 10 L d −1 for 223,224,226, 228Ra, respectively, which are an order of magnitude larger than total mean fluvial discharge into the Venice Lagoon (3.1 × 10 9 L d −1). The SGD as a source of nutrients in the Venice Lagoon is also discussed and, though significant to the nutrient budget, is likely to be less important as the dominant control on SGD is recirculated seawater rather than freshwater.

Exceptional mixing events in meromictic Lake Lugano (Switzerland/Italy), studied using environmental tracers

The deep northern basin of Lake Lugano was permanently stratified over the last 4 decades because of mineralization in response to strong eutrophication. However, two consecutive cold and windy winters (2004‐2005 and 2005–2006) destabilized the water column and led to two exceptionally strong mixing events. The conductivity, temperature, and depth time‐series data from 1995 to 2006 allowed the reconstruction of the evolution of the water body that made deep convective mixing possible. Over the years 1995‐2006, the stability of the water column decreased continuously in winter, reaching a neutral stability at the end of the study period. The Schmidt stability values observed in the winters of 2004–2005 and 2005–2006 were virtually zero. Analyses of helium isotopes, tritium, sulfur hexafluoride, and chlorofluorocarbons in water samples collected immediately after the two mixing events revealed large changes in the tracer concentration profiles and permitted comparisons of the apparent water ages in Lake Lugano with previous measurements. Tracer concentration profiles became more homogeneous and approached atmospheric equilibrium concentrations in the time series. The tracer data, along with changes observed in the physical parameters of the water column, demonstrate the considerable deepwater renewal and gas exchange with the atmosphere that has taken place.

A time series of environmental tracer data from deep meromictic Lake Lugano, Switzerland

An 11‐yr (1990–2001) time series of tritium‐helium‐3 (3H‐3He) apparent water ages as well as one sulfur hexafluoride (SF6) profile were used to study the development of the vertical mixing dynamics of the deep, meromictic northern basin of Lake Lugano. The density stratification of the water column was dominated by an increase in dissolved ions with depth, which remained approximately constant during the 1990s. The deep‐water temperature increased steadily during this period, passing a threshold above which cooling of the surface water could force convection. However, increasingly mild winter temperatures prevented the occurrence of a turnover until 2005. The maximum apparent 3H‐3He water age increased from about 16 yr in 1990 to 23 yr in 2001. The maximum apparent SF6 age in 2001 was 12.8 yr. The large difference between the apparent 3H‐3He and SF6 ages is at least partly due to nonlinear effects of mixing, causing SF6 ages to underestimate the true mean deep‐water residence time, whereas 3H‐3He ages overestimate it. The decreasing concentrations of 3H and 3He are more reliable indicators of the continuous deep‐water exchange in the lake than are the apparent ages. Budget calculations using the tracer concentrations reveal an annual renewal of the deep water below 100 m in depth by about 8% and enable the calculation of long‐term mean profiles of the effective vertical turbulent diffusivity Kz. No trend in the mixing intensity during the 1990s could be determined. The radiogenic He flux into the lake is comparable to estimates of the whole crustal degassing flux.

Estimates of flushing times, submarine groundwater discharge, and nutrient fluxes to Okatee Estuary, South Carolina

A physical model based on determining the fraction of the tidal prism that returns to the estuary on the next high tide is used to estimate the flushing time of the Okatee River estuary. The return flow factor (b) of 0.81 yields a flushing time of 2 days. A mass balance model of 228Ra and salinity is also used to estimate b. This model yields an average b = 0.79, virtually the same as the physical model. A third model based on the decay of 224Ra relative to 228Ra is used to determine the apparent age of water in the estuary. These ages range from 1.6 to 5 days, with an average of 3.4 days. These three independent estimates are in remarkably close agreement, certainly within the error of each estimate. We use these residence times to develop a mass balance model for the radium isotopes in the Okatee estuary. We consider decay, mixing, sedimentary input, river input, and submarine groundwater discharge (SGD). The major loss term for each isotope is mixing with water in Port Royal Sound; the major input for each isotope is SGD. At steady state these terms must balance. Knowing the water age and the radium isotope composition of groundwater entering the Okatee allows us to estimate an average SGD flux of 1 m3/s. The SGD flux is a factor of 3–4 greater during the summer relative to the winter. This SGD supplies a considerable quantity of nutrients and carbon into the Okatee system.

Rapid deep‐water renewal in Lake Issyk‐Kul (Kyrgyzstan) indicated by transient tracers

Simultaneous profiles of the transient tracers sulfur hexafluoride (SF6), 3H‐3He, and the chlorofluorocarbons CFC‐11 and CFC‐12 were measured in Lake Issyk‐Kul, a large, deep lake in Kyrgyzstan. Apparent water ages derived from these measurements suggest rapid mixing, with a deepwater renewal rate >10% yr−1 at 650 m depth. SF6 and 3H‐3He ages agree reasonably well, whereas CFC ages are significantly greater. The discrepancy is explained by the nonlinear relationship between tracer age and tracer concentration and by the flattening of the atmospheric growth curves for CFCs. Novel to physical limnology is the application of SF6 dating, which proves to be an excellent tool for the study of mixing in lakes, complementing 3H‐3He and CFC dating techniques.

Noble gas and major element constraints on the water dynamics in an alpine floodplain.

The hydrogeological system of an ecologically sensitive alpine floodplain in the Valle di Blenio, Switzerland, was investigated using hydrochemical and 3H-3He dating methods. Water samples from six wells and from different surface locations were analyzed. The analysis of the concentrations of major ions in conjunction with age determination by the 3H-3He-method allowed the main hydrological properties of the system to be consistently characterized. Two geochemically distinct water zones can be distinguished: Ca-SO4-dominated water from the main river and Ca-HCO3-dominated floodplain water. The floodplain water component characterizes the whole floodplain including the surficial hillslope drainage system. Within the ground water samples, two spatially and temporally different types of water can be determined. A younger (age < 1.5 years), less mineralized water is found in the upper part of the aquifer during the summer season. The underlying aquifer zone contains older and more highly mineralized water. However, the general hydrochemical characterization of both types of ground water is similar. In winter, the water ages increase with decreasing ground water levels. Because precipitation is stored temporarily in the snow cover, the contribution of the younger near-surface ground water decreases, resulting in higher apparent water ages and higher mineralization in the upper zone of the aquifer. Water exchange between the main river and the ground water system is limited to ground water exfiltration from the shallow aquifer zone, whereas the hydrochemical separation of the deeper aquifer zone indicates the isolation of the deeper ground water from the main river.

Analysis of deep-water exchange in the Caspian Sea based on environmental tracers

In order to quantify deep-water exchange in the Caspian Sea, the world's largest inland water body, water samples were analyzed for the transient tracers H 3 , He 3 , He 4 , CFC-11, CFC-12 and atmospheric noble gases. Measurements of temperature, salinity (calculated from conductivity for the ionic composition of Caspian Sea water), and dissolved oxygen were employed to investigate the processes responsible for deep-water renewal. The Caspian Sea consists of two deep basins, the southern and central basins, separated by a sill, and a shallow northern basin. The deep water (below 200 m) accounts for almost 60% of the total water mass. Below 200 m the concentrations of H 3 and He 3 are much lower in the southern basin than at the same depths in the central basin, but this is not the case for either of the CFCs. However, apparent water ages calculated from H 3 – He 3 and from CFC-12 concentrations are the same for the deep water of the southern and central basins, and yield deep-water exchange rates of approximately 7% per year for each of the two basins. This implies volume fluxes across the 200-m level of about 2220 km 3 yr −1 within the southern basin and 770 km 3 yr −1 within the central basin. Based on the apparent water ages, the oxygen depletion in the deep water is estimated to be about 0.35 mg l −1 yr −1. The processes responsible for deep-water exchange have not yet been identified conclusively. However, vertical temperature and salinity gradients observed during two expeditions, in September 1995 and 1996, suggest that within the southern and central basins large-scale convection cannot be triggered by seasonal cooling alone, but requires the surface water to be cold/saline or to contain high suspended sediment loads. In the central basin the increase in salinity occurring during ice formation in early winter is possibly sufficient to cause convection. In late summer, the horizontal transport of water from the upper 170 m of the central basin into the southern basin results in mixing down to 400 m. In winter this process might result in convection down to the maximum depth. Alternatively, the data are also consistent with the hypothesis that rare events cause large-scale convection down to the maximum depth in the southern and in the central basin simultaneously, followed by slight mixing that mainly affects only the top 500 m. According to apparent water ages from below 500 m, the last such major mixing event could have occurred in 1976 shortly before the water level of the Caspian Sea began to rise.

Uppsala Natural Radiocarbon Measurements IV

The following list covers most of the samples measured at the Uppsala C14 laboratory since the last list (Uppsala III) except for all the samples utilized for determining the increase of the C14/C12 ratio due to explosion of nuclear devices and the few samples measured with a new proportional counter.The technique used is the same as previously described by Olsson (1958) and the pretreatment is that which has been used earlier (wood, charcoal, peat, gyttja and other organic sediments are boiled with HC1, 1 to 2%, washed with distilled water, kept in NaOH, 1 to 2%, at +80°C over night, washed with distilled water and finally acidified to pH about 3 before being dried) except for Foraminifera tests, see below.The reference sample is 95% of the activity of the NBS oxalic-acid standard. Any corrections for apparent water ages are thus not included here, but will be discussed in later papers dealing with the marine samples. Corrections for deviations from the normal C13/C12 ratio (-2S.0% in the PDB scale) are applied for the unknown samples. Our oxalic acid was measured by Craig (1961) and has a C13/C12 ratio of -18.97% and corresponds to the accepted standardized value, -19%, which should be used for age determinations (Editorial Statement in Radiocarbon, v. 3). Two new combustions of oxalic acid have not shown any significant difference in their C13 content relative to the oxalic acid 1 sample measured by Craig.The value 5570 yr has been used for the half-life of C14. Results are expressed in years before 1950 (b.p.). Errors include the standard deviations (a) of the counted particles as well as the error in the δC13 values. When the activity is very low, so that 2σ corresponds to a possibility of infinite age, 2σ has been used instead of σ.Several samples had to be diluted with CO2 from an old source to bring them to the normal working pressure of 3 atm.