Sampling Design

Wells were chosen to obtain age-tracer concentrations throughout the MRVA extent and at various depths (fig. 1). Selected wells screened in the MEAS were sampled to better understand groundwater interactions between the MRVA and some underlying aquifers. One additional well in an adjacent terrace aquifer (USGS site number 324627091505203) was sampled and age dated (Gratzer and others, 2025); however, because the well lies outside the extent of the MRVA, the sample is not discussed in this report. Samples were collected primarily from production or monitoring wells—as opposed to irrigation wells which are abundant across the MRVA—to limit exposure of sample water to the atmosphere which can alter some age-tracer concentrations. Groundwater from some wells could not be analyzed for dissolved gas concentrations because the pumps used to sample these wells aerated the water.

In 14 locations, samples were collected from 2 or 3 nearby wells with different depths in the MRVA or in the MRVA and the underlying MCAQ (fig. 1B). Paired MRVA wells were used to assess the stratification of age in the MRVA. Paired MRVA and MCAQ wells were used to help assess the likelihood of hydraulic connection and groundwater mixing between the MRVA and MCAQ.

Samples were collected by following protocols in the USGS National Field Manual (USGS, variously dated). Prior to collecting samples, at least three casing volumes were pumped from the well, and pH, temperature, specific conductance, and dissolved oxygen were monitored for stabilization. Stabilization of pH, temperature, specific conductance, and dissolved oxygen signals that the water entering the well is likely representative of the groundwater in the aquifer rather than water that has remained inside the well for an extended period and acquired a different chemical composition. A submersible pump with Teflon tubing and stainless-steel fittings was used for sampling monitoring wells. At production wells, sample tubing was connected to a spigot at the wellhead that discharged the groundwater prior to any treatment. When collecting samples to be analyzed for the concentration of a dissolved gas, containers were filled by using procedures that prevented any bubbles from being trapped in the samples. Trapped bubbles, or “headspace,” can change the concentrations of dissolved gases in water because of fractionation of the gas as it is exchanged between the water and the bubble. All equipment was cleaned following standard procedures in the USGS National Field Manual (USGS, variously dated) after each well was sampled.

Alkalinity, General Chemistry, Stable Isotopes of Water, and Dissolved Organic Carbon

Each groundwater sample was analyzed for alkalinity, general chemistry (cations, anions, silica, trace elements, nitrate, and total dissolved solids [TDS]), and stable isotopes of water, and 10 groundwater samples collected in 2020 were also analyzed for dissolved organic carbon (DOC) (Gratzer and others, 2025). Samples collected for the determination of alkalinity, some general chemistry analytes, and DOC were collected through a 0.45-micron filter. The bottles for samples collected for analyses of alkalinity and some general chemistry analytes were rinsed with the filtered groundwater before being filled. Samples collected for the determination of general chemistry and DOC were analyzed by the USGS National Water Quality Laboratory in Lakewood, Colorado.

Alkalinity samples were collected in 250-mL polyethylene bottles. Samples were titrated in the field by the inflection point method using sulfuric acid delivered by a digital titrator.

Samples for analyses of cations, silica, and major and trace elements were collected in acid-rinsed 250-milliliter (mL) clear polyethylene bottles; nitric acid preservative was added to these samples. Samples were analyzed for cations and silica by inductively coupled plasma (ICP) atomic emission spectroscopy and ICP optical emission spectroscopy (Fishman, 1993; American Public Health Association, American Water Works Association, and Water Environment Federation, 1998). Samples were analyzed for trace elements by ICP mass spectrometry and cell ICP mass spectrometry (Garbarino, 1999; Garbarino and others, 2006).

Samples for analyses of anions and TDS were collected in 250-mL polyethylene bottles. Anions were analyzed by ion chromatography, and TDS was analyzed by the residue on evaporation method (Fishman and Friedman, 1989). Samples for analysis of the sum of nitrite plus nitrate were collected in 125-mL brown polyethylene bottles and analyzed by using colorimetry by enzymatic reduction (Patton and Kryskalla, 2011).

Samples for analysis of stable isotope ratios of water (δ²H and δ¹⁸O) were collected unfiltered in a 125-mL polyethylene bottle and analyzed at the University of Arkansas Stable Isotope Laboratory with a Thermo Scientific DELTA V Plus isotope ratio mass spectrometer. Results were reported in delta (δ) notation, relative to the Vienna Standard Mean Ocean Water (VSMOW) standard:

Samples for analysis of DOC were collected in 125-mL baked amber glass bottles. Sulfuric acid preservative was added to these samples. These samples were analyzed by using the high-temperature combustion method (National Environmental Methods Index, 2023).

Major inorganic constituents and stable isotope ratios of water were used in the USGS speciation program NetpathXL to calculate the speciation of each sample (Parkhurst and Charlton, 2008). Concentrations were not adjusted for charge balance. The carbonate speciations of samples were required to correct ¹⁴C for subsequent age dating. The mineral-saturation indices provided by each speciation helped to constrain the conceptual model of chemical processes that likely affected the ¹⁴C activity of each sample.

Tritium

Groundwater samples were collected from 68 MRVA wells, 17 MCAQ wells, and 2 LWAQ wells for the analysis of tritium (Gratzer and others, 2025). Samples were collected in 1-liter (L) clear polyethylene bottles with poly-seal cone caps and analyzed at the University of Miami Tritium Laboratory by gas-proportional counting with electrolytic enrichment (University of Miami Tritium Laboratory, 2023).

Tritium can be used to identify groundwater recharged since about 1953 (table 2) (Lindsey and others, 2019). Tritium data were used to categorize each sample (Gratzer and others, 2025) as “modern” (recharged after 1953), “premodern” (recharged before 1953), or “mixed” (a mixture of water recharged after 1953 and water recharged before 1953) by using the methods of Lindsey and others (2019). Tritium-based age categories provided an initial framework for modeling groundwater age.

In the USGS software TracerLPM (Jurgens and others, 2012), the tritium concentration of each sample was modeled relative to the tritium input function, which is the time series of tritium in the precipitation assumed to have recharged the aquifer. Tritium concentrations in precipitation vary spatially and temporally. Michel and others (2018) compiled tritium input functions for each latitude-longitude quadrant (2 degrees latitude x 5 degrees longitude) of the continental United States. These tritium input functions were used in TracerLPM for estimating ages of samples with tritium. The recharge zone of each sample was assumed to be in the same latitude-longitude quadrant as the well from which the sample was collected. In this report, the “recharge zone” of an aquifer refers to the areas in which recharge to the aquifer takes place as well as the groundwater in those areas. The recharge zone of a sample refers to the portion of an aquifer’s recharge zone in which the water in the sample recharged the aquifer.

Dissolved Gases

Concentrations of dissolved nitrogen (N₂) and argon (Ar) were used to estimate recharge water temperatures (hereinafter referred to as “recharge temperatures”) and excess air concentrations to correct SF₆, ³He_trit, and ⁴He_terr data. Excess air refers to air that dissolved in the groundwater after recharge, for example, water that was trapped between a wetting front and the water table and then dissolved beneath the water table under hydrostatic pressure. Samples for each site were collected without headspace in two 125-mL pre-weighed glass bottles with rubber stoppers, chilled, and shipped to the USGS Groundwater Dating Laboratory in Reston, Virginia, for analysis by gas chromatography (USGS Groundwater Dating Laboratory, 2023a, d).

The software package DGMETA (Jurgens and others, 2020) was used to fit the Unfractionated Excess Air (UA) model (Heaton and Vogel, 1981) to the measured N₂ and Ar concentrations of each sample to estimate recharge temperature and the amounts of N₂ and air that were dissolved in the water after it recharged the aquifer (that is, excess N₂ and excess air). Recharge temperature, excess N₂ concentration, and excess air concentration must be known to determine the concentrations of SF₆ and helium in water when it recharged the aquifer, and these concentrations must be known to use SF₆, ³He_trit, and ⁴He_terr for estimating the age of groundwater.

The following assumptions were made when estimating recharge temperature, excess N₂ concentration, and excess air concentration:

The assumption that the salinity of the groundwater was zero, though likely incorrect, was appropriate for dissolved gas modeling in this system. The maximum specific conductance of the groundwater in the MRVA may be approximately 10,200 microsiemens per centimeter at 25 degrees Celsius (Kresse and others, 2014), or a salinity of 6 per mil (‰) (USGS, 2011). The difference between an SF₆ concentration corrected assuming a salinity of 0‰ instead of 6‰ is likely less than 5 percent.

Noble Gases

Concentrations of noble gases—helium (He), neon (Ne), Ar, krypton (Kr), and xenon (Xe)—also were used to estimate recharge temperatures and excess air concentrations to correct SF₆ and He tracer data. Samples for noble gas analysis were collected in air-tight copper tubes under back pressure to ensure no head space; samples were analyzed at the Lamont-Doherty Earth Observatory in New York, New York, with a MAP 215-50 semi-automated noble gas mass spectrometer. Noble gas concentrations were reported in cubic centimeters of gas at standard temperature and pressure per gram of water. Helium-3 abundances (δ³He) were reported as percentages (%) by using the following equation, which includes the ratio of helium-3 (³He) to helium-4 (⁴He):

where

The closed-system equilibration (CE) model (Aeschbach-Hertig and others, 2000) or the UA model was fit to noble gas concentrations to estimate recharge temperatures and concentrations of fractionated or unfractionated excess air. Similar assumptions were made when fitting models to noble gases as those made when fitting models to N₂ and Ar; however, the CE model, which requires noble gas concentrations, allows for none, some, or all entrapped air in groundwater to remain in the gaseous phase rather than dissolve, thus making the CE model a more realistic excess air model than the UA model. The CE model assumes that excess air results from groundwater equilibrating with entrapped air at constant hydrostatic pressure (Aeschbach-Hertig and others, 2000).

A helium mass balance was computed for each sample by using DGMETA because sources of helium in the measured ³He and ⁴He other than radioactive decay must be accounted for; that is, to be used for groundwater age estimation, ³He_trit and ⁴He_terr concentrations must only include the ³He formed by tritium decay (half-life ≈ 12.43 years) and the ⁴He formed by uranium-238 decay (half-life ≈ 4.47×10⁹ years) and thorium-232 decay (half-life ≈ 1.4×10¹⁰ years) in the aquifer after recharge (Senftle and others, 1956; Clark and Fritz, 1997; Jurgens and others, 2020). Potential helium sources and sinks that could bias age interpretations include helium dissolved in water before it recharges the aquifer, helium from the mantle, helium that diffuses into the aquifer from neighboring units, crustal helium that migrates into the aquifer through the Reelfoot rift and active faults of the New Madrid seismic zone, dissolution of entrapped air (addition of excess air), and loss of helium to diffusion out of groundwater parcels (Clark and Fritz, 1997; Aeschbach-Hertig and others, 2000). The recharge temperature and excess air concentration (based on the CE or UA model fit to a sample’s N₂ and Ar or noble gas concentrations) were used to estimate how much helium was dissolved in the sample water when it recharged the aquifer and how much helium was added to the sample from excess air. It was assumed that in the aquifer, no helium diffused into or out of the sampled water from or to other groundwater parcels in the aquifer. The atmospheric ³He/⁴He ratio was assumed to be 1.384×10⁻⁶, and the ³He/⁴He ratio of helium from uranium and thorium decay was assumed to be 2.8×10⁻⁸ (Andrews, 1985; Pearson and others, 1991; Solder, 2020). Amounts of ⁴He_terr and ³He_trit were estimated for 21 samples from the MRVA and 9 samples from the MEAS (table 7 of Gratzer and others, 2025). In TracerLPM, ³He_trit was used to date groundwater recharged since approximately 1953; the ³He_trit abundance of each sample was compared to ³He_trit abundances calculated for groundwater of any given age based on the tritium input function (table 2) (Jurgens and others, 2012). The accumulation of ⁴He_terr can be used to date groundwater that was recharged on the order of 10 to 100 million years ago (table 2) (Solomon and others, 1996). The ⁴He_terr accumulation rate in the aquifer must be known to use ⁴He_terr to estimate groundwater age. Because of the uncertainty of estimating the ⁴He_terr accumulation rates for the aquifers sampled, ⁴He_terr was used qualitatively to inform LPMs; that is, greater amounts of ⁴He_terr were assumed to represent progressively older groundwater.

Sulfur Hexafluoride

SF₆ can be used to date water recharged since about 1970 (table 2) (Busenberg and Plummer, 2000). Samples for analysis of SF₆ were collected in two 1-L amber glass bottles (replicates) without headspace and were analyzed by gas chromatography at the USGS Groundwater Dating Laboratory in Reston, Virginia (USGS Groundwater Dating Laboratory, 2023b). SF₆ concentrations were reported in femtograms of SF₆ per kilogram of water. The laboratory made an approximate correction for headspace, if any, in each sample and also reported the maximum percentage of uncertainty that may have resulted from headspace. These uncertainties as well as comments by the laboratory on sample-specific issues are available in table 6 of Gratzer and others (2025). Potential sources of SF₆ contamination to groundwater, that is, dissolved SF₆ that did not enter the aquifer as gas dissolved in water in equilibrium with the recharge atmosphere, include excess air and geogenic SF₆ (Busenberg and Plummer, 2000).

Recharge temperatures and excess air concentrations, estimated by using the CE or UA model, were used to correct measured SF₆ concentrations. Corrected SF₆ concentrations are expressed in parts per trillion by volume (pptv) and represent atmospheric gas-mixing ratios. SF₆ atmospheric gas-mixing ratios are atmospheric SF₆ concentrations in equilibrium with concentrations in recharge water. The SF₆ tracer input function in TracerLPM is a historical record of tropospheric SF₆ concentrations compiled by the USGS Groundwater Dating Laboratory (USGS Groundwater Dating Laboratory, 2023c). Based on the extrapolation by Jurgens and others (2012) of the SF₆ atmospheric mixing ratio timeseries, the current and highest SF₆ atmospheric mixing ratio in history is about 10 pptv. Therefore, no SF₆ values greater than 10 pptv were used to estimate groundwater age.

Carbon-14

The ¹⁴C isotope (half-life of about 5,730 years) of dissolved inorganic carbon (DIC) can be used to estimate the age of water recharged up to about 52,000 years ago (table 2) (Godwin, 1962; National Ocean Sciences Accelerator Mass Spectrometry, 2020). Samples were collected from 70 MRVA wells and 18 MEAS wells for analysis of ¹⁴C (Gratzer and others, 2025); samples were filtered through 0.45-micron filters and collected in 1-L plastic-coated glass bottles with poly-seal cone caps. Samples were stored on ice and shipped to the Woods Hole Oceanographic Institution’s National Ocean Sciences Accelerator Mass Spectrometry facility for ¹⁴C/¹²C and ¹³C/¹²C analyses. The laboratory reported the ¹⁴C abundance of each sample in units of absolute percent modern, an expression of the difference between the ¹⁴C/¹²C ratio of the sample and that of the “modern” standard. The “modern” standard is defined as 95 percent of the ¹⁴C concentration of the National Bureau of Standards Oxalic Acid I standard normalized to a δ¹³C of −19‰ (Olsson, 1970). The ¹³C isotopic composition of each sample was reported relative to the Vienna Pee Dee Belemnite (VPDB) standard:

Each sample was measured 10 times, and a ¹⁴C counting error was reported that accounted for the magnitude of the ¹⁴C activity or the variability in all of the measurements of the sample (the larger of the two derived errors), the error associated with normalization of the measured value to the standard, and the error associated with correcting the sample ¹⁴C activity based on the ¹⁴C activity of the process blank (National Ocean Sciences Accelerator Mass Spectrometry, 2020).

The laboratory reported a normalized ¹⁴C activity (¹⁴C_reported) for each sample, based on an assumption that the initial δ¹³C composition of the sample was −25‰ and that the measured δ¹³C composition (δ¹³C_measured) of the sample resulted from isotopic fractionation that affected both ¹³C and ¹⁴C, in proportion to their atomic weights. The laboratory normalized the ¹⁴C activity of each sample by adjusting the sample’s measured ¹⁴C activity (¹⁴C_measured) to the ¹⁴C activity that the sample would have if its δ¹³C composition was −25‰, using equation 5:

The laboratory performed this normalization procedure in order to undo the assumed isotopic fractionation and determine the ¹⁴C activity that the sample would have if the only process affecting the ¹⁴C activity was radioactive decay. However, the assumed initial δ¹³C composition of −25‰ may be incorrect, as the δ¹³C composition of recharge can vary widely based on various aspects of the unsaturated zone (Clark and Fritz, 1997). Also, correcting ¹⁴C activities for the processes that likely altered them is more appropriate than applying a general fractionation correction (Jurgens and others, 2012). Therefore, we calculated a denormalized ¹⁴C activity from the reported ¹⁴C activity of the sample using equation 5. When ¹⁴C_reported is expressed in percent modern and δ¹³C_measured is expressed in per mil (‰), the value of ¹⁴C_measured calculated by equation 5 is in units of absolute percent modern carbon (pmc).

Processes other than radioactive decay can alter groundwater DIC’s ¹⁴C activity, leading to an inaccurate estimate of groundwater age based on the ¹⁴C activity. Based on previous studies, as well as speciation results for samples collected during this study, carbonate mineral dissolution likely occurs in the MRVA (Kresse and Fazio, 2002; Borrok and others, 2018; Voll and others, 2019). If the carbonate mineral has a different ¹⁴C activity from that of the groundwater DIC, dissolution of the mineral changes the groundwater DIC’s ¹⁴C activity. The graphical method from Han and others (2012), as implemented in NetpathXL (Parkhurst, 2016), was used to determine whether a sample’s ¹⁴C activity likely was altered by geochemical processes and whether that alteration likely occurred predominantly in an environment open or closed to soil carbon dioxide (CO₂), that is, the gaseous CO₂ in the unsaturated zone atmosphere. In this method, the δ¹³C composition, DIC concentration, and ¹⁴C activity of each sample are compared to those of four DIC end members referred to as points A, B, C, and O: (point A) dissolved CO₂ (CO₂(aq)) in carbon isotopic equilibrium with gaseous soil CO₂; (point B) bicarbonate (HCO₃⁻) in carbon isotopic equilibrium with calcite; (point C) HCO₃⁻ in carbon isotopic equilibrium with gaseous soil CO₂; and (point O) DIC that is half derived from gaseous soil CO₂ and half derived from calcite (through a process where groundwater became saturated with respect to gaseous soil CO₂ in an environment open to gaseous soil CO₂, referred to as the open system, and then became saturated with respect to calcite in an environment closed to gaseous soil CO₂, referred to as the closed system). Based on the results of the graphical method, if a sample’s composition suggested open- or closed-system carbonate mineral dissolution and, in some cases, carbon isotopic exchange with CO₂ or carbonate minerals, the open- or closed-system revised Fontes and Garnier ¹⁴C correction model (Han and Plummer, 2013) (eq. 6 or 7, respectively), as implemented in NetpathXL (Parkhurst, 2016), was used to estimate ¹⁴C_0,corrected; the ¹⁴C activity of recharge DIC accounting for gaseous soil CO₂ dissolution, carbonate mineral (calcite) dissolution, and, in some cases, corresponding carbon isotopic exchange. Some ¹⁴C activities were interpreted to require no correction, and the age distributions estimated for these samples, if estimated using ¹⁴C, were based on ¹⁴C_measured (Gratzer and others, 2025).

The inverse geochemical modeling software NetpathXL (Parkhurst and Charlton, 2008) was used to calculate the carbonate speciation (H₂CO₃, HCO₃⁻, and CO₃²⁻ concentrations) of each sample. The carbonate species concentrations, temperature, ¹⁴C activity, and δ¹³C of each sample requiring correction were used in the open- or closed-system revised Fontes and Garnier ¹⁴C correction model (eqs. 6 and 7, respectively) to calculate a corrected ¹⁴C activity of DIC before decay (¹⁴C_0,corrected), which was then used to calculate a corrected groundwater ¹⁴C activity at the time of sample collection (¹⁴C_t,corrected) using equation 8 (Han and Plummer, 2013).

To correct for alteration of ¹⁴C by a process that predominantly took place in an environment open to soil CO₂, the following equation was used:

where

To correct for alteration of ¹⁴C by a process that predominantly took place in an environment closed to soil CO₂, the following equation was used:

where

In the open- and closed-system revised Fontes and Garnier ¹⁴C correction models (eqs. 6 and 7, respectively), values were assumed for the ¹⁴C activity and δ¹³C of soil CO₂ and carbonate minerals (calcite) based on compositions that would be characteristic of a landscape dominated by C₃ plants—plants that use the C₃ photosynthesis pathway—with marine carbonates present in the subsurface. For all corrections, the ¹⁴C activity of soil CO₂ (¹⁴C_g) was assumed to be 100 pmc, the approximate ¹⁴C activity of the atmosphere for the past 4,000 years (excluding the period during and following thermonuclear bomb testing) (Clark and Fritz, 1997). For all corrections, the ¹⁴C activity of calcite (¹⁴C_s) was assumed to be 0 pmc; that is, all carbonate minerals in the open and closed systems of the MRVA were assumed to have lost all their ¹⁴C to decay. Four possible values were assumed for δ¹³C of soil CO₂ (δ¹³C_g):

Three possible values were assumed for δ¹³C of calcite (δ¹³C_s) (−2‰, 0‰, and 2‰) based on typical compositions of marine carbonates (Clark and Fritz, 1997). For each sample that needed correction of its ¹⁴C activity, the 12 possible combinations of δ¹³C_g and δ¹³C_s values were used to compute 12 corrected ¹⁴C activities of DIC before decay (¹⁴C_0,corrected) with equation 6 or 7. If a groundwater sample’s carbon composition suggested open-system carbonate mineral dissolution, values of ¹⁴C_0,corrected generated from equation 6 were assumed to be equiprobable estimates of ¹⁴C_0,corrected when dating a sample in TracerLPM. Similarly, values of ¹⁴C_0,corrected generated from equation 7 were given equal consideration when dating a sample that had a DIC concentration, δ¹³C, and ¹⁴C activity suggesting closed-system carbonate mineral dissolution.

The ¹⁴C_0,corrected values were used to calculate ¹⁴C_t,corrected values, the actual values entered in TracerLPM, by using equation 8:

where

Groundwater Age Estimation Using TracerLPM

Groundwater age distributions were estimated using LPMs fit to tracer concentrations with the USGS software TracerLPM (Jurgens and others, 2012). An LPM can account for mixing of groundwaters of different ages and leverage multiple tracer concentrations to constrain an age distribution. The LPM approach to estimating groundwater age is intermediate in complexity and expense between estimating an apparent piston flow age and estimating an age distribution by developing a mass-transport model. This intermediate approach to estimating groundwater age was appropriate for the goals and regional scale of the study.

TracerLPM contains five single-mixture LPM types—the piston flow model (PFM), dispersion model (DM), exponential mixing model (EMM), partial exponential model (PEM), and exponential piston flow model (EPM)—that represent different aquifer geometries. A PFM is the simplest LPM and describes a sample consisting of water parcels that have traveled the same flow path at the same rates and therefore have the same age. The assumptions of the PFM did not fit the conceptual model of MRVA groundwater flow, so PFMs were not used to estimate ages of samples. The DM describes water that has mixed with water flowing at different velocities through the aquifer. A parameter of the DM, the dispersion parameter (DP), is defined as the dispersion coefficient divided by the product of velocity and position and describes the ratio of dispersion to advection of the tracers being modeled and controls the ratio of the width to the height of the age distribution (Jurgens and others, 2012). The EMM describes a sample collected from a well screened through the saturated thickness of an unconfined aquifer. The PEM describes a sample collected from a well screened through a portion of the saturated thickness of an unconfined aquifer. Two parameters of the PEM, the upper and lower PEM ratios, describe where the bottom and top of the well screen lie in relation to the bottom and top of the saturated thickness. The EPM describes a sample collected from a well screened through the saturated thickness of a confined aquifer. A parameter of the EPM, the EPM ratio, describes the length of the part of a flow path that is in the confined portion of the aquifer divided by the length of the part of that flow path that is in the unconfined portion of the aquifer where recharge occurs. The EMM, PEM, and EPM are the most physically realistic LPM types and were therefore used when possible. Each single-mixture LPM models a sample as a mixture of waters of different ages, an approximation of the mixture that results from the increase in age with depth along the length of a well screen.

An additional LPM, the binary mixing model (BMM), can be used for samples conceptualized as consisting of water from two distinct sources; for example, a BMM may be used to model a sample containing a mixture of water from two different aquifers or a sample containing a mixture of water from precipitation that recharged the aquifer far away and water gained by the aquifer from a losing stream near the well. The water from each distinct source has its own age distribution, so the resulting BMM is bimodal. If the conceptual model for a sample involves more than one distinct source but a single-mixture LPM can be fit to the sample, it may suggest that one of the sources of water to the sample is dominant or that the multiple sources of water to the well have similar age distributions. However, if a sample contains significant amounts of waters from two sources with dissimilar age distributions, a BMM is likely the only LPM that fits the sample’s set of tracer concentrations. Any of the five LPM types can be combined for a BMM. The LPM type used for each component of the BMM is the same LPM type that would be used to model that component alone. For example, if the conceptual model for a sample was a mixture of younger water that recharged the MRVA and traveled to the well under unconfined conditions and older water from a deeper confined aquifer that flowed up into the MRVA, a PEM would be used for the young component, an EPM would be used for the old component, and the LPM type for the sample would be referred to as a BMM-PEM-EPM.

The simplest LPM consistent with the conceptual model for the hydrologic setting of a well was chosen for each sample in this study. Attempts were made to fit a single-mixture LPM, that is, one individual EMM, PEM, EPM, or DM, to the sample before attempting to fit a BMM to the sample (fig. 2, table 3).

The conceptual model for the aquifer geometry influencing the paths to a well screen was informed by the well screen interval, potentiometric surface maps (Haugh and others, 2020; McGuire and others, 2020; McGuire and others, 2021), well logs (USGS, 2019), and hydrogeologic information products based on airborne electromagnetic data and (or) borehole geophysical data (Hart and others, 2008; Torak and Painter, 2019; James and Minsley, 2021). The datasets were used to identify the well screen location relative to the extents of the upper and lower confining units of the aquifer, the depths of the top and bottom of the saturated thickness of the aquifer, and the extents of connected reaches of upgradient losing streams. Generally, wells identified as being in unconfined portions of the aquifer were modeled with a PEM, EMM, or DM, and wells identified as being in confined portions of the aquifer were modeled with an EPM or DM, in accordance with the definitions of these LPM types (fig. 2).

For the selected LPM type and observed tracer concentrations, TracerLPM is used to find the optimum mean age and parameter values that produce an age distribution for which modeled tracer concentrations most closely match observed tracer concentrations. An LPM should be fit to as many tracers as possible to yield a better-constrained solution. Because of the oscillation of atmospheric tracer concentrations through time, one tracer concentration alone may correspond to several different ages; therefore, it is often necessary to measure multiple tracers in a sample to determine the most likely age of the sample. Also, the number of tracers determines the number of model parameters that TracerLPM can optimize.

For some samples, no LPM could be fit to all the available tracers for that sample, likely because of errors (such as sampling or measurement errors), uncertainty (such as in tracer correction models or input functions), the simplifying assumptions made by a given LPM type, or an incorrectly assumed LPM type. For these samples, an LPM was fit to a subset of the sample’s tracers and, if necessary and applicable, the DP or EPM ratio was estimated by graphically evaluating the model fit for different values of the parameter. If enough tracer concentrations were available for a sample, the TracerLPM software was used to optimize DPs and (or) EPM ratios (Jurgens and others, 2012). For five samples, more than one possible age distribution was reported because more than one conceptual model of the physical hydrology affecting the sample was probable or the sample had more than one corrected ¹⁴C, SF₆, or ³He_trit concentration to which an appropriate LPM could be fit.

For all samples, the unsaturated zone residence time was assumed to be zero, no mixing of waters with different tracer abundances was assumed to have occurred in the unsaturated zone, and the recharge added to the aquifer at a given time was assumed to be in equilibrium with the atmosphere or rain at that time. Generally, using groundwater sample age distributions rather than mean ages is preferable when using groundwater age to inform decisions because age distributions better represent the variety of travel times from recharge zones to a well (Eberts and others, 2012). Gratzer and others (2025) contains the parameters necessary to reproduce the full age distribution(s) estimated for each sample. The mean ages of the distributions are used in this report to summarize results. Hereinafter, the “age” of a sample refers to the mean of the sample’s age distribution.

Relations of Groundwater Age to Hydrogeology and Stressors

The depositional history of the MAP shaped the MRVA and the sediment and soil that overlie it (Saucier, 1994). The properties and geometry of materials overlying the MRVA, as well as precipitation rates and land use, influence recharge rates. Recharge rates, aquifer properties and geometry, and discharge rates affect groundwater flow velocities. Recharge rates and groundwater flow velocities control groundwater age. Because the age of a groundwater parcel is affected by several factors along its path and because the age of a groundwater sample pumped from a well is affected by mixing along paths and mixing of parcels pulled into the well from all directions, the spatial distribution of age might not reflect the spatial pattern of any one controlling factor. However, if one or more factors with similar spatial patterns have the greatest influence on groundwater age in the aquifer or a region of the aquifer, the spatial distribution of those factors might be reflected in the spatial distribution of age.

Mean ages of MRVA groundwater samples were compared to several variables hypothesized to influence recharge rates, groundwater flow velocities, and (or) groundwater age. These variables included well depth, soil saturated hydraulic conductivity (Soil Survey Staff, 2020), net infiltration (potential recharge) (Westenbroek and Nielsen, 2023), groundwater use (Wilson, 2021), electrical resistivity of the MRVA saturated thickness (James and Minsley, 2021), and the degree of potential for hydraulic connection between the MRVA and an underlying unit (James and Minsley, 2021). Well depth can be a proxy for position within the groundwater flow system because deep wells likely capture longer flow paths and thus relatively older groundwater than shallow wells. Investigating the controls on the full age distribution estimated for each sample, as opposed to the mean age estimated for each sample, was beyond the scope of this study. Therefore, the effect of well screen length on the age distribution of each sample was not examined. A longer well screen is likely to capture a wider range of ages of water parcels. Soil hydraulic conductivity can affect where recharge occurs. Groundwater use varies throughout the MRVA (Kresse and others, 2014) and affects hydraulic gradients and thus groundwater paths. Electrical resistivity was used as a proxy for hydraulic conductivity because sediment with low clay content tends to have higher resistivity and hydraulic conductivity than sediment with a high clay content (Mazáč and others, 1985). Groundwater in an area of high hydraulic conductivity is expected to be young. Additionally, the electrical resistivity of the sediment within 82 ft of the contact between the MRVA and the underlying unit was used to estimate the potential for hydraulic connection between the MRVA and the underlying unit (James and Minsley, 2021). Groundwater where the MRVA is in hydraulic connection with an underlying unit is expected to be old.

Selected gridded spatial variables (that is, rasters) representing hydrogeologic conditions across the MAP (soil saturated hydraulic conductivity, recharge, groundwater use, resistivity of the saturated thickness of the MRVA, and conductance of the base of the MRVA) were clipped to the area within 1.24 miles (mi) of each well, and the area-weighted averages of the values of the grid cells within 1.24 mi of the well were assigned to the well. The 1.24-mi radius was chosen based on the estimated distance a water parcel might travel through the MRVA in 160 years, which is the median of the mean ages estimated using TracerLPM for MRVA samples in this study. Each variable was compared to age, first considering all the MRVA wells and then considering the wells in each region of the MAP separately (Ladd and Travers, 2019) (fig. 11). Regions of the MAP are separated by Crowleys Ridge or major rivers. Several of these features act as groundwater divides for the aquifer (Renken, 1998; Kresse and others, 2014).

Tritium Concentrations and Age Categories

Tritium concentrations in historical samples and samples from this study collected between 1988 and 2020 from the MRVA (n=187) ranged from below the detection limit (about 0.2 tritium unit [TU]) to 16.3 TU, with a median of 1.9 TU (Gratzer and others, 2025). Of the samples from the MRVA, 43 percent were categorized as modern (recharged after 1953), 41 percent were mixed (a mixture of water recharged after 1953 and water recharged before 1953), and 14 percent were premodern (recharged before 1953). The remaining 2 percent could not be classified because of censored tritium values with censoring limits greater than categorical thresholds (Gratzer and others, 2025).

Throughout much of the MRVA, no systematic spatial distribution of modern, mixed, or premodern groundwater was observed (fig. 3A). An exception was that samples collected in the northern part of the MRVA (southeastern Missouri and northeastern Arkansas) were predominantly modern (fig. 3A). No substantial difference was observed in the depths of wells for the three tritium-based age categories (fig. 4A).

The samples from the MEAS had lower tritium concentrations than those from the MRVA. Tritium concentrations in 344 MEAS samples collected between 1989 and 2020 ranged from below the detection limit (about 0.2 TU) to 14.1 TU, with a median concentration below the detection limit (Gratzer and others, 2025). Based on tritium concentrations, 16 percent of the samples collected from the MEAS were modern, 24 percent were mixed, and 56 percent were premodern; the remaining 4 percent could not be classified. Modern groundwater was generally near or in outcrop areas of MEAS units near the eastern and western edges of the embayment (fig. 3B). Throughout the entire embayment, especially where the MRVA overlies the MEAS (fig. 3B), groundwater samples were classified as premodern and mixed. Modern samples generally were collected from shallower wells than mixed and premodern samples (fig. 4B).

Recharge Temperatures and Excess Air Concentrations

Sixty-eight MRVA samples and 17 MEAS samples were analyzed for dissolved N₂ and Ar. Of those samples, 26 MRVA and 12 MEAS samples were also analyzed for He, Ne, Xe, Kr, and ³He. Recharge temperatures (ranging from 6.6 to 20 degrees Celsius) and excess air concentrations based on the UA model fit to N₂ and Ar concentrations were used to correct concentrations of SF₆ in 54 samples (Gratzer and others, 2025). Recharge temperatures (ranging from 10.5 to 14.3 degrees Celsius) and excess air concentrations based on the UA model fit to noble gas concentrations were used to correct SF₆ concentrations in seven samples and helium tracer data in six samples (Gratzer and others, 2025). Recharge temperatures (ranging from 7.7 to 18.3 degrees Celsius) and excess air concentrations based on the CE model fit to noble gas concentrations were used to correct SF₆ concentrations in 23 samples and helium tracer data in 24 samples (Gratzer and others, 2025). Recharge temperatures and excess air concentrations estimated using dissolved N₂ and Ar did not exhibit strong positive correlations with recharge temperatures and excess air concentrations estimated using noble gases for the same samples, suggesting that the assumption made by the UA model of complete dissolution of entrapped air was inaccurate for the recharge zones of these samples. Excess air concentrations were similar in samples collected from the MRVA and from the MEAS (fig. 5A); recharge temperatures were higher for the samples from the MRVA than for samples from the MEAS (fig. 5B) (Gratzer and others, 2025).

Helium Tracers

Samples collected from the MRVA had similar R/Ra values and concentrations of helium, ⁴He_terr, and ³He_trit to those of samples collected from the MEAS. The fraction R/Ra is an expression of the isotopic composition of dissolved helium, where R is the ratio of ³He to ⁴He in the groundwater sample and Ra is the ratio of ³He to ⁴He in air.

Sulfur Hexafluoride

MRVA samples had higher SF₆ concentrations than MEAS samples had (fig. 6). Corrected SF₆ concentrations ranged from 0.3 to 246.5 pptv with a median of 2.6 pptv in MRVA samples, and concentrations ranged from 0.2 to 1.6 pptv with a median of 0.4 pptv in MEAS samples. Two corrected SF₆ concentrations greater than 10 pptv (the highest natural atmospheric mixing ratio in recorded history) in MRVA samples are not shown on figure 6 because these high concentrations suggest interaction with SF₆ sources in addition to SF₆ from recharge.

Based on all the MRVA and MEAS samples, SF₆ concentrations were lower in samples classified as premodern than in mixed and modern samples (fig. 6). Although SF₆ concentrations were higher in mixed and modern samples than in premodern samples, each premodern sample had an SF₆ concentration suggesting an age of 51 years or less, which conflicts with the tritium-based age classification. Incompatibility between tritium and SF₆ age results suggests that SF₆ was added to these samples by a source other than recharge, likely a geogenic source based on the pervasiveness of this excess SF₆. Solder (2020) found evidence of geogenic SF₆ contamination in samples collected from the south Atlantic and Gulf Coast principal aquifer systems, including the MEAS.

Carbon-14

Denormalized, uncorrected ¹⁴C activities of MRVA samples (ranging from 19.98 to 111.4 pmc, with a median of 71.83 pmc) were higher than those of MEAS samples (ranging from 0.14 to 86.76 pmc, with a median of 27.61 pmc) (Gratzer and others, 2025).

Groundwater from the MRVA and MEAS was interpreted to have undergone processes other than radioactive decay that may have influenced its carbon isotopic composition (Han and others, 2012). Figure 7 illustrates carbon compositions of samples relative to those of two likely sources of carbon to groundwater: gaseous soil CO₂—with an assumed composition of δ¹³C_g = −25 ‰ and ¹⁴C_g = 100 pmc (labeled as the dark orange diamond in fig. 7) and calcite—with an assumed composition of δ¹³C_s = 0 ‰ and ¹⁴C_s = 0 pmc (labeled as the light blue diamond in fig. 7). Figure 7 shows three possible carbon isotopic composition end members of DIC that have interacted with these two carbon sources (soil CO₂ and (or) calcite): CO₂(aq) (labeled as “A” in fig. 7) in isotopic equilibrium with gaseous soil CO₂; HCO₃⁻ (labeled as “C” in fig. 7) in isotopic equilibrium with gaseous soil CO₂; HCO₃⁻ (labeled as “B” in fig. 7) in isotopic equilibrium with calcite; and total DIC (assumed to equal the sum of CO₂(aq) and HCO₃^-; labeled as “O” in fig. 7) that is half derived from gaseous soil CO₂ and half derived from calcite (Han and others, 2012; Parkhurst, 2016). The Tamers X and Y lines in figure 7 are vertical and horizontal extensions, respectively, of point O that aid in comparing carbon isotopic compositions of samples to that of DIC at point O (Parkhurst, 2016).

Figure 7 can be used to interpret geochemical processes other than radioactive decay which may have affected the carbon compositions (DIC, δ¹³C, and ¹⁴C activity) of the samples (Han and others, 2012; Parkhurst, 2016). In figure 7, most MRVA samples have higher DIC and ¹⁴C than point O and δ¹³C between points C and O, thus appearing in the upper left quadrant of the plot, which is consistent with open-system carbonate mineral dissolution (Han and others, 2012). Most MEAS samples have lower DIC and ¹⁴C than point O and plot near the Tamers X line of figure 7, which is consistent with closed-system carbonate mineral dissolution. Based on observations from figure 7, processes such as carbonate mineral dissolution likely influenced the ¹⁴C/¹²C and ¹³C/¹²C of groundwater DIC in the MRVA and MEAS. The revised Fontes and Garnier ¹⁴C correction models (Han and Plummer, 2013), as implemented in NetpathXL (Parkhurst, 2016), were used to correct ¹⁴C activities of samples with carbon compositions that suggested carbonate mineral dissolution.

Corrected ¹⁴C activities using the twelve assumed combinations of carbon isotopic compositions of soil CO₂ and calcite were generally greater for MRVA samples than for MEAS samples for open- and closed-system correction models (fig. 8). Most samples from the MRVA and from the MEAS had wide ranges (greater than or equal to 50 pmc) of open-system corrected ¹⁴C activities. Most samples from the MRVA had wide ranges of closed-system corrected ¹⁴C activities, but most samples from the MEAS did not have wide ranges of closed-system corrected ¹⁴C activities. The range of corrected ¹⁴C values for each sample reflects the sensitivity of the revised Fontes and Garnier ¹⁴C correction models to the possible soil CO₂ and calcite compositions and open- versus closed-system assumptions used for corrections as well as the measured ¹⁴C activity of the sample.

Not all ¹⁴C values required correction because the carbon compositions of some samples were consistent with no dilution of ¹⁴C; uncorrected ¹⁴C activities were used for 41 percent of MRVA samples and 61 percent of MEAS samples for which LPMs were fit to ¹⁴C (table 4). Corrected ¹⁴C activities used for estimating ages of samples ranged from 51.34 to 121.1 pmc for the MRVA and from 7.24 to 102.7 pmc for the MEAS (Gratzer and others, 2025). Table 4 summarizes the number of samples for which each combination of correction model (open- or closed-system revised Fontes and Garnier ¹⁴C correction model), δ¹³C_s assumption, and δ¹³C_g assumption was used to correct a sample’s ¹⁴C activity. Of the samples for which a corrected ¹⁴C activity was used to date the sample, most MEAS samples were corrected using the closed-system revised Fontes and Garnier ¹⁴C correction model, and most MRVA samples were corrected using the open-system revised Fontes and Garnier ¹⁴C correction model (table 4).

Groundwater Age Lumped Parameter Models

Mean ages of 71 MRVA samples ranged from 12 to 22,000 years, with a median of 140 years (fig. 9). Most MRVA sample mean ages were less than 500 years old, and about one-third of the mean ages were less than 50 years. Most of the LPMs used for MRVA samples were BMMs or PEMs (table 3). Most of the LPMs for these samples were fit to tritium and ¹⁴C concentrations or tritium and SF₆ concentrations.

Mean ages of 18 samples from the MEAS ranged from 230 to 52,000 or more years, with a median of 13,500 years, similar to results from a larger scale study of MEAS groundwater age (Solder, 2020). Most MEAS samples were at least 10,000 years old (fig. 9). Most MEAS samples were modeled as DMs; however, four MCAQ samples were modeled as EPMs, and two MCAQ samples were modeled as BMMs (table 3). Most MEAS models were fit to ¹⁴C alone. Four MCAQ models, including two BMMs and one EPM, were fit to ¹⁴C and tritium.

Tracer concentrations exhibited general relations between old and young tracers, suggesting that results of tracer measurement and any necessary corrections were reasonable (fig. 10). For example, corrected SF₆ concentrations in premodern samples (based on tritium) were lower than concentrations in most mixed and modern samples (figs. 6, 10). Also, ¹⁴C activities (for corrected and uncorrected samples) generally increased with increasing corrected SF₆ concentrations. Figure 10 also highlights the wider range of tracer concentrations in the MRVA compared to the MEAS. For example, samples in each tritium-based age category in the MRVA had a wide range of ¹⁴C activities, suggesting the presence of old groundwater in parts of the MRVA, also highlighting the importance of understanding carbon cycling in the MRVA to accurately interpret groundwater age using ¹⁴C.