Environ. Sci. Technol. 2007, 41, 1949-1955
Noble Gas Excess Air Applied to Distinguish Groundwater Recharge Conditions RICHARD G. S. INGRAM, KEVIN M. HISCOCK,* AND PAUL F. DENNIS School of Environmental Sciences, University of East Anglia, Norwich, NR4 7TJ, UK
The application of geochemical tracers in groundwater studies can provide valuable insights into the rates and sources of groundwater recharge, residence times, and flow dynamics that are of significant value in the management of this important natural resource. This paper demonstrates the application of noble gas excess air to distinguish groundwater bodies with different recharge histories in a layered sandstone aquifer system in the east of England. The sampled groundwaters are all supersaturated with respect to neon, indicating the presence of excess air. The lowest excess air concentrations occur where the aquifer is unconfined (∆Ne, the proportion of neon in excess of saturation, ) 12-26%) and recharge occurs directly to the outcrop. Groundwater in the confined part of the aquifer can be divided into two hydrochemical types based upon the dissolved ion chemistry: Type 1 groundwaters contain more excess air (∆Ne ) 115-120%) than Type 2 (∆Ne ) 2262%). The difference in excess air concentrations confirms that groundwater enters the confined aquifer along two discrete pathways. Furthermore, excess neon concentrations predicted from the magnitude of annual water table fluctuation observed in the different recharge areas are in good agreement with those measured in the corresponding groundwaters. We therefore recommend that excess air may be usefully employed as a direct indicator of the volume of long-term net annual groundwater recharge.
Introduction Groundwater is an important natural resource. Worldwide, more than 2 billion people depend on groundwater for their daily supply (1). A large proportion of the world’s agriculture and irrigation is dependent on groundwater, as are a large number of industries. To better manage groundwater, the vulnerability of groundwater resources to drought, overabstraction, and quality deterioration must be assessed both now and in the context of climate change (2). An integral part of such groundwater management is the development of assessment methods, for example the application of natural and anthropogenic tracers that can provide information on the rates and sources of groundwater recharge, residence times, and the dynamics of groundwater flow. Commonly measured geochemical tracers in groundwater include stable isotopes of water (δ18O, δ2H), tritium (3H), and radiocarbon (14C). Additional tracers include the noble gases (He, Ne, Ar, Kr, and Xe) and when applied as part of * Corresponding author phone: +44 1603 593104; fax: +44 1603 591327; e-mail:
[email protected]. 10.1021/es061115r CCC: $37.00 Published on Web 02/13/2007
2007 American Chemical Society
multitracer studies can enable the reconstruction of paleoenvironmental conditions and give insight into the history of evolution of the flow system (3-7). In regional aquifers where groundwater residence times are greater than 105 years, such interpretations have been used to study the climatic amelioration that occurred following the last glacial period through the calculation of noble gas temperatures (NGTs) as a proxy for mean annual air temperatures (3-6). It has also been possible to distinguish mountain recharge from local lowland recharge in alpine valley systems (8) and to locate the recharge area for thermal spring waters (9) by determining the elevation at which recharge occurred by comparing calculated NGTs and noble gas pressures with local atmospheric lapse rates. However, while applications of the equilibrium component of the dissolved atmospheric noble gases are understood, the super-saturated component resulting from bubble entrapment (“excess air”) has been underutilized in groundwater studies. This is despite the documented potential of excess air to distinguish between groundwater bodies recharged in different areas (10) and qualitative evidence linking excess air with climatic humidity (11-13). Indeed, excess air is usually treated as a phenomenon to be corrected for so that equilibrium conditions can be determined. Atmospheric gases become dissolved in groundwater during recharge in two ways: by equilibrium dissolution following Henry’s Law and through bubble entrapment during sediment imbibition. Equilibrium dissolved gas concentrations are proportional to the gaseous partial pressures and inversely proportional to the ambient temperature and the ionic strength of the solution. By determining the equilibrium dissolved concentrations of atmospheric gases in groundwater, it is possible to back-calculate the temperature, pressure, and salinity conditions present at the water table during groundwater recharge (14). Trapping of atmospheric gas in the voids of porous material during wetting is commonly observed (15), explaining the presence of excess air in most groundwaters (14). The formation of excess air is unique to water flowing through porous media: surface waters contain very little excess air (16) whereas excess air develops in groundwaters within a few days or maybe even hours of recharge (17, 18). In most natural cases, excess air is entrained only at the water table because it is assumed that no atmospheric gas bubbles remain within the saturated aquifer due to long-term flushing. However, in situations where aquifers have become recently saturated (e.g., beneath reservoirs or artificial recharge ponds), excess air has been shown to accumulate during flow through the saturated zone (19). Examination of the mathematical models used to separate the two atmospheric components has theoretically linked excess gas concentrations with the magnitude of water table fluctuation during recharge, with larger fluctuations dissolving more trapped gas because the hydrostatic pressure exerted is greater (20). This paper presents an example of the use of dissolved noble gases to distinguish groundwater bodies with different recharge histories within a more general investigation of the hydrochemistry of a layered aquifer system and demonstrates the value of noble gases to estimate excess air rather than just recharge temperatures. The relationship between excess air concentration and water table fluctuation is also explored and suggests that excess air may be applicable as a direct indicator of long-term average net annual groundwater recharge. VOL. 41, NO. 6, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 1. Location map showing the geology of west Norfolk and the locations where groundwater samples and/or water level observations were taken.
Experimental Section Study Area Hydrogeology. West Norfolk is a low-lying coastal region in eastern England. Hills reach a maximum elevation of 92 m above sea level in the northeast (Figure 1). A succession of easterly dipping Upper Jurassic and Cretaceous sediments form a layered aquifer system up to 200 m thick. There are two important water-bearing formations: the foraminiferal limestone of the Chalk at the top of the succession and the fine-grained glauconitic arenites of the Sandringham Sands and Dersingham Beds beneath (collectively termed the Sands aquifer). Groundwater flow in the Chalk occurs mainly within a network of fissures developed by solutional weathering along bedding plane openings and fractures (21). The Sands are generally poorly consolidated and unable to support fracturing so groundwater flow is principally intergranular, although controlled to some extent by lithological variations between individual members. The Chalk and the Sands are separated by two impersistent and lithologically heterogeneous clay formations, the Gault Clay and the Snettisham Clay. Where present, the clays confine the Sands beneath as proven by short-term pumping tests and the occurrence of artesian (nonflowing) conditions in observation wells. Unconfined groundwater conditions occur in both the Chalk and the Sands where they are at outcrop. The Chalk of west Norfolk is sparsely covered by Quaternary glacial sediments in contrast to the Sands outcrop where 60% of the area is covered by Quaternary deposits (mostly glacial till), although these are not thick or extensive enough to allow confined conditions to develop. A notable Quaternary feature in the region is an incised channel of late Pleistocene age that arcs from east to west in the central part of the region. The channel is infilled with till, sand, and gravel and 1950
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TABLE 1. Hydrochemical Properties of Sands and Chalk Groundwaters from West Norfolka confined Sands species (mg L-1)
unconfined Sands (n ) 31)
13 - 214 (95 ( 52) Mg2+ 2.8 - 22.1 (7.0 ( 4.7) b Fetot b.d. - 20.1 (5.5 ( 6.2) HCO310 - 402 (199 ( 99) Cl18 - 124 (54 ( 30) SO42b.d. - 190 (76 ( 47) NO3 b.d. - 122 (13 ( 70) SiO2 1.8-14.0 (7.4 ( 3.2) δ18O -7.5 - 6.9 (‰ VMSOW) (-7.2 ( 0.3) Ca2+
Type 1 (n ) 10)
Type 2 (n ) 17)
Chalk (n ) 18)
77 - 95 (85 ( 7) 3.2 - 6.8 (4.1 ( 1.2) b.d. - 2.8 (1.0 ( 0.8) 244 - 291 (263 ( 17) 12 - 18 (15 ( 3) 9 - 21 (12 ( 5) b.d. - 0.2 (0.0 ( 0.2) 9.4-10.8 (9.6 ( 0.4) -7.6 - 7.1 (-7.4 ( 0.2)
83 - 214 (99 ( 10) 0.9 - 2.9 (1.5 ( 0.5) b.d. - 0.8 (0.3 ( 0.3) 206 - 344 (241 ( 22) 14 - 46 (19 ( 3) 23 - 190 (39 ( 14) b.d. - 2.7 (0.3 ( 1.4) 5.4-9.0 (7.2 ( 0.6) -7.6 - 7.3 (-7.5 ( 0.1)
107 - 146 (130 ( 20) 1.3 - 2.8 (2.0 ( 0.8) b.d. - 0.2 (0.02 ( 0.05) 220 - 312 (273 ( 56) 23 - 111 (43 ( 22) 17 - 57 (39 ( 20) 37 - 101 (66 ( 32) 6.0-10.5 (7.2 ( 1.0) -7.7 - 7.1 (-7.5 ( 0.1)
a Concentration ranges are given for all parameters with mean ( 2σ values given in brackets. b.d. ) below detection. b Fetot ) total Fe concentration measured as Fe2+.
cuts through the Chalk and confining clays so that the valley fill deposits rest directly on the Dersingham Beds. Groundwater flow is generally from east to west, even in the confined Sands aquifer, although some convergence of flow can be observed between the Sands and Chalk outcrops due to the topography of the region (Figure 2). The decline
FIGURE 2. Map showing groundwater head distribution in the studied aquifers (October, 2003) and the distribution of hydrochemical types (see text for description) within the confined Sands. Mean annual water table fluctuations are shown in square brackets for representative sites in the Chalk and unconfined Sands. Further details of these are given in the Supporting Information. in potentiometric head toward the west in the confined Sands aquifer indicates that it is not recharged from the outcrop but instead recharged by leakage from the Chalk. This most probably occurs in the north of the area where the Gault Clay grades into the more permeable Red Chalk (Hunstanton Formation) creating a pathway along which water can flow from the Chalk into the Sands. Sample Collection. Groundwater samples were collected from boreholes in the Chalk and Sands aquifers during August and September of 2002 and 2003. Sample locations are shown in Figure 1. Where submersible pumps were not installed, a portable Grundfos MP1 pump was used. Pumped water was passed into a flow-through cell in which pH, Eh, dissolved oxygen concentration, electrical conductivity (EC), and temperature probes were placed. Boreholes were purged until
EC measurements stabilized before any samples were taken. Samples of raw water for alkalinity analysis by titration were taken in 500 mL polythene bottles. Samples (60 mL) for dissolved cation and anion analysis were filtered using 0.45 and 0.2 µm cellulose acetate syringe filters, respectively, and collected in polyethylene centrifuge tubes. Samples for cation analysis were acidified using concentrated HNO3. Further raw water samples were collected in 150 mL glass bottles with rubber-lined metal screw caps for analysis of stable isotopes of water. Noble gas samples of approximately 20 cm3 were collected in 10 mm diameter copper tubes that were sealed with swaging clamps (22). Sample Analysis. Alkalinity was measured by titration to pH 4.5 using 0.01 M HCl and BDH 4.5 indicator. Cation concentrations were analyzed by ICP-OES (Varian Vista) and anion concentrations were analyzed using ion chromatography (Dionex 4000i). Charge balance errors were used to check sample consistency and were better than ( 5% in all cases. Additionally, sites exhibited little variation in groundwater composition between 2002 and 2003. δ18O ratios were analyzed using a modification of the H2O-CO2 equilibration technique (23) using a Europa SIRA II isotope ratio mass spectrometer. Concentrations of Ne, Ar, Kr, and Xe were analyzed by isotope dilution using a VG AN-5T quadrupole mass spectrometer operated in static mode (24). The 20 cm3 water samples were split into two 5 cm3 samples for repeat analysis. Splitting was undertaken by placing additional swaging clamps approximately 10 cm centerward from the clamps at either end of the sample tube. The samples were separated by cutting the center of the copper tube with a pipe cutter. This process created a straight, perpendicularly cut tube section that could be securely mated to the gas extraction line. Splitting the samples will not have altered the dissolved noble gas concentrations because the tubes remain sealed and the internal pressure is maintained. Calibration of the mass spectrometer was checked using water and air standards containing known noble gas concentrations. Standard water samples were taken from large aspirators that had been left to equilibrate with the atmosphere for at least 7 days in different, temperature-controlled environments (25). Following calibration checks it was necessary to use calibration curves to relate mass spectrometer response to gas volume because the usual single point calibrations appeared unreliable. Despite these corrections, Kr concentrations were unable to be measured with a satisfactory precision. The correction procedure reduces the precision of Ne, Ar, and Xe concentration determinations compared to other studies (e.g., 24, 26). Noble gases were measured successfully in samples from three unconfined Sands and eight confined Sands sites.
Results and Discussion Hydrochemical Conceptual Model. Groundwater in the Sands has similar hydrochemical characteristics in both the confined and unconfined aquifers being reducing and CaHCO3-SO4 dominated. Where the Sands aquifer is unconfined, the patchy nature of the overlying till cover and the low carbonate content of the aquifer mean that large variations in ionic hydrochemistry are observed (Table 1). In the confined Sands, groundwater chemistry is more consistent and two distinct hydrochemical types can be identified. Type 1 groundwaters found to the north of the Babingley River have higher Mg2+ and SiO2 concentrations and lower SO42- concentrations than Type 2 groundwaters that are found in the confined Sands to the south of the river (Table 1 and Figure 2). Chalk groundwater is hydrochemically very uniform, Ca-HCO3 dominated and oxidizing, quite different from the groundwater in the Sands. NO3- concentrations in Chalk groundwaters often exceed 50 mg L-1, indicating that VOL. 41, NO. 6, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 3. Conceptual model of groundwater flow in west Norfolk as implied by groundwater chemistry illustrated along the section A-A′ (Figure 1).
TABLE 2. Concentrations of Noble Gases Measured in Groundwater Samples from the Sands Aquifer and the Parameters Derived through Fitting the CE Model to These Values (Sample Site Locations Are Shown in Figure 1) noble gas concentrations (cc STP g-1)
CE-modeled results NGT (°C)
Ae (× 10-3) (cc STP g-1)
Ne (× 10-7)
Ar (× 10-4)
Xe (× 10-8)
21 39 46a
2.46 ( 0.32 2.53 ( 0.34 2.31 ( 0.15
3.75 ( 0.21 4.00 ( 0.22 4.19 ( 0.09
1.28 ( 0.04 1.31 ( 0.04 1.42 ( 0.04
unconfined Sands 11.1 ( 0.9 1.8 ( 1.5 10.4 ( 1.0 2.7 ( 1.6 7.8 ( 0.7 1.6 ( 0.7 (8.0 ( 0.9) (11.6 ( 8.2)
18 23 28
4.31 ( 0.17 4.41 ( 0.34 4.46 ( 0.38
n.d.d n.d.d 4.69 ( 0.25
1.40 ( 0.01 1.41 ( 0.04 1.48 ( 0.04
confined Sands, Type 1 10.3 ( 0.2 12.7 ( 1.0 10.2 ( 0.9 13.2 ( 1.9 8.8 ( 1.0 11.6 ( 1.8
29a
2.69 ( 0.38
4.49 ( 0.26
1.49 ( 0.04
31 40 43a
2.49 ( 0.33 c 2.62 ( 0.23
4.00 ( 0.22 4.31 ( 0.26 4.37 ( 0.11
1.38 ( 0.04 1.37 ( 0.04 1.45 ( 0.08
49
3.27 ( 0.34
4.37 ( 0.27
1.42 ( 0.15
site no.
confined Sands, Type 2 6.8 ( 0.9 3.6 ( 1.8 (7.1 ( 1.0) (9.3 ( 6.1) 8.9 ( 0.9 2.0 ( 1.6 9.5 ( 1.3 4.8 ( 3.5 7.4 ( 1.3 3.2 ( 1.2 (7.7 ( 1.4) (7.0 ( 3.2) 9.7 ( 2.6 6.6 ( 1.9
F (-)
∆Ne (%)
q (-)
Dw (m)
p (%)
0 0 0 (0.78)
24 ( 16 26 ( 17 12 ( 7 (13 ( 7)
1.09 1.13 1.07 (1.08)
0.9 1.3 0.7 (0.8)
40 86 69 (99)
115 ( 9 120 ( 17 119 ( 19
1.62 1.64 1.55
6.3 6.5 5.6
1.16 (1.18) 1.09 1.23 1.14 (1.17) 1.31
1.6 (1.8) 0.9 2.3 1.4 (1.6) 3.1
0 0 0 0 (0.49) 0 0 0 (0.44) 0
29 ( 18 (30 ( 18) 22 ( 16 43 ( 19 c 27 ( 11 (27 ( 11) 62 ( 17
b b 12 83 (99) 58 b 83 (99) 64
Alternative model solutions are given in brackets for sites where sensitivity analysis indicated that solutions with F ) 0 did not correspond with maximum p values. b No assessment of p is possible for these samples as there are insufficient degrees of freedom. c ∆Ne for site 40 is determined using CNe and C*Ne back-calculated using the T and Ae values determined by fitting the Ar and Xe concentrations with the CE model. d n.d. ) not determined. a
water quality in the aquifer is being adversely affected by recent agricultural practice. Stable isotope analyses showed that all the groundwaters sampled in west Norfolk are of modern, meteoric origin. Even in the confined aquifer, the most depleted δ18O value measured was -7.63‰ VSMOW, consistent with other modern groundwaters in eastern England (27) and more enriched than the -7.8 to -7.9‰ VSMOW values that are characteristic of paleowaters elsewhere in Norfolk (28) and the UK (29). Combined, the chemical data were used to construct a conceptual model of groundwater flow in the region (30), the main features of which are shown in Figure 3. Noble gas data are interpreted in the context of this model. Noble Gas Results and Model Fitting. Measured Ne, Ar, and Xe concentrations are presented in Table 2. Noble gas 1952
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temperatures and excess air concentrations were calculated by fitting the Closed-system Equilibration (CE) model (31) to the observed data using the inverse modeling computer routine, Noble90 (32). The CE model describes the dissolved concentration of gas i (Ci) as follows:
Ci(T, S, P, Ae, F) ) C/i (T, S, P) +
(1 - F)Aezi 1 + FAezi/C/i
(1)
where C/i is the moist air solubility equilibrium concentration of gas i as a function of system temperature (T), groundwater salinity (S), and atmospheric pressure (P), Ae is the concentration of dry air initially trapped in the saturated zone, F is the fractionation factor (0 ) total dissolution of Ae, 1 ) no excess air), and zi is the atmospheric abundance ratio of gas i. The results of the modeling are given in Table 2.
To increase the number of degrees of freedom available during modeling, P and S were given assumed values because the average atmospheric pressure in the study area is known (P ) 0.99 atm) and the sampled groundwaters are recharged only by rainfall (S ) 0.0 ‰). F was also fixed at 0 during initial model fitting. The goodness of fit of modeled data to experimental data is assessed internally by Noble90 using a χ2 test (16). The results of the modeling given in Table 2 show that where sufficient free parameters are available to carry out the χ2 test, modeled solutions are acceptable at the standard 5% confidence level (16). The sensitivity of modeled solutions to F was examined by modeling the data using different assumed F values. For most samples p decreases with increasing F, from a maximum at F ) 0. However, in the analyses from sites 29, 43, and 46, p maxima are encountered at higher F values (Table 2). Although there is uncertainty in the interpretation of F and Ae in the groundwaters, mainly due to the low precision of the analyses, T and ∆Ne (the neon excess, ∆Ne ) [(CNe/C/Ne) - 1] × 100%) vary negligibly with F, except where F approaches 1 and p < 5% (see Supporting Information for further details). Calculated NGTs in all water types agree within error with the 20-year mean annual air temperature in the study area of 9.8 ( 1.4 °C and are within the 9-12 °C range typical for modern groundwaters in the UK (4, 33). Therefore, both the stable isotope and NGT data are in agreement that the groundwater is modern indicating that the confined Sands aquifer is actively flushed. The most obvious pattern in the noble gas data is in the excess air parameter ∆Ne. Unconfined Sands groundwaters have low excess air concentrations (∆Ne ) 12-26%), Type 2 confined groundwaters typically have higher concentrations (∆Ne ) 22-62%) and Type 1 confined groundwaters have very high concentrations (∆Ne ) 115-120%). Groundwaters recharged in the same area should have similar excess air concentrations because the water table fluctuations leading to the entrapment of excess air will be of a fairly consistent magnitude. The unconfined Sands groundwaters and Type 1 confined Sands waters must therefore be recharged in different areas as indicated in the conceptual model. The intermediate ∆Ne values in Type 2 groundwaters could indicate that this type is a mixture between unconfined Sands groundwaters and Type 1 waters. This seems unlikely given the low Cl- concentration of Type 2 water in relation to the unconfined waters (Table 1) and also the groundwater flow directions indicated by the groundwater head gradients. Thus, the excess air data confirm that the confined Sands are recharged along two discrete pathways, giving rise to the two hydrochemical types observed. Excess Air and Water Table Fluctuation. The relationship between ∆Ne and water table fluctuation was investigated by comparing measured ∆Ne with water table fluctuations in the recharge areas calculated using borehole water level records. Comparison of this nature is appropriate because the stable isotope and NGT data presented above indicate that the groundwaters sampled in west Norfolk are modern such that the water masses sampled are representative of recharge during the measurement period. Monthly records of water levels in observation boreholes across west Norfolk were obtained from the Environment Agency and mean annual water level fluctuations (∆hav) were calculated for each site based upon at least 10 years of data (see Supporting Information). The geographical distribution of ∆hav is illustrated using a number of representative sites (Figure 2) that are at least 2 km from the nearest municipal water supply sources in the Chalk such that the range of fluctuations reported should reflect the response to modern groundwater recharge with little artificial influence. Groundwater levels in the region fluctuate with annual frequency and are typically highest between January and March and lowest between
FIGURE 4. ∆Ne plotted against ∆hav for Sands groundwater types. The parameters are well correlated, confirming the importance of hydrostatic overpressure in the entrainment of excess air, and show good agreement with the theoretical relationship derived from the CE model (see text). September and November. In the unconfined Sands, ∆hav varies between 0.32 and 1.26 m (mean ) 0.83 m) whereas in the Chalk ∆hav is greater, between 1.23 and 9.23 m (mean ) 4.54 m). The difference in ∆hav between the Chalk and unconfined Sands is due to the difference in the specific yield (Sy) of the aquifers. The fissured Chalk in the study area has a very low Sy (0.011, 34) so large changes in the water table occur following winter recharge. ∆hav in the Chalk also tends to increase with elevation, being greater in interfluvial areas and lower in valley locations. In the Sands, Sy is greater (0.15 ( 0.05, 35) meaning that the response of the aquifer to recharge is more subdued. The recharge areas of the confined Sands groundwaters can be constrained from their geographical occurrence and the conceptual model. Type 1 occurs north of the River Babingley and is recharged from the Chalk where the Red Chalk is present. Here, ∆hav varies between 4.4 and 6.9 m. Conversely, in the area around the incised buried valley where Type 2 is recharged, ∆hav is lower, 1.9-3.0 m, due to the low-lying valley location. In the unconfined Sands, the range of ∆hav observed in the aquifer as a whole is used for comparison with measured ∆Ne since the range in ∆hav is small. A good correlation is seen between ∆hav and ∆Ne (Figure 4). This demonstrates that excess air entrainment and water table fluctuations in the recharge area are closely linked and explains why there is such a difference in ∆Ne between groundwater of Type 1 and those from the unconfined Sands. The correlation between ∆hav and ∆Ne suggests that previously recognized differences in ∆Ne between limestone and sandstone aquifers are likely to be related to the Sy of the aquifers and not strictly the lithology as previously thought (36). The CE model is able to describe the theoretical relationship between excess air concentrations and water table fluctuations (20). The model assumes that air bubbles are trapped in pore spaces as the water table rises during recharge periods and that it is the hydrostatic pressure (Ph) exerted by the depth of water above the trapped bubbles (Dw) that acts to dissolve the trapped gas. Although very small trapped bubbles can dissolve spontaneously due to surface tension VOL. 41, NO. 6, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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forces (i.e., irrespective of Ph), creating significant amounts of unfractionated excess air (20), experimental work has shown that immobile interstitial water held in the smallest pores of sediments prevents such small bubbles being trapped (17). The derivation of Dw is presented in the Supporting Information and is calculated from
Dw )
(P - e)(q - 1) Fg
(2)
where P is the atmospheric pressure, e is the saturation water vapor pressure, F is the density of water, and g is the acceleration due to gravity. The product Fg is equal to 0.0968 atm m-1 at 10 °C. The parameter q is a measure of the overpressure exerted upon the trapped bubbles that acts to dissolve the trapped gas and can be calculated from (20)
q)
[ ]
∑z i
zi 1 + Ae C/i
i
zi
(3)
1 + FAe C/i
where q is expressed as the summation of the partial pressures of all dissolved atmospheric gases (mostly N2, O2, and Ar). The value of q is determined following fitting eq 1 to measured noble gas concentrations. It has been shown using eq 3 that ∆Ne and q are well correlated, having an approximately linear relationship almost independent of other parameters (20). Theoretical relationships between ∆Ne and Dw calculated using eqs 2 and 3 are illustrated in Figure 4 assuming that Dw is directly equivalent to ∆hav. Good agreement is seen between the calculated relationship and the observed correlation. These results indicate that hydrostatic pressure is an important factor governing excess air generation under natural conditions, supporting the conclusions of column experiments and kinetic modeling (17, 37). The good agreement between theoretical and observed relationships implies that the process of excess air entrainment under natural conditions is more closely approximated by flow-through column experiments than by water level fluctuation experiments, in which consistently lower ∆Ne concentrations were found despite Dw being the same (17). Mechanistically, this suggests that excess air accumulates over time as water moves through the part of the saturated zone containing entrapped air and not through instantaneous bubble dissolution in response to the applied hydrostatic pressure. Excess Air as an Indicator of Recharge Provenance and Rate. The relationship between ∆hav and ∆Ne illustrated in Figure 4 suggests that concentrations of dissolved atmospheric noble gases can be used to determine ∆hav for the time and in the location that the sampled groundwater was recharged. ∆hav determined in this way could be used to link a sampled groundwater with a specific recharge area if the hydrometric conditions in the recharge area are well-known. However, the use of excess air to aid recharge provenance identification is probably limited to hydrogeological situations similar to west Norfolk where recharge areas with different specific yields have been shown to derive groundwaters with significantly different ∆Ne concentrations. This application shows that dissolved atmospheric noble gases can be usefully applied as tracers in young groundwaters in contrast to their traditional use in paleoclimate studies. Excess air concentrations may also be able to be applied as a direct indicator of long-term average net annual groundwater recharge. Using a modification of the borehole 1954
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hydrograph method where net annual recharge, R, is equal to the product ∆hSy (38) it may be possible to calculate longterm average R (Rav) from Dw if the specific yield of an aquifer is known
Rav ) DwSy
(4)
The precision with which annual recharge quantities could be determined using this relationship should consider the period over which the dissolved gases record the average ∆h. Smoothing of the NGT record due to hydrodynamic dispersion, mixing, and the rate at which groundwater moves away from the water table removes a significant amount of the high-frequency climatic variation visible in other climate proxies (3) so it seems likely that such an effect will limit the resolution of past recharge determination from excess air. A constraint on the resolution of ∆h or Dw determined using the model is the analytical precision. Theoretically, a change in ∆h of
