2.1. Sonde Deployment and Hydrogeological Setting
 This study was conducted in a 5 cm diameter monitoring well located at 42°18.496′N, 83°45.982′W in the unconfined upper aquifer of the Glacial Drift Aquifer in Ann Arbor, Michigan (Figure 1). The aquifer, with a saturated thickness of ∼11.2 m consists of unconsolidated sand and is bounded by a massive clay layer at the bottom. The unsaturated zone is ∼13.2 m thick and consists of an intercalation of gravel and sand layers as described in the auxiliary material of Sun et al. . The monitoring well has a total depth of 24.38 m and is screened over the lower 12.19 m [cf. Sun et al., 2008], i.e., over the entire saturated portion of the aquifer. The well was screened over the entire thickness of the aquifer to ensure that natural conditions with respect to water flow remain as undisturbed as possible, in addition to reproducing sampling conditions of typical noble gas studies. This allows for the comparison of our results with previous studies. A well that is screened throughout the entire saturated thickness of the aquifer results in some vertical mixing during noble gas sampling. However, as discussed in detail by Sun et al. , mixing is restricted to a small vertical region near the pump.
Figure 1. Location map showing the study area. The location of the study area within the 48 contiguous states of the United States is shown in the inset map in the top right (red circle), and below that the study area within the lower peninsula of the state of Michigan is also indicated. The location of the monitoring well is indicated by a red cross. Surface topography is shown as shades of gray together with equipotential lines shown as brown contours (labeled in meters). The direction of groundwater flow is indicated by dashed black lines. GIS data used to construct the map are from the Michigan State Geographic data library (http://www.mcgi.state.mi.us/mgdl/).
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 Our study site is located on the northern side of a hill whose peak lies ∼18 m above, in an extended plateau (Figure 1). In the vicinity of our well, water flows downward toward the Huron River with a NNE direction under a hydraulic gradient of 0.025. Horizontal and vertical hydraulic conductivities estimated in the upper aquifer at a site nearby are ∼5.3 × 10−4 m s−1 (model B [Cypher and Lemke, 2009]), leading to a pore velocity of 3.8 × 10−5 m s−1 (3.3 m d−1) for a porosity of 35%, a value typical of unconsolidated sand [e.g., Freeze and Cherry, 1979]. If one takes these values as representative of the average hydraulic conductivity in and around our study area, this implies that any changes of noble gas composition and other measured parameters observed within hours or a few days of a rainfall episode are mostly the result of local recharge rather than mixing with water recharged at other locations. It is possible, however, that some degree of mixing might occur. Horizontal and vertical hydraulic conductivities might present some spatial variation in the area (e.g., model C [Cypher and Lemke, 2009]). Such variability might lead to horizontal and vertical hydraulic conductivity values as high as ∼9 × 10−4 m s−1, corresponding to a pore velocity of 6.4 × 10−4 m s−1 (5.5 m d−1). In anisotropic media, horizontal and vertical hydraulic conductivities down to ∼9 × 10−5 m s−1 (horizontal pore velocity of 6.4 × 10−6 m s−1 or 0.6 m d−1) and ∼9 × 10−6 m s−1 (vertical pore velocities of 6.4 × 10−7 m s−1 or 0.06 m d−1), respectively, might be observed. However, such values are likely to be extremes.
 A YSI model 600XLM sonde, equipped with a model 6562 dissolved oxygen (DO) sensor, was deployed in the well on 29 March 2008. All times in plots for this study are relative to days after 29 March 2008. The sensor was calibrated to 100% O2 saturation using water-saturated air prior to insertion into the well. The sonde was programmed to automatically measure DO, water depth, water temperature, salinity, pH and oxidation reduction potential (ORP) every 15 min. At the time of the deployment, a Proactive model P-10330 12V DC pump was placed 0.656 m below the sonde's sensors so that water sampling could be performed while the sonde remained in place. Typically, when water was sampled for noble gas analysis, data was offloaded from the sonde using an RS-232 data link. The initial water table depth was 13.18 m from the surface, which was 0.99 m below the top of the well screen.
 Water depth data collected refers to the position of the cluster of sonde sensors relative to the water table. The sonde was held at a fixed position relative to the surface and therefore an increase in water depth at the position of the sensor corresponds to an equal rise in the water table level. Water samples were from the water inlet of the pump that was 0.656 m below the sensors. As noted by Sun et al. , there is an effective vertical mixing within the well casing. A simple flow model was developed to estimate the effective mid point water depth of a pumped water sample (see Sun et al. [2008, auxiliary material] for details). With a typical pump depth of roughly 1.5–2 m, a pumping rate of 4 L min−1 and a sampling duration of about 10 min, we estimate the effective mean depth of the water retrieved for noble gas analysis to be approximately 3.5 m.
 The sonde remained undisturbed until day 57 of the experiment (25 May 2008) when it was noticed that the depth of the sensors below the water table was approaching 1 m and it was feared that water might damage some electrical connections above the sonde and therefore the sonde was raised 0.374 m. On day 154 (30 August 2008), the sonde was removed from the well and repositioned because the water table had dropped to the point where it was feared that the sonde sensors soon might no longer be immersed in water. On that day, it was noticed that the DO sensor could no longer be calibrated to water-saturated air. Therefore, the DO sensor's membrane was replaced and the sensor was recalibrated. Following the membrane replacement, the sonde was redeployed into the well, but at a depth 0.374 m below its previous depth. We estimate that the DO data is likely only to be reliable for ∼20–30 days after the initial deployment and for a similar period after the membrane replacement. The water depth record has been corrected accordingly by removing the offsets created on days 57 and 154 so that a continuous record of water table depth variation could be deduced. However, the offsets do affect the other measured parameters, especially ORP, and this should be taken into account when interpreting results from the sensors near the times of the sonde relocations.
 It should be noted that all sensors were calibrated before deployment, but the DO sensor was the only sensor that was recalibrated during the deployment. This means that calibration drift might affect the absolute accuracy of some parameter readings, but it was decided that the highest priority was to acquire continuous data. Indeed, the absolute accuracy of the measurements is much less important in this study than detecting relative changes. On the other hand, conductivity (i.e., salinity) and depth can retain accurate readings for many months, and temperature readings cannot be recalibrated in the field (Gary Lorden at YSI, personal communication, 2011). In addition, the remarkable correlation observed between water depth and barometric pressure as shown below clearly indicates that water table variations were being properly measured by the sonde, an observation consistent with information provided to us by YSI. The main focus of the experiment was to be able to detect sampling artifacts and the effects of recharge from precipitation events. All sensors responded to both sampling and precipitation throughout the duration of the experiment and slow calibration drift would not invalidate the response time lags seen in the sonde data. In addition, recalibration would have introduced discontinuities within the sensor records that would make interpretation more difficult.
 Meteorological data was collected from the NOAA national climate data center (http://cdo.ncdc.noaa.gov/qclcd/QCLCD?prior=N) for the weather station at the Ann Arbor Municipal Airport (AAMA) so that changes within the well could be correlated with meteorological events. The AAMA data are based on local standard time while the sonde's clock was set to daylight savings time. Sonde data were time shifted by 1 h to match the times for the AAMA data. In addition, to perform data analysis for the two data sets, it was convenient to standardize the measurement times to the same values. Thus, AAMA measurement times were used as the standard, and sonde data were linearly interpolated to AAMA times using the R approx function.
 It was noticed that AAMA measured atmospheric pressure had a significant degree of correlation with the sonde depth data (Figure 2). The 600XLM sonde is equipped with a pressure compensation system that uses an air tube running from the water depth sensor to the surface that eliminates the effect of varying atmospheric pressure upon the pressure sensor that is used to estimate water depth. Despite this compensation system, depth could be seen to move in concert with changes in atmospheric pressure and the sense of the correlation is opposite to the effect one would see if the compensation system was not working correctly. The correlation coefficient between water depth and variations of atmospheric pressure about the mean was –0.2508. An air pressure increase can immediately be felt in the center of the well, and if such a pressure increase propagated instantly through the ∼13 m of sediment in the unsaturated zone, no change in water depth would occur. However, if the increase in air pressure away from the well takes much longer to reach the vicinity of the water table, there will be a drop in the water level within the well (i.e., a decrease in the depth reading). In other words, an increase in air pressure will push water out of the well casing into the surrounding saturated zone until the pressure imbalance in the unsaturated zone can be restored.
Figure 2. Raw water depth as measured by the sonde pressure sensor (dashed line) and corrected depth record offset down by 0.05 m for clarity (solid line). The corrected record was fit by the BETCO program [Toll and Rasmussen, 2007] using a 24 h maximum lag response function. Barometric pressure was from the Ann Arbor Municipal Airport (AAMA) meteorological record, and synthetic Earth tide data were estimated for the well site using the TSOFT program [Van Camp and Vauterin, 2005]. The inset shows the unit response function produced by the BETCO program.
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 This barometric effect on water head was quantitatively investigated by Rasmussen and Crawford , who set out a method for fitting a pressure response function to water head data using barometric pressure. The instantaneous response, or barometric efficiency is defined as α = − W/ B, where W and B are the water head and barometric pressure, respectively. The complete pressure response is defined as a series of α values as a function of the time lag from an instantaneous unit step function change in pressure. Toll and Rasmussen  describe a software package called BETCO that fits a step function response water to head data taking both barometric pressure and earth tide effects into account. Synthetic earth tide data for the duration of the field experiment at the well site were calculated using the TSOFT program [Van Camp and Vauterin, 2005] and this was combined with AAMA barometric pressure data as input into the BETCO program with a maximum lag time of 24 h. The results of this fit are shown in Figure 2, with both the raw and corrected water depth records plotted (the latter offset down by 0.05 m for clarity). The inset in Figure 2 shows the step function response for this site and the barometric efficiency at zero lag (i.e., α(0)) is 47%. It is possible that the ∼1–1.5 m of open screen above the water table provides a shortened pathway for air to enter the unsaturated zone near the water table, which would have the effect of muting the air pressure response within the well and thereby reducing the initial barometric efficiency.
 The step function response is typical for those shown by Rasmussen and Crawford  for unconfined aquifers. However, it should be noted that the step response function is essentially flat from 12 h to the maximum assumed lag of 24 h. This suggests that there is a long-term delay in the pressure response of the unsaturated zone to changes in atmospheric pressure. Figure 2 also shows that the Toll and Rasmussen  algorithm is very successful in removing most of the high-frequency noise seen in the water depth record.
 A portable CO2 sensor was also initially deployed with the sonde and pump stack, but contact with groundwater damaged the sensor and no useable data from it was obtained. However, Sun et al.  reported measured CO2 concentrations in air within the well near the water table on five dates from 14 July to 7 October 2007. The concentrations dropped from a high of 1.56% in summer to a low of 0.16% in the fall. Over this same period, the dissolved oxygen concentration in water at the water table ranged from 25.6% to 43.7%, which corresponds to an O2 concentration in air that ranges from 5.4% to 9.2%. Using the measured dissolved oxygen to estimate pO2 in soil gas near the water table and adding this to the CO2 concentrations, the sum of O2 and CO2 in air near the water table ranged from 6.1% to 10.0%. Given that free air has an O2 concentration of 21%, the apparent drop in the partial pressure of O2 at the water table is not completely compensated for by an equivalent rise in CO2 concentration, and Sun et al.  suggested that this was due to the high solubility of CO2 in water.
2.4. Noble Gas Analysis
 Water samples for noble gas analysis were collected in 3/8″ Cu tubes clamped at both ends and analyzed for He, Ne, Ar, Kr, and Xe isotopes at the University of Michigan using an automated noble gas extraction system connected to a MAP215 mass spectrometer which has been modified to have sufficient mass resolution for measuring 3He/4He ratios. The mass spectrometer source was operated at an electron trap current of 500 μA. Sampling and measurement procedures are those as reported by Ma et al.  with further details on noble gas procedures of Saar et al.  and Castro et al. .
 Noble gases were separated using an Air Equipped cryogenic separator, with gas release points at 35, 65, 170, 200, and 270 K for He, Ne, Ar, Kr, and Xe, respectively. The original technique described by Saar et al.  was modified such that the gas sample was inlet into the cryoseparator at a temperature of 280°K and all gases were pumped into the activated charcoal chamber as it was cooled to ∼10°K. Gases were then released as the cryoseparator was warmed through the release point of each noble gas. This modification of the earlier one documented by Saar et al.  was done to reduce the possibility of interference from one gas upon another in the trapping efficiency of the cryoseparator. With the exception of He, all other noble gas isotope ratios were identical to air within measurement precision. Noble gas volume measurements are estimated to be accurate to 1.5%, 1.3%, 1.3%, 1.5% and 2.2% for He, Ne, Ar, Kr, and Xe, respectively (1σ).