Snowmelt processes result in diel fluctuations in streamflow and stream stage that propagate into riparian aquifers and cause a daily pumping of the hyporheic zone. This diel pumping was observed in stream stage and water table records collected in Tuolumne Meadows, Yosemite National Park, California. A model was developed using Fourier analysis to represent the stream stage fluctuations and a solution to the 1-D, linearized Boussinesq equation for groundwater flow. The modeling demonstrates that a substantial volume of water is pumped in and out of the aquifer via this process on a daily basis. In addition, since the snowmelt-induced groundwater fluctuations exhibit both reduced amplitudes and increased time lags at distances away from the stream, the model can be used to estimate the hydraulic parameters of the riparian aquifer. Snowmelt-induced hyporheic pumping may have implications for biogeochemical processes in the hyporheic zone and may provide important ecosystem services related to water filtration, thermal buffering, nutrient cycling, and water quality. Consideration should be given to recognizing, quantifying, and monitoring snowmelt-induced pumping of the hyporheic zone and the ecosystem services it provides since climate and land use changes may alter the magnitude of this process in the future.
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 The daily pattern of solar radiation causes temporal variation in snowmelt, which peaks in the afternoon and reaches a minimum just before dawn. This results in diel patterns of streamflow that have a 24 h period, which are common in regions with snowmelt-dominated hydrology [Caine, 1992; Lundquist and Cayan, 2002]. In this study, snowmelt-induced hydrologic exchange processes between mountain streams and connected riparian aquifers were observed in the field and quantified through modeling. Diel snowmelt-induced variations in streamflow cause the stream stage to rise and fall over a 24 h period. This induces flow into the riparian aquifer during periods of high stage and results in drainage of the aquifer toward the stream during periods of low stage.
 In coastal environments, tidal influences also result in periodic fluctuations of seas and estuaries. For decades, the effects of fluctuating surface water levels on coastal aquifers have been well studied and have been shown to result in predictable hydrologic exchange between groundwater in coastal aquifers and connected surface water bodies [Jacob, 1950; Dominick et al., 1971; Parlange et al., 1984; Nielsen., 1990; Townley, 1995; Li and Jiao, 2002, 2003a, 2003b; Li et al., 2006; Kim et al., 2007; Rotzoll et al., 2008]. The propagation of snowmelt-induced stream stage fluctuations into alluvial aquifers is analogous to the propagation of tidal-induced fluctuations into coastal aquifers, and this extensive body of literature can be used to help understand snowmelt-induced pumping of the hyporheic zone.
 The purpose of this paper is (1) to present data showing that snowmelt-induced stream stage fluctuations result in diel pumping of a meadow aquifer in the Sierra Nevada, California, (2) to develop a model describing the propagation of irregular stage fluctuations into riparian groundwater systems, (3) to quantify the magnitude of this exchange process, and (4) to discuss potential implications of this relatively undocumented hydrologic process.
2. Snowmelt-Induced Fluctuation Data
2.1. Site Description
 Tuolumne Meadows, located in Yosemite National Park, California, is one of the largest high-elevation meadow systems in the Sierra Nevada. The Tuolumne River runs through the meadow, draining a 237 km2 watershed, which ranges from the meadow elevation of 2600 m to mountain peaks reaching 4000 m. The geology of the watershed is characterized by intrusive bedrock (predominantly granodiorite), thin soils, and late Pleistocene glacial moraines and outwash deposits [Huber, 1987, 1990]. The watershed receives approximately 100 cm of precipitation annually, the vast majority of which occurs as snowfall between November and March. The system has characteristic snowmelt-dominated hydrology, which is driven by the spring snowmelt, and thus peak stream discharge typically occurs in May or June.
 Tuolumne Meadows itself has an area of approximately 2 km2, the meadow length is ∼4 km, and the meadow system has an average width of about 400 m. Both the meadow aquifer and streambed sediments consist of coarse-grained sand and gravel that have been deposited by the Tuolumne River. Particle size analysis shows that most of the aquifer grains are within the range of 1–10 mm in size. National Park Service records of test well drilling adjacent to Tuolumne Meadows found soil depths of 2.4–2.7 m consisting of tan to reddish soil with gravel and boulders underlain by solid granodiorite. The depth of the alluvial aquifer within the meadow itself is not known with certainty; however, drive point piezometers have been installed to depths of 3 m in the meadow. We will assume an average thickness of 5 m.
2.2. Data Set
 Two stage recorders (Solinst pressure transducers) were installed in the Tuolumne River where it flows through Tuolumne Meadows in Yosemite National Park. The barometric pressure was subtracted from the absolute pressure recorded by the pressure transducer so that the height of water above the sensor could be monitored. These stream stage records show pronounced diel fluctuations caused by snowmelt (Figure 1).
 Three piezometers were installed in the alluvial aquifer adjacent to the channel by hand augering through the sand and gravel sediments to a depth of approximately 1.5 m. The locations of piezometers A, B, and C are shown in Figure 2 and are approximately 17, 52, and 100 m from the bank of the Tuolumne River, respectively. These wells were equipped with pressure transducers (Hobo) for a portion of the summer of 2007 to determine the extent to which the diel fluctuations of stream stage propagated into the aquifer. The records were corrected for changes in barometric pressure, and the deviations of the water table position from the mean over the analysis period are plotted in Figure 3 for all three piezometers and for the average of the two stream stage records.
3. Modeling and Analysis
3.1. Analytical Model of Periodic Water Table Fluctuations
 The Boussinesq equation governs the transient groundwater flow in an unconfined aquifer. If the change in water table position is small compared to the saturated thickness of the aquifer [Smith, 2008], then a linearized form of the one-dimensional groundwater flow equation can be written as
where SY is the specific yield (dimensionless), h is the hydraulic head [L], T is the transmissivity [L2/T], x is the distance from the stream boundary [L], w is a source/sink term [L/T], and t is time [T]. Because of the linearity of equation (1), solutions can be obtained individually for distinct hydrologic processes (i.e., recharge, drainage, stream stage fluctuations, and pumping) and then superimposed to describe overall hydrologic behavior. In our case, we are only interested in hydrologic phenomena associated with stream stage fluctuations, and other processes (including sources and sinks) are neglected. The boundary conditions for the system considered here include a fluctuating stream stage, which represents the water table position at the stream bank and can be expressed as a periodic fluctuation about the detrended stream stage (hfluc):
where Aj, ωj, and αj are the amplitude, angular velocity, and phase angles of a Fourier series, respectively. The other boundary condition is
where L is the half width of the riparian zone, or the distance between the stream and the boundary of the riparian aquifer, which is taken as the edge of the meadow.
 Since the boundary condition is periodic, there is no well-defined initial condition. In practice, a warm-up period should be simulated prior to the period of interest so that the analysis period is not affected by the transition from one period to the following (identical) one. This practice is particularly important if the magnitudes or shapes of diel fluctuations at the beginning and end of the analysis period differ significantly from each other.
This solution describes the propagation in space and time of snowmelt-induced water table fluctuations through a riparian aquifer. This solution assumes (1) homogenous hydraulic properties; (2) no transmission losses across the streambed interface; (3) a linear stream adjacent to an aquifer of half width, L; (4) a no-flow boundary at L, which is preserved by an image stream at 2L; (5) a horizontal aquifer base; (6) isothermal conditions; and (7) small water table fluctuations relative to the saturated thickness of the aquifer. This solution only describes the component of groundwater flow due to stream stage fluctuations; additional terms would have to be added to account for sources or sinks to the aquifer other than exchange with the stream [Montalto et al., 2007].
 The deviation in water stored due to snowmelt-induced fluctuations (ΔS) per unit width of riparian aquifer (0 < x < L) is
The change in storage due to stream stage fluctuations over a diel cycle can be calculated as the maximum of S minus the minimum of S during that period. The flux of water (F) to (positive value) or from (negative value) the stream per unit width of aquifer due to snowmelt-induced pumping is given by
3.2. Data Processing Procedures
 During this analysis, a 15 day period from 2 July 2007 (Julian day 184) to 17 July 2007 (Julian day 199) was simulated. The first half of this period was used to spin up the model, and only results from the analysis period (Julian days 192–199) are shown. First, the mean stream stage for the period was subtracted to produce a record of the deviation from the mean (Figure 3). After the records from the stream stage recorders, which are at different elevations along the stream, were converted to deviation from the mean, they were then averaged to produce a representative stream stage record. This record was then detrended using linear regression to isolate only the hydrologic process associated with diel stream stage fluctuations and not long-term hydrologic processes. A Fourier analysis was then performed to determine coefficients Aj, ωj, and αj to represent the time series for the boundary condition, which can be reconstructed with equation (2) (where j is determined by the number of data points in the record). The water table fluctuations recorded at the three piezometers were detrended using the same procedure.
 The model was then run using a range of SY and T values in order to determine the combination of parameter values that produced the best fit between the modeled and observed water table fluctuations. Given that the aquifer consists of coarse sand and gravel and is likely a few meters thick, the range of SY values considered was 0.1–0.45, and the range of T values was 500–12,000 m2/d. The root-mean-square error (RMSE) was used as a measure of goodness of fit both for each piezometer individually and as an equally weighted mean of the three observation locations. Once the best fit parameter values were determined, equations (5) and (6) were evaluated through numerical integration and differentiation of equation (4) to determine the change in groundwater storage in the riparian zone and the flux rate between the aquifer and the stream associated with this process.
Figure 1 shows snowmelt-induced diel stream stage fluctuations at two stream cross sections along the meadow for 2007. The shapes of the fluctuations are similar at the two sites; however, the magnitude is slightly greater at stream stage 1. The difference in magnitude is caused by differences in the channel morphology, slope, and channel roughness. The stage of each pool and riffle will respond slightly differently to the same diel variation in streamflow; however, the average of these two records is considered representative of the reach. The magnitude of these fluctuations peaks in the late spring but continues throughout the summer because of melting of permanent snowfields and glaciers. Figure 3 shows the propagation of stream stage fluctuations into the riparian aquifer. These water table fluctuations exhibit both reduced amplitudes and increased time lags at greater distances away from the stream. Figures 4a–4d are contour plots of the RMSE function for piezometers A, B, and C and an equally weighted mean of all three piezometers, respectively. Inspection of these contour plots and equation (1) reveals that a unique parameter set cannot be obtained; rather only the ratio of T and SY (the hydraulic diffusivity) can be determined. On the contour plots, this minimum ratio of T and SY occurs along the axis of the valleys, and it is clear that analysis of each well individually would result in different best fit parameter estimates. We choose to use an equally weighted mean of RMSE from all three peizometers (Figure 4d) to determine the optimal parameter set, though other weighting schemes may be necessary for other cases. However, since there is not a unique solution, either SY or T needs to be known. Since SY varies over a much smaller range for a given sediment texture than does transmissivity, we choose to assume a reasonable value of 0.30 based on typical hydrologic properties for clean sand and gravel [Carsel and Parrish, 1988; Loheide et al., 2005; Johnson, 1967]. Once a value of SY is known, the optimal transmissivity can be determined by locating the minimum on a graph of the root-mean-square error versus transmissivity. As shown in Figure 5, the optimal value is well constrained; if only record A, B, or C were available, the best fit value of T would be 1500, 4500, or 3000 m2/d, respectively. Given a value of SY = 0.30, the optimal estimate of T using all records was determined to be 3500 m2/d. This value is reasonable for a relatively thin sand and gravel alluvial aquifer; using an assumed thickness of 5 m, this corresponds to a hydraulic conductivity of 700 m/d. According to relationships between hydraulic conductivity and mean grain size given by Shepherd  for channel deposits, this corresponds to a mean grain size of ∼3 mm, which is consistent with the range of meadow sediment sizes observed in the field, where the median observed particle size fell between 2.4 and 4.8 mm.
 Given the optimal parameter values, the best fit modeled water table fluctuations are compared to the observed water table fluctuations in Figure 6. To avoid overlap of the graphs of this data, arbitrary offset values of 0.20, 0.15, 0.10, and 0.05 m were added to the deviation from mean stream stage and water table records for wells A, B, and C, respectively. The root-mean-square errors for sites A, B, and C are 2.8, 2.2, and 3.1 mm, respectively. The match between the observations and the model are quite good and represent the salient features of this process. In particular, the model and observations show (1) that the amplitude of the diel fluctuation is attenuated as the distance from the stream increases and (2) that the time of maximum and minimum water levels occurs at slightly later times as the distance from the river increases.
Figure 7 shows the deviations in water table position which occur as a result of stream stage fluctuations. The curves represent snapshots in time at 0.4 day (9.6 h) intervals from day 192 through day 199. As a whole, the curves show maximum variability near the stream (x = 0) with significant attenuation of the water table fluctuations within the first 200 m. Therefore, the majority of the change in storage within the aquifer occurs within 200 m of the stream.
 The change in the volume of water stored per unit length of stream in the aquifer on one side of the channel relative to the mean detrended water table position (i.e., the exchange due to snowmelt-induced hyporheic pumping) is obtained through integration of curves such as those shown in Figure 7, which are then multiplied by the specific yield as shown in equation (5). The resulting time series of aquifer storage over the analysis period is shown in Figure 8. The case discussed here is for exchange along a neutral stream; however, it is important to note that the actual exchange could be much less if the stream is strongly gaining or losing. Assuming neither gaining nor losing conditions, it is evident that between 0.2 and 0.5 m3 of water is exchanged each day on each side of the channel per meter length of stream. The mean streamflow during this period was ∼70,000 m3/d. Given the approximately 4000 m length of Tuolumne Meadows, the volume of water exchanged on both sides of the channel for a day during this period is approximately 1600–4000 m3/d. This indicates that approximately 2–6% of the water flowing through Tuolumne Meadows experiences a subsurface flow path due to snowmelt-induced hyporheic pumping. As can be seen by the amplitude of stream stage fluctuations during peak snowmelt (days 115–155 in Figure 2), the process is of much greater magnitude at peak snowmelt. However, since streamflow is also greater, the relative importance is actually less. Given (1) the many tens of kilometers of meadow along the Lyell Fork and the Dana Fork of the Tuolumne as well as other tributaries and (2) the persistence of diel snowmelt-induced stage fluctuations during the times of the year when most runoff occurs, it is likely that a significant fraction of water leaving this watershed has experienced a subsurface flow path due to snowmelt-induced hyporheic pumping.
5. Conclusions: Potential Significance of Snowmelt-Induced Hyporheic Exchange
 In systems with snowmelt-dominated hydrology, including the mountain meadow system studied here, the diel snowmelt pattern creates fluctuations in stream discharge that propagate from the stream into the meadow aquifer (Figures 3 and 6). Higher stream stage during the late evening [Lundquist et al., 2005], resulting from snowmelt, promotes the flow of stream water into the meadow aquifer; conversely, lower stream stage during the late morning promotes drainage of groundwater from the meadow sediments toward the stream. Until now, this diel snowmelt-induced hyporheic pumping remained an unexplored topic in meadow hydroecology, although a similar mechanism has been identified as an important process in tidal wetlands [Ursino et al., 2004; Wilson and Gardner, 2006; Montalto et al., 2007]. This process may be critical in filtering sediment from the stream water, cycling nutrients in the aquatic ecosystem, and promoting biogeochemical processes in the hyporheic zone. Through the development and application of a model describing this mechanism, we were able to estimate the magnitude of this exchange process.
 This model draws on classic literature investigating the effects of tidal fluctuations in coastal aquifers and demonstrates the novel application of this approach to snowmelt-induced diel fluctuations in mountain meadows. The sensitivity of the model to near-stream hydrologic properties indicates that there is potential to use naturally occurring periodic fluctuations to determine aquifer properties as has been done with periodic stage fluctuations in other environments [Ferris, 1952; Nevulis et al., 1989; Hsieh et al., 1987]. Exploitation of this signal to help characterize the transmissive nature of the aquifer sediments as demonstrated here has three primary benefits. First, the hydraulic test is passive, under natural gradients, and therefore does not necessitate extraction of large volumes of water that would be required for pumping tests that would be difficult to conduct in wilderness settings. Second, the spatial scale of the fluctuations samples a large volume of the aquifer, providing much larger scale estimates of transmissivity than could be obtained with slug tests. Third, the snowmelt-induced fluctuations cause flow between the stream and the aquifer and therefore provide information on the flow paths that are most important for understanding stream-aquifer interactions. A limitation of this methodology is that only the ratio of transmissivity to the specific yield (the hydraulic diffusivity) can be determined. In order to determine the transmissivity, we assumed a specific yield of 0.3; however, if this estimate of specific yield was either high or low by 0.15, the estimate of transmissivity would be higher or lower by 50% (Figure 4).
 The observational field data collected at Tuolumne Meadows and the model developed in this study present a fundamental understanding of the diel pumping of water across the stream sediment interface resulting from snowmelt-induced streamflow variations. These regular fluctuations result in daily exchange and mixing of surface and subsurface waters in the hyporheic zone that may facilitate many biogeochemical processes important to the aquatic ecosystem. Diel fluctuations in trace metals, for example, have been observed in many mountain streams [Nimick et al., 2005], which may be due to light-sensitive Fe redox reactions [McKnight et al., 1988; McKnight and Bencala, 1989; Sullivan et al., 1998; McKnight et al., 2001], temperature-induced changes in sorption to solid phases [Gammons et al., 2005], diel pH variation induced changes in adsorption and desorption [Fuller and Davis, 1989], and photosynthesis- and respiration-induced variations in dissolved oxygen and pH [Brick and Moore, 1996]. Some of the streams studied have observed diel fluctuations in streamflow, and the others at least have potential variation in hyporheic exchange [Brick and Moore, 1996]. Therefore, diel pumping of the hyporheic zone may also play a role in some cases where diel variations in aqueous stream chemistry are observed.
 The daily pumping of the hyporheic zone induced by diel fluctuations in snowmelt may provide an ecosystem service by playing a role in water filtration. About 40 km downstream of Tuolumne Meadows, the flow of the Tuolumne River is captured in the Hetch Hetchy Reservoir, which was created by the construction of O'Shaughnessy Dam. The reservoir supplies ∼0.8 × 106 m3 (∼220 × 106 gallons) per year of high-quality water to the San Francisco Bay area. It is the sixth largest municipal water system in the country and one of the few that has a filtration exemption because of the high water quality (B. McGurk, Hetch Hetchy Water and Power, personal communication, 2008). Future research is needed to determine whether, and to what extent, snowmelt-induced hyporheic pumping may provide an ecosystem service that contributes to the high water quality of these systems. This exchange process could potentially play a role in filtering suspended solids from the water and in providing geochemical heterogeneity that promotes degradation and transformation of some dissolved constituents.
 Processes that change the channel morphology and roughness may also affect the magnitude of hyporheic pumping. For example, overgrazing has long been recognized as a cause of stream widening [Trimble and Mendel, 1995], which would cause a smaller-amplitude fluctuation in stream stage for a given diel cycle of stream discharge. The result would be a decrease in the volume of water pumped through the hyporheic zone. On the other hand, narrowing the channel or increasing the roughness of the channel will result in larger-amplitude fluctuations in stream stage for a given diel cycle of stream discharge. Therefore, land managers should consider the impact that land use changes and stream restoration practices that change channel morphology and/or roughness might have on snowmelt-induced hyporheic pumping. In cases where this ecosystem service is impaired, it could be possible to simulate diurnal fluctuations in river stage and enhanced mixing in the hyporheic zone through periodic releases or peaking operations from reservoirs, as observed by Arntzen et al.  and Curry et al. .
 The work presented here demonstrates that snowmelt-induced diel pumping of the hyporheic zone occurs in Tuolumne Meadows, Yosemite National Park, California, and that the process can be modeled by applying techniques that have been applied to coastal aquifers that are influenced by tidal signals. This process may be significant in terms of ecosystem function and biogeochemical processes; however, currently, these potential linkages remain untested. The geographic extent over which this process is significant is unknown, as are the temporal trends in the magnitude of this process that may be driven by climate and land use changes. Further work is needed to evaluate (1) the ecosystem services provided by snowmelt-induced hyporheic pumping, (2) the extent to which this process occurs in other environments, and (3) historic changes in the magnitude of this process, as well as changes that can be expected in the future.
 This material is based upon work supported by the National Science Foundation under grant CBET-0729838. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. We would like to thank the National Park Service for allowing us to conduct this research in Yosemite National Park and for providing access to their facilities. We would also like to thank Fred Lott, David Cooper, Evan Wolf, Brian Huggett, and Jim Roche for assistance with piezometer installation and data acquisition. Finally, we would like to thank Bayani Cardenas, the associate editor, and two anonymous reviewers for their constructive comments and suggestions which improved this manuscript.