Recharge characteristics of a phreatic aquifer as determined by storage accumulation J. Neil Ketchum Jr. ´ Joseph J. Donovan William H. Avery

Abstract The cumulative storage accumulation curve (CSAC) is a tool for saturated-volume fluctuation (SVF) analysis of transient recharge to shallow phreatic aquifers discharging only to springs. The method assumes that little underflow or phreatic evapotranspiration occurs. The CSAC is a modified water-table hydrograph that distinguishes storage increase caused by recharge from loss due to springflow-induced recession. Required for the analysis are water-table fluctuations at a single representative location within the catchment of a single spring and either direct measurements or robust interpolations of springflows at different aquifer stages. The method employs empirical manipulation of head observations, varying spring catchment area to minimize CSAC water-level changes in late portions of long recessions. Results include volumetric estimates of recharge integrated over individual events and instantaneous rates of recharge to the water table, at the temporal resolution of the water-level sampling interval. The analysis may also yield physically realistic information on spring catchment and recharge focusing. In a test case in West Virginia, USA, recharge estimates by this technique were consistent with integrated springflow time series but greater than estimates based on potential evapotranspiration. Results give insight into

Received: 28 January 2000 / Accepted: 24 May 2000 Published online: 7 September 2000  Springer-Verlag 2000 J.N. Ketchum Jr. Groundwater Sciences Corporation, 2601 Market Place Street, Suite 310, Harrisburg, Pennsylvania 17110, USA J.J. Donovan ()) Department of Geology and Geography, West Virginia University, Morgantown, West Virginia 26506-6300, USA E-mail: [email protected] Fax: +1-304-2936522

dynamic recharge behavior over time as well as an indication of recharge catchment size. RØsumØ La courbe cumulative de stockage est un outil d'analyse de la fluctuation du volume de la zone saturØe en recharge transitoire de nappes peu profondes se dØchargeant uniquement par des sources. La mØthode suppose que les effets de la drainance ou de l'Øvapotranspiration sont faibles. La courbe cumulative de stockage est un hydrogramme de nappe modifiØ qui fait la distinction entre l'accroissement du stockage dß à la recharge et les pertes dues à la rØcession liØe à l'Øcoulement aux sources. Sont nØcessaires pour cette analyse les fluctuations de la nappe en un point unique reprØsentatif du bassin d'alimentation d'une source unique et soit des mesures directes soit des interpolations robustes des Øcoulements à la source pour les diffØrents Øtats de l'aquif›re. La mØthode recourt à une manipulation empirique des observations de la piØzomØtrie, faisant varier l'extension du bassin d'alimentation de la source, afin de minimiser les variations du niveau de la nappe liØes à la courbe cumulative de stockage dans les parties lointaines des longues rØcessions. Les rØsultats prennent en compte les estimations de volume de la recharge intØgrØ sur des ØvØnements individuels et sur des taux instantanØs de recharge de la nappe, pour une rØsolution temporelle de l'intervalle d'observation de la nappe. L'analyse peut aussi fournir une information physiquement rØaliste sur le bassin d'alimentation de la source et sur la concentration de la recharge. Dans un test effectuØ en Virginie occidentale (États-Unis), les estimations de la recharge par cette technique concordaient avec la chronique des dØbits de la source, mais Øtaient supØrieures à celles basØes sur l'Øvapotranspiration potentielle. Les rØsultats donnent un aperçu sur le comportement de la recharge dynamique au cours du temps aussi bien qu'une indication sur l'Øtendue de l'aire de recharge.

W.H. Avery Leggette, Brashears, and Graham, Inc., 426 Brandywine Parkway, West Chester, Pennsylvania 19380, USA

Resumen La curva acumulativa de incremento de almacenamiento (acrónimo CSAC, en inglØs) es una herramienta para analizar la fluctuación del volumen saturado debida a la recarga transitoria en acuíferos freµticos someros que descargan ‚nicamente por medio de manantiales. El mØtodo presupone que la

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DOI 10.1007/s100400000088

580

evapotranspiración desde el nivel freµtico es pequeæa. El CSAC es un hidrógrafo modificado del nivel freµtico, que permite distinguir el aumento de almacenamiento causado por la recarga de la descarga a travØs de los manantiales. El anµlisis requiere conocer las fluctuaciones del nivel freµtico en un punto representativo dentro de la cuenca de un manantial y, o bien medidas o bien interpolaciones robustas de los caudales en el manantial, en distintas zonas del acuífero. El mØtodo emplea la manipulación empírica de las medidas de nivel, modificando el µrea de la zona de captación del manantial para minimizar los cambios de nivel en la CSAC, en el tramo final de series largas de recesión. Los resultados incluyen estimaciones volumØtricas de la recarga, integrada sobre eventos individuales, y tasas de recarga instantµneas del acuífero, dentro de la resolución temporal del intervalo de medida del nivel. El anµlisis tambiØn puede proporcionar información realista de las zonas de captación y de recarga. Los valores de recarga estimados mediante esta tØcnica en un caso de Virgina Occidental (Estados Unidos) fueron coherentes con las series temporales integradas del caudal del manantial, pero superiores a las estimaciones basadas en la evapotranspiración potencial. Los resultados proporcionan información sobre la evolución temporal de la recarga, ademµs de una aproximación al tamaæo de la zona de captación. Keywords groundwater recharge/water budget ´ unconfined aquifers ´ numerical modeling ´ USA

Introduction Infiltration and Recharge Infiltration is water that seeps from the surface into the vadose zone, whereas recharge is that portion of infiltration that ultimately reaches the water table (Rushton and Ward 1979). Recharge may occur in either of two categories: rapid (ªmacroporeº) recharge, through extremely conductive vadose channels, or slow (ªmatrixº) recharge, through granular or fractured media (Stephens 1996). The rate of recharge influences both flux through and water chemistry within soils and aquifers (Wu et al. 1996). Therefore, a need exists for representative and accurate methods to describe recharge rates for aquifer management. Recharge cannot be measured directly, so its quantification is often error-prone, requiring validation by comparisons among various methods (Lerner et al. 1990). Rate estimates may be based on either hydrometeorologic, potentiometric, or surface-water flow methods (Sophocleous 1991). The most common hydrometeorological method is the fluid-mass-balance (FMB) approach (Rushton and Ward 1979), which calculates land-surface water budgets by subtracting known or estimated evapotranspiration (ET) plus runoff from precipitation. The most common potentioHydrogeology Journal (2000) 8 : 579±593

metric approach employs aquifer saturated-volume fluctuations (SVF), which involves relation of watertable fluctuations to recharge (van Tonder and Kirchner 1990; Sophocleous 1991). Flow-based estimates commonly employ integral hydrograph separation (IHS) of streamflow or springflow time series. All these methods focus on different perspectives of the groundwater flow system, as shown in Fig. 1. FMB methods rely exclusively on surface estimates of ET, precipitation, and runoff, and in this way are ªinfiltration coupled.º IHS techniques, on the other hand (Fig. 1), rely solely on baseflow or springflow measurements and thus are ªdischarge coupled.º SVF methods, in contrast to FMB and IHS, are coupled to infiltration processes in the overlying vadose zone (a source of storage increase), as well as to downgradient discharge processes (a cause of storage decline). Therefore, SVF is in principle a robust analysis. These methods have different sources and magnitudes of error. FMB is generally based on calculated values of potential evapotranspiration that frequently overestimate the actual value and underestimate recharge (Lerner et al. 1990). Calculated recharge by SVF requires an independent estimation of specific yield, as well as several assumptions regarding aquifer recession characteristics (Sophocleous 1991); both may be subject to significant errors. IHS hydrograph methods may be based on sparse or inaccurate flow measurements and involve subjectivity in the separation of runoff from baseflow, apportionment of flow across surface-water divides, and quantification of underflow (Rutledge and Daniel 1994). Water-table fluctuations in shallow aquifers are easily measured with high accuracy. The water table is both infiltration- and discharge-coupled, giving its measurement the potential to yield robust recharge estimates. However, discharge coupling carries with it the necessity (and difficulty) of quantifying aquifer recession during and following recharge events. That is, storage may tend to decline due to aquifer discharge at the same time that it is increasing due to arrival of recharge at the water table. This storage loss must in general be compensated to allow recharge estimates by SVF. Figure 2 shows a typical SVF well hydrograph for a phreatic aquifer receiving recharge. A characteristic time lag occurs between initial and maximum storage increase induced by recharge. This time lag is quite brief for macropore recharge but may be extended (days to months) for matrix recharge, depending on vadose-zone characteristics, depth to water table, and other factors (Stephens 1996). Stage recession prior to and during recharge-induced storage increase is frequently exponential, similar to flow recession in streams, and is caused by diminishing baseflow discharge as the water table declines. The portion of the hydrograph that represents recharge is the time-integration between the head following onset of recharge and the recession projected from antecedent values DOI 10.1007/s100400000088

581 Fig. 1 Approaches to recharge estimation in phreatic aquifers

Fig. 2 Water-level fluctuations in response to infiltration of precipitation, showing time lag between initial and maximum storage increase and projected stage recession

prior to recharge (Fig. 2; Meyboom 1961). Therefore, a model to infer recharge rates from SVF storage observations must consider head changes caused by recession as well as those induced by infiltration.

Purpose and Approach The purpose of this research is to develop and test a technique to quantify recharge for shallow phreatic aquifers drained by springs alone. The proposed method employs a hybrid SVF±IHS approach that is both infiltration- and discharge-coupled (Fig. 1). Using cross-correlation between aquifer heads and springflows, spring discharge is calculated continuously to estimate storage losses and applied in a SVF analysis, similar to methods described by van Tonder and Kirchner (1990). Many have noted a correlation Hydrogeology Journal (2000) 8 : 579±593

between groundwater storage and springflow (Freeze 1969). Bredenkamp et al. (1995) observed that even in hydrologically complex dolomitic aquifers, the relationship between stage and springflow is approximately linear. The proposed SVF approach would be generally applicable to unconfined aquifers, including those discharging to stream baseflow; however, the relationship between spring discharge and aquifer storage is more tractable than that between stream discharge and aquifer storage. Therefore, this analysis is restricted in the present discussion to above-drainage aquifers with negligible underflow. To demonstrate the application of the technique, two shallow unconfined aquifers were selected as a case study. Both aquifers occur well above stream base level and discharge primarily by springflow, i.e., underflow is negligible. Both aquifers are formed by waste rock from a mine, or ªspoil,º which is heterogeDOI 10.1007/s100400000088

582

Fig. 3 Groundwater conditions in a typical heterogeneous minespoil aquifer

neous-sized fill emplaced over a shale aquitard following mining. Aquifers of this hydrogeological setting, for which a typical example is shown in Fig. 3, display several characteristics that are useful for examination of recharge processes. First, infiltration is the only source of recharge, as neither aquifers nor streams occur upgradient. Second, aquifer-margin springs constitute the only significant discharge. Because such aquifers are extremely heterogeneous, with coarse highly permeable zones as well as finer materials, both macropore and matrix recharge types are observed. For this reason, recharge rates are generally greater for such aquifers than for most natural aquifers. Their spring discharges are also closely coupled to aquifer stage, and this correlation may be quantified, using changes in aquifer stage measured in wells (Avery et al. 1999). The approach applied to this area included: (1) collection of data describing hydrometeorology, SVF fluctuations at the water table, and spring discharges; (2) quantification of discharge-stage correlation; and (3) estimation of recharge by storage accumulation analysis, for comparison with conventional FMB and IHS estimates.

Estimation of Recharge Storage Accumulation Method The rapidity and magnitude of storage increase at the water table may be used to estimate recharge rates (Besbes and de Marsily 1984). Such calculations require the magnitude of storage increase associated with individual events, as well as estimates of specific yield (Sy). As an example, Sophocleous (1985) used a numerical soil-water flow model to simulate the filling of a ªclosed-endº soil column by infiltration. The model was only infiltration-coupled, because no outflows occurred; therefore, storage gradually accumulated in the column and measurement of this rate constitutes a recharge measurement. Figure 4 shows results from his model. Sophocleous estimated timevariable recharge rate directly from the storage accumulation using a specific-yield parameter. The storageaccumulation approach of Sophocleous is appealing because no error in storage accumulation caused by discharge occurs. For aquifers in which recessional Hydrogeology Journal (2000) 8 : 579±593

Fig. 4 Relation between time and a water-table storage accumulation and b inferred infiltration rate, for saturation of two soils during column experiments. (After Sophocleous 1985)

drainage also occurs, however, the Sophocleous technique must be modified to compensate for recession, for results similar in form to Fig. 4 to be interpreted as recharge. For a phreatic aquifer drained only by springs, a fluid mass balance may be used to describe groundwater-storage fluctuations at the water table in response to recharge and springflow-induced recession: @h R…t† ˆ @t Sy

Q…t† Sy A

…1†

where P ih/it=rate of head change at the water table (L/T) P R(t)=recharge from infiltration (L/T) P Q(t)=spring discharge flux (L3/T) P Sy=specific yield (1) P A=catchment area for spring (L2). ih/it is an instantaneous measure of the net rate of head change, with positive values indicating net recharge and negative values net recession. The partial derivative alludes to spatial variability in head. Integrating both sides with respect to time over an arbitrary time interval T yields a cumulative storage difference, which may be expressed as a uniform hydraulic head fluctuation, Dh(T), over the full area of the catchment area: DOI 10.1007/s100400000088

583

h…t†jT0 ˆ
h…T † ˆ

1 Sy

Z

T 0

R…t†@t

1 Sy A

Z

T 0

Q…t†@t

…2†

Rearranging Eq. (2), storage accumulation due to recharge over time interval T, expressed as aquifer hydraulic head, is a cumulative storage accumulation, or CSA: Z Z T 1 T R…t†@t ˆ Q…t†@t ‡ Sy
h…T † …3† CSA ˆ A 0 0 CSA is the net storage increase caused by recharge over any time interval. It is equivalent to observed storage increase caused by infiltration plus storage loss due to recession caused by springflow and/or ET. Quantification of transient recharge by storage accumulation, according to Eq. (3), requires concurrent measurement (or estimation) of both spring discharge and aquifer head. In contrast to water levels, frequent springflow measurements are commonly impractical and may require interpolation between measurement times. Avery et al. (1999) observed non-linear correlation between well stage and spring discharge for hydraulically continuous well-spring pairs in a phreatic aquifer. Discharge may be estimated from aquifer heads using a variety of models, such as power-law or exponential forms: Q…t† ˆ ah…t†b

…4†

Q…t† ˆ cedh…t†

…5†

where a, b, c, and d are model parameters. The power-law form (Eq. 4) is a log-log relationship, whereas the exponential form (Eq. 5) is semilogarithmic. Combining Eq. (5) with Eq. (3): Z 1 T dh…t† ce @t ‡ Sy
h…T † …6† CSA ˆ A 0 Using this cross-correlation between flows and heads, CSA (i.e., cumulative recharge) may by estimated from head fluctuations over any specific time interval, provided that the stage discharge function [first term

on right-hand side of Eq. (6)] and the parameters Sy and A may be reasonably estimated. As suggested by Eq. (6) and characteristic of all SVF methods, cumulative recharge estimation is linearly influenced by the catchment-area parameter, and so results are very sensitive to this value; however, the influence of the Sy estimate is multiplied by the net head difference over any time interval, which may be small over long time intervals of observation. Therefore, the Sy term in Eq. (6) may have only a minor effect on the CSA estimate, and at any rate much less than that of A. Figure 5 shows a plot of CSA versus time, a modified form of a well hydrograph that is referred to as a cumulative storage accumulation curve (CSAC). The CSAC of Fig. 5 is derived from the water-level hydrograph of Fig. 2. Long periods of exponential stage recession following recharge appear as horizontal segments (zero slope) on the optimally parameterized CSAC (horizontal ªplateausº in Fig. 5). The slope of the CSAC increases sharply immediately after the onset of recharge, declining again to a near-horizontal line after recharge arrival at the water table is complete. Appropriately fitted CSACs have a multiplestep appearance, with the rising limbs between successive ªplateausº corresponding to storage increases from individual recharge events. Storage increase is less evidently ªsteppedº on the CSAC when recharge occurs in a series of overlapping events. However, the total recharge for a discrete ªevent,º such as intense precipitation followed by dry weather, is the magnitude of associated storage accumulation between successive plateaus (expressed as cumulative water-table rise). If an estimate of Sy is available, this watertable rise may be converted to a height of water, as for any SVF method. It is possible to obtain poor CSAC fits of two general types. Consistently negative slopes during recession limbs (Fig. 5) may be obtained by (1) overestimation of the parameter A, or (2) underestimation of calculated spring discharge. Conversely, positive slopes during recessional periods (Fig. 5) suggest either underestimation of A or overestimation of spring discharge. The result is relatively insensitive to the value of the parameter Sy.

Fig. 5 Example of a cumulative storage accumulation curve (CSAC), showing periods of recession (plateaus) and storage accumulation (positive slopes), interpreted for the well hydrograph of Fig. 2

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584 Fig. 6 Example of a rate of storage accumulation curve (RSAC), showing periods of recession (zero values) and net storage accumulation (positive values)

Figure 6 shows a plot of CSAC ih/it versus time. This form of hydrograph, here referred to as a rate of storage accumulation curve, or RSAC (Fig. 6), plots the time derivative of Dh in the CSAC (Eq. 3; Fig. 5) and is the instantaneous rate ih/it of recharge head increase, equivalent to R(t)/Sy. In principle, only two values are feasible for ih/it: positive ones (indicating storage increase due to recharge) and zero values (periods of recession without recharge). Negative values necessarily represent errors in fitting of the CSAC, which should filter all storage decreases induced by springflow recession. Thus negative values indicate fitting or parameterization error. Long-term non-stationarity in aquifer storage (e.g., seasonal or interannual trends) may cause gradual ªdriftº in the RSAC and small deviations from the zero-value line. In this investigation, CSACs and RSACs are employed to analyze and quantify rates of recharge using water-level fluctuations in wells. Both curves have only two parameters, A and Sy, both assumed to be approximately time-invariant. Because Sy is not a sensitive parameter, catchment area (A) alone is varied to empirically approximate a zero-slope CSAC condition during long periods of pure recession (Fig. 5). Stage-discharge correlations for well-spring pairs are required to estimate springflow as a function of aquifer head. Such correlation must be obtained by frequent flow measurements during and following precipitation events, as described by Avery et al. (1999). The robustness of the CSAC fit may be evaluated by comparison with other estimates of recharge and by the degree of correspondence between catchment area estimated by fitting to other independent estimates. As an additional check, the RSAC for each fit should yield only positive values.

Other Methods In addition to the method proposed above, recharge may also be estimated by other conventional methods, such as FMB: R = P±ETp Hydrogeology Journal (2000) 8 : 579±593

(7)

where R is recharge, P is precipitation, and ETP is potential evapotranspiration. FMB estimates may be based exclusively on meteorological data, provided runoff is negligible. These estimates are typically minimum values, because calculated ETp is a potential (maximum) rate. FMB models assume that recharge is not spatially focused. Recharge may also be estimated by direct IHS of springflows. Like streams, springs in shallow phreatic aquifers display recession. To remove contributions to spring discharge from antecedent recharge, springflow hydrograph separation must be performed. Numerous hydrograph separation methods exist (e.g., Nutbrown and Downing 1976; Rutledge and Daniel 1994; Mau and Winter 1997). Flow recession in these aquifers may be adequately fit by a first-order linear model: Q…t† ˆ Q0 e

at

…8†

where Q(t) is springflow at time t after t0, the arbitrary start of recession; Q0 is flow at t0; and a is the recession constant. Using discharges estimated from well stage by Eq. (4), values of a were calculated for all recessional periods longer than 5 days, then averaged for each spring. Discharge values projecting recession from the beginning of each continuous observation period at each spring were calculated using Eq. (8) for subtracted antecedent recharge from head-estimated springflow. Recharge was then estimated by integration of this difference, with compensation for net storage change between the beginning and end of the reference period: Z Z T 1 T R…t†@t ˆ …Qobs Qrec †@t ‡ Sy
h…T † …9† A 0 0 where Qobs is springflow calculated from well stage (L3/T) and Qrec is springflow of recession line (L3/T). The integral on the right-hand side of Eq. (9) was evaluated using the trapezoidal rule. The values of A and Sy employed were the same as those used to fit CSAC plots, for consistency with these calculations. An example of a recession-corrected flow hydrograph, integrated to yield estimated recharge, is shown in Fig. 7. DOI 10.1007/s100400000088

585 Fig. 7 Example of integral hydrograph separation (IHS) for estimating recharge from springflows. Shaded area represents integrated flows after time zero until end of observation period (time T)

Application of the Storage Accumulation Method Description of Study Site The study area is a reclaimed coal surface mine in central West Virginia, USA, where two small unconfined aquifers occur; locations are shown in Fig. 8. Following mining between 1974 and 1982, these aquifers were emplaced by backfilling of mine excavations with heterogeneous unconsolidated waste rock. The emplaced mine-spoil deposits (white areas in Fig. 8) constitute aquifers overlying the former pit floor (shale). During reclamation, a thin topsoil layer was applied to the spoil and medium-height grasses were planted. Infiltration through this soil occurs readily, and recharge has induced a saturated zone 2±7 m thick over the aquitard. The bedrock strata dip slightly to the northwest; as a result, both the pit floor (aquitard) and water table (Fig. 8) generally slope in this direction. Discharge from the spoil occurs along a discontinuous line of springs and seeps along or near the down-dip outcrop of the pit floor. The aquitard is exposed in some locations but covered with colluvium or waste-rock in others. This study is focused on the ªXº and ªYº aquifers, located in adjacent areas of the site (Fig. 8). The hydrogeology of both aquifers is typical of that associated with aquifers of this type (Hawkins and Aljoe 1991) and has been examined in detail (Donovan and Frysinger 1997; Daly 1998). The X aquifer (Fig. 8a) covers approximately 48 ha of relatively flat topography, flanked by steeply dipping slopes approximately 15±20 m in height. The Y aquifer, located to the east, is approximately 18 ha in area and topographically similar, but with a broad depression at its center, flanked by elevated areas near wells Y04 and Y09 (Fig. 8b). Some areas of focused recharge do occur on both sites, in depressions and impoundments within the central portions of both aquifers. The impoundments are only intermittently saturated, during occasional use for disposal of sludge from site water-treatment operations. Bedrock outcrops between the two aquifers suggest that no hydraulic connection exists between them. The upgradient boundary of each aquifer is a buried highwall, consisting of unmined bedHydrogeology Journal (2000) 8 : 579±593

rock. An extreme conductivity contrast exists between the unconsolidated aquifers and in-place bedrock.

Data Collection and Analysis One spring catchment was chosen for each of the two aquifers, to examine water-table response to recharge using storage-accumulation techniques. In the Y aquifer, well Y04, within the catchment of spring MA1, occupies a topographic high near the upgradient boundary of the aquifer. The estimated catchment of spring MA1 is outlined on Fig. 8. For the X aquifer, well X19, within the catchment of spring C01, lies upgradient of this spring in a linear topographic depression flanked by sloping topography (Fig. 8). Wells X19 and Y04 were chosen for analysis of water-level response because their association with their respective springs is unambiguous, and because their hydraulic heads correlate well with springflows, showing little discernible time lag. Hydrometeorologic data were collected using a CR-10 weather station, located on the X aquifer (Fig. 8). The station was operated from between January 1995 and September 1996 and from April 1997 to August 1998. Instrumentation included a tippingbucket rain gauge, anemometer, temperature/relativehumidity probe, and a pyranometer. Hourly potential evapotranspiration (ETP) was estimated using the Penman-Monteith equation (Monteith 1965, 1981). Monthly precipitation and ETP results calculated from these data are shown in Table 1. Water levels were measured continuously at Y04 and X19, as well as at other wells in the X and Y aquifers. The two periods of measurement were from March 1995 to September 1996 and from January 1997 to July 1998. Measurements used either datalogger-coupled 5-psi pressure transducers (Global Water, 0.02 m accuracy) or continuous float-type drum recorders (Stevens Type F, 0.005 m accuracy). Data-loggers were set to sample at 15-min intervals. Gaps of short duration (2±5 days) occurring in the stage time-series for well Y04 were ªpatchedº using water-level trends from nearby wells Y03 and Y09, DOI 10.1007/s100400000088

586

Fig. 8 Water-table elevation contours, aquifer boundaries, and well and spring locations for X (above) and Y (below) aquifers. Wells X19 and Y04 and springs C01 and MA1 are labeled

whose heads closely correlated with those of Y04. The Y04 hydrograph is thus considered representative of other wells interpreted to be in the MA1 catchment. Discharges were measured at the two springs in the periods before and after several recharge events during spring to summer 1996 (six events) and winter to spring 1998 (five events). Springs were impounded and their discharge funneled through 15-cm-diameter pipe or 2.5-cm-throat Parshall flumes, located as near as possible to the springs themselves. Very soon following intense precipitation, discharges through these structures included some interflow and overland flow Hydrogeology Journal (2000) 8 : 579±593

(runoff), but flow decreased to include what is interpreted as only aquifer discharge within 2 h after precipitation ceased. Early flow measurements (within 2 h of end of rain) were thus discarded. Measurements were made for up to 7 days following precipitation events, at intervals as close as 15 min and as great as 24 h. A stopwatch and volume-calibrated container were used to measure flows, taking three replicate measurements to assess measurement error and calculate mean estimates. For accuracy, container volumes were chosen so that the fill time was 10±45 s. DOI 10.1007/s100400000088

587 Table 1 Monthly precipitation and potential evapotranspiration from weather-station data Month

Jul 95 Aug 95 Sep 95 Oct 95 Nov 95 Dec 95 Jan 96 Feb 96 Mar 96 Apr 96 May 96 Jun 96 Jul 96 Apr 97 May 97 Jun 97 Jul 97 Aug 97 Sep 97 Oct 97 Nov 97 Dec 97 Jan 98 Feb 98 Mar 98 Apr 98 May 98 Jun 98 Jul 98

Precipitation, P (mm)

Potential evapotranspiration, ETp (mm)

Daily maximum

Monthly total

Daily minimum

Daily maximum

Daily average

Monthly total

Monthly P-ETp

Daily P-ETp

16.8 48.5 19.6 20.3 15.2 19.1 21.3 20.8 13.2 19.6 39.6 15.2 57.9 11.4 16.3 27.7 37.9 26.4 51.3 15.6 30.2 10.7 22.1 11.9 21.8 32.3 13.5 41.2 23.4

173.7 133.8 147.5 162.5 176.0 178.2 172.4 167.3 175.4 181.3 244.6 156.6 239.8 140.4 199.3 176.7 182.0 104.7 179.0 115.0 119.9 136.6 193.2 175.4 185.1 100.3 169.1 215.7 163.3

2.1 1.2 0.2 0.4 0.0 0.1 0.1 0.1 0.1 0.2 0.4 1.5 0.5 0.5 0.4 1.1 1.4 0.3 0.5 0.2 0.1 0.0 0.1 0.1 0.2 0.3 0.4 0.6 1.4

15.5 15.4 14.5 13.6 12.6 12.1 11.5 12.5 12.9 15.7 15.9 15.3 15.3 14.8 14.8 15.2 15.3 14.4 14.4 13.5 11.8 11.5 16.6 12.2 15.0 14.0 15.4 14.6 14.9

4.1 3.7 2.4 2.1 0.7 0.5 0.5 0.8 1.4 2.7 2.8 3.8 3.2 2.4 2.8 3.3 3.7 2.9 2.6 2.0 0.6 0.5 0.6 0.8 1.6 2.5 2.9 2.7 3.3

128.0 114.1 173.1 164.1 121.5 116.6 116.7 123.5 145.5 181.4 186.3 115.0 198.5 172.7 187.6 198.5 113.5 188.6 177.4 161.4 119.1 116.2 118.2 122.6 150.1 174.2 190.3 182.1 103.3

±54.4 ±80.3 ±25.6 1±1.7 54.4 61.7 55.7 43.8 29.9 1±0.1 158.3 ±58.3 141.3 ±32.3 11.8 ±21.8 ±31.4 16.1 11.6 ±46.4 100.8 20.4 75.0 52.9 35.0 26.1 ±21.2 133.6 ±40.0

±1.75 ±2.59 ±0.85 ±0.05 1.81 1.99 1.80 1.51 0.96 0.00 5.11 ±1.94 4.56 ±1.08 0.38 ±0.73 ±1.01 0.52 0.05 ±1.50 3.36 0.66 2.42 1.82 1.13 0.87 ±0.68 4.45 ±1.29

Figure 9 shows daily precipitation for the X-aquifer CR-10 station over two periods: from June 1995 to August 1996 and from January 1997 to July 1998. Also shown are periods of water-level observation at X19 and Y04 during these periods. The 1995±1996

period was initially dry, with more than a full month of zero precipitation in late summer. Later, in May 1996 and July 1996, periods of high rainfall ended this drought. Precipitation was more uniformly distributed in the 1997±1998 period. Intense storms (cumulative

Fig. 9 Precipitation at the study site (X aquifer) during experimental periods. Arrows indicate intervals of waterlevel observation at the two well-spring pairs (X19±C01, X aquifer; Y04±MA1, Y aquifer)

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DOI 10.1007/s100400000088

588 Table 2 Transient head rises and specific-yield estimates for wells X19 and Y04

Well

Date

Precipitation amount (m)

Maximum head rise (m)

Specific yield

X19 X19 Y04 Y04 Y04 Y04

05/12/97 05/26/97 07/02/98 07/14/98 08/01/98 09/12/98

0.077 0.075 0.044 0.033 0.016 0.099

0.960 1.150 0.203 0.370 0.248 0.969

0.08 0.07 0.22 0.09 0.07 0.10

rainfall >3 cm) occurred at intervals of every 1±3 months and were more frequent in the second observation period. Catchment areas were estimated by two independent techniques: by flow weighting and by analysis of groundwater flow models (GFMs). First, flows from all springs for both the Y and X aquifers were measured synchronously between June 1997 and May 1998. The ratios of individual spring discharges (C01 and MA1) to cumulative discharge from each aquifer were calculated over this time period and used to estimate spring catchment area, assuming that (1) recharge is spatially homogeneous on large (e.g., spring-catchment) scale; (2) ET from the water table is minor; and (3) limited infiltration from sludge disposal had occurred. Second, GFMs describing steady-state conditions were developed for the X and Y aquifers (Daly 1998; Avery et al. 1999). Both models treated springs as constant-flux boundaries, based on average measurements from 1-year periods in 1995 and 1997, respectively, and the aquifer as a single unconfined layer, with bottom elevation (the aquitard) interpolated from drilling and outcrop observations. Both models required some heterogeneity in hydraulic conductivity to effect calibration, but none within the spring catchments of interest. Both GFMs employed a uniformly distributed areal recharge rate (Y aquifer, 2.3 mm/d; X aquifer, 1.1 mm/d) as well as greater, focused recharge over the sludge pond, which accounted for water disposal (Fig. 8). Pathline analysis using MODPATH (Pollock 1989) was used to discriminate Y aquifer spring catchments based on steadystate heads from Daly (1998). Specific yield was estimated for the vicinity of wells Y04 and X19 from rapid hydrograph rise following recharge. Estimated recharge rate is based on FMB, assuming negligible runoff and phreatic evaporation. This recharge rise was divided by observed maximum water-table rise to provide an estimate of Sy. Sophocleous (1991) used a similar method to calculate ªeffective storativityº for an unconfined aquifer in Kansas, USA. Six recharge events in 1997±1998 were employed. Table 2 lists observed head rise, calculated specific yield, and the mean of these results for wells X19 and Y04. Values suggest that Sy at Y04 ranges from 0.07±0.22, with a mean of about 0.12; and at X19 it ranges from 0.07±0.08 (mean 0.075). To calculate stage-discharge relationships for both well-spring pairs, springflows were plotted against conHydrogeology Journal (2000) 8 : 579±593

current measurements of well stage from transducer or recorder data. Model parameters were determined using an exponential model (Eq. 5), for which a slightly higher coefficient of determination (R2) was obtained than for the power-law form.

Results Fitting of Stage-Discharge Relationships The stage-discharge cross-correlations and R2 values for well-spring pairs Y04±MA1 and X19±C01 are shown in Figs. 10 and 11. The stage-discharge relationship for Y04±MA1 shows more error variance than for X19±C01, most of which is associated with early

Fig. 10 Relation between measured springflow and water-table elevation, well X19 and spring C01

Fig. 11 Relation between measured springflow and water-table elevation, well Y04 and spring MA1 DOI 10.1007/s100400000088

589 Fig. 12 Relation between cumulative storage accumulation and time (CSAC; top) and rate of head change and time (RSAC; bottom) for well Y04, 1995±1996 (see Eqs. 1±4)

response at the onset of recharge. This higher variance is ascribed to minor (<2 days) time lag between stage rise and discharge response for the case of Y04±MA1.

Cumulative Storage Accumulation Analysis Both CSAC and RSAC were developed for well Y04, shown in Figs. 12 and 13, and for well X19, shown in Figs. 14 and 15, for each of the two time intervals shown in Fig. 9. The CSAC and RSAC for each interval are plotted together, for comparison. The CSACs illustrate accumulated recharge, whereas the corresponding RSAC time series illustrate recharge timing and relative rates. Individual recharge events, as they arrive at the water table, appear as positive deflections above zero on the RSAC. The duration, amplitude, and shape of each RSAC event relate to the magnitude and duration of individual precipitation events, as well as to unsaturated-zone properties. The CSACs were developed using catchment areas and stage-discharge parameters fitted to springflows (Figs. 10 and 11). The Sy value employed was based on the average of head-rise estimates for individual recharge events at wells Y04 and X19 (Table 2). Catchment area was estimated empirically by adjustment to yield approximately zero CSAC slope and minimum absolute values of RSAC rates during longHydrogeology Journal (2000) 8 : 579±593

duration recessions; that is, A was the fitting parameter for the CSAC model. The CSAC fitting process is not easily amenable to quantitative error analysis, because fitting is based primarily on response during long recessional periods. In periods of frequent precipitation, recession periods are too short to attain zero CSAC slope and cumulative storage continuously rises; this is analogous to overlapping recession curves during periods of frequent storms. Much uncertainty may be associated with the fit, depending on whether short or long periods of recession were available. Other errors may occur as a result of uncertainty in the stage-discharge model at high flow, of vertical aquifer variations in Sy, or of transient changes in the catchment area. The possibility also exists for recharge focusing or ponding during intense storms, unaccounted for in the model. Such non-systematic or stage-dependent variations cannot be accounted for using a model parameterization scheme in which A and Sy are treated as temporally uniform. Results of the CSAC calculations are presented in Table 3 for the two wells. The CSAC interpretation yielded the fitting parameter (catchment area) as well as cumulative head change and recharge over the time period. Using this area parameter value, average recharge rates and recharge efficiency (the cumulative DOI 10.1007/s100400000088

590 Fig. 13 Relation between cumulative storage accumulation and time (CSAC; top) and rate of head change and time (RSAC; bottom) for well Y04, 1997±1998 (see Eqs. 1±4)

recharge divided by the total precipitation) were calculated over the periods of observation. For comparison, values of cumulative recharge and recharge rate are shown as calculated for IHS and applied to the GFMs. The catchment area from the CSAC analysis was also employed for the IHS rate calculation. The GFM rates are independent of this catchment area. For Y04, total cumulative storage increase (in meters of recharge) was 0.875 m in period 1 and 0.728 m in period 2. For the catchment areas indicated by the fit (15,000 and 19,000 m2, respectively), these represent 64.0% and 46.4% of incident precipitation, respectively. For X19, total cumulative storage increase was 0.621 m in period 1 and 0.466 m in

period 2. These represent 79.6% and 83.3%, respectively, of incident precipitation for these partial-year periods, occurring between February and August only.

Recharge Rates For both catchments, the calculated average recharge rates are similar between the CSAC and IHS interpretations. This is a quite reasonable result, because a significant difference would indicate bias in one or the other method, both based fundamentally on the same flow data. The largest difference was observed for the second period at Y04, where the CSAC was 18% higher than IHS. This difference is mainly ascribed to

Table 3 Comparison of recharge estimated by various methods for wells X19 and Y04 Well

X19 X19 Y04 Y04

From

To

CSACa head change (m)

3/7/96 2/7/98 6/8/95 1/14/97

8/22/96 7/27/98 8/21/96 7/21/98

8.15 6.44 7.29 6.07

Date

Specific yield, Sy

CSACa catchment area (m2)

Cumulative precip. (m)

Cumulative recharge (m)

Recharge rate (mm/d)

CSACa

IHSb

FMBc

CSACa

IHSb

GFMd

CSACa recharge effciency (%)

0.075 0.075 0.12 0.12

80,000 90,000 15,000 19,000

0.768 0.580 1.367 1.569

0.611 0.483 0.875 0.728

0.621 0.466 0.693 0.598

0.364 0.177 0.382 0.397

3.64 2.84 1.99 1.32

3.70 2.74 1.58 1.08

1.11 1.11 2.33 2.33

79.6 83.3 64.0 46.4

a

CSAC, Cumulative storage accumulation curve, b IHS, Integral hydrograph separation, c FMB, Fluid mass balance, d GFM, Groundwater flow modeling

Hydrogeology Journal (2000) 8 : 579±593

DOI 10.1007/s100400000088

591 Fig. 14 Relation between cumulative storage accumulation and time (CSAC; top) and rate of head rise and time (RSAC; bottom) for well X19 in 1996 (see Eqs. 1±4)

the fact that the trailing portion of the flow hydrograph ± the flows resulting from the last month or so of recharge ± was not added to the IHS estimates, which are therefore slightly conservative. Within the limits of error in fitting, the two methods agree. Both CSAC and IHS recharge flux estimates are substantially higher (50±165%) than the FMB rates based on modified Penman-Monteith potential evapotranspiration (Table 3) for equivalent periods. The FMB estimates are based on hydrometeorological data alone and independent of both IHS and CSAC methods. The calculated average recharge rates also differ between the two areas, about 100% higher for X19 compared to Y04 for both periods. Part of this discrepancy is ascribed to the difference in time interval for the two locations; the X19 observations were in both periods collected from late winter to mid summer, and did not include late summer and autumn, which are relatively drier seasons. Part of this difference may also be real spatial variability, resulting from differences in topography between the two areas. The GFM rate estimates are slightly different for Y04 and substantially different for X19. The GFM for the Y aquifer was based on baseline flows for the period January to December 1997, and also incorpoHydrogeology Journal (2000) 8 : 579±593

rated sludge leakage. The model for the X aquifer employed the lower flows observed in 1995, averaged over a full year. The catchment areas determined by fit of the CSAC plots of Figs. 12, 13, 14, and 15 are compared in Table 4 with those from flow-weighting and GFM. For both, areas estimated by the CSAC were generally similar to those obtained for flowweighting. The larger discrepancy was observed for X19, which was 40% higher for flow weighting. The GFM estimates both poorly fit the areas estimated by CSAC. The Y-aquifer estimate by GFM was likely influenced by sludge-pond loadings, which would tend to increase the size of this catchment; several flowlines from the pond terminate at spring MA1. The X aquifer catchment is substantially smaller, attributed to the lower flows used for this spring during the dry weather in 1995 (Fig. 9). The unexpected result of CSAC analysis is that the indicated recharge catchments differ substantially from the estimates based on earlier GFMs of these aquifers. Examination of the GFM boundary conditions, however, suggests that their steady-state springflows were not consistent with the flow (and assumed recharge) behavior during the weather conditions of this study. The flow models were based on earlier and much shorter flow measurements, which DOI 10.1007/s100400000088

592 Fig. 15 Relation between cumulative storage accumulation and time (CSAC; top) and rate of head rise and time (RSAC; bottom) for well X19 in 1998 (see Eqs. 1±4)

Table 4 Comparison of catchment area estimated by CSAC analysis, flow weighting, and GFM

Well

X19 X19 Y04 Y04 a

Catchment area (m2)

Date From

To

CSACa

Flow weighting

GFMb

03/07/96 02/07/98 06/08/95 01/14/97

08/22/96 07/27/98 08/21/96 07/21/98

80,000 90,000 15,000 21,000

134,000 134,000 175,000 117,500

25,800 25,800 34,700 34,700

CSAC, Cumulative storage accumulation curve, b GFM, Groundwater flow modeling

are probably less representative of long-term conditions. Thus these recharge estimates by CSAC and IHS would have been of utility in improving parameter estimates for GFM.

Discussion Fitting of the CSAC model allows stage recession caused by springflow to be compensated for dynamically. The analysis allows discrimination of the time rate of recharge for successive recharge events. Information is gained during the fitting process regarding average aquifer catchment area. The calculated spatial recharge rate is linearly sensitive to this area estimate Hydrogeology Journal (2000) 8 : 579±593

but nearly independent of Sy. The area estimate is based on its assumed stationarity in time as well as the assumed spatially uniform recharge rate (no focusing). In addition, the discharge-coupled recession rate at the well location is assumed to be similar to the spatial-average rate within the catchment. All these assumptions are unlikely to be perfectly met in all cases. The appropriateness of specific applications, however, should be reflected in the quality of the CSAC fit, i.e., zero-slope recession and zero rate of storage accumulation after all recharge has arrived at the water table. The CSAC and IHS recharge estimates in both locations are similar to each other and substantially higher than the FMB estimates. This result is not DOI 10.1007/s100400000088

593

unexpected because (1) the calculated ETp rates are potential rates only, and (2) the IHS and CSAC rates are based on fundamentally similar discharge estimates. The CSAC analysis, however, is considered to be of greater utility than integrated flows because it is both infiltration- and discharge-coupled. Its characteristics allow insight into the groundwater flow system (e.g., catchment area) and temporal variations in recharge. These results should help constrain and improve analysis of recharge processes, as well as support implementation of recharge rates in groundwater flow models.

Conclusions 1. The cumulative storage accumulation curve (CSAC) is proposed as a useful tool to model storage accumulation caused by recharge. CSACs are recessioncorrected hydrographs that display storage accumulation in aquifers due to recharge. CSACs are derived from water-level fluctuations in wells and allow quantification of recharge rate over short intervals (days to months). They require estimates of the parameters Sy and spring catchment area, as well as accurate measurements or estimates of spring discharge for the recharge period. 2. The rate of storage accumulation curve (RSAC) indicates the rate and timing of water-level rise associated with recharge. These curves may be used to represent time series of recharge flux. 3. The catchment-area parameter may be used to fit recessional limbs on the CSAC, in conjunction with bringing the RSAC close to zero after arrival of recharge to the water table has occurred. This fitting is most unambiguous if observations from long recession periods (dry intervals following discrete recharge events) are used. 4. Using CSAC for Y04±MA1, recharge rates were estimated to be 46±64% of incident precipitation. Using the X19±C01 CSAC, recharge was estimated for shorter subannual intervals to be 79±83%. Both sets of estimates are significantly higher than fluidmass-balance (FMB) values during these periods. The CSAC estimates are, however, similar to integral hydrograph separation (IHS) estimates over identical time frames. 5. The quality and accuracy in stage-discharge estimation over a wide range of flows is fundamental to the analysis and a potential source of error in CSAC application. Stage-discharge relationships are the foundation of the method. 6. Results here are for very small catchments of a hydrologically responsive shallow aquifer, in which recharge lag is minimal (<1 d). For larger aquifers, response will likely display greater lag, between both precipitation and recharge and stage and springflow increase. Hydrogeology Journal (2000) 8 : 579±593

Acknowledgments This research was conducted under a grant from the US Environmental Protection Agency to J.J.D. Field assistance and results from Matt Daly and Chuck Reed, students at West Virginia University, are acknowledged.

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DOI 10.1007/s100400000088