Analysis of temporal variation and scaling of hydrological variables based on a numerical model of the Sagehen Creek watershed

Temporal variations of the main hydrological variables over 16 years were systematically investigated based on the results from an integrated hydrological modeling at the Sagehen Creek watershed in northern Sierra Nevada. Temporal scaling of these variables and damping effects of the hydrological system as well as its subsystems, i.e., the land surface, unsaturated zone, and saturated zone, were analyzed with spectral analyses. It was found that the hydrological system may act as a cascade of hierarchical fractal filters which sequentially transfer a non-fractal or less correlated fractal hydrological signal to a more correlated fractal signal. The temporal scaling of simulated infiltration (SI), simulated actual evapotranspiration (SET), simulated recharge (SR), measured baseflow (MBF), measured streamflow (MSF) exist and the temporal autocorrelation of these variables increase as water moves through the system. The degree of the damping effect of the subsystems is different and is strongest in the unsaturated zone compared with that of the land surface and saturated zone. The temporal scaling of the simulated groundwater levels (Sh) also exists and is strongly affected by the river: the temporal autocorrelation of Sh near the river is similar to that of the river stage fluctuations and increases away from the river. There is a break in the temporal scaling of Sh near the river at low frequencies due to the effect of the river. Temporal variations of the simulated soil moisture (Sθ) is more complicated: the value of the scaling exponent (β) for Sθ increases with depth as water moves downwards and its high-frequency fluctuations are damped by the unsaturated zone. The temporal fluctuations of measured precipitation and SI are fractional Gaussian noise, those of SET, SR, MBF, and MSF are fractional Brownian motion (fBm), and those of Sh away from the river are 2nd-order fBm based on the values of β obtained in this study.     

Groundwater recharge through an alluvial fan in the Atacama Desert,northern Chile: mechanisms,magnitudes and causes

The Chacarilla fan in the Atacama Desert is one of several formed in the Late Miocene at the foot of the Pre‐Andean Cordillera overlying the large, complex, Pampa Tamarugal aquifer contained in the continental clastic sediments of the fore‐arc basin. The Pampa Tamarugal aquifer is a strategic source of water for northern Chile but there is continuing doubt over the resource magnitude and recharge. During January 2000 a 1 in 4 year storm in the Andes delivered a 34 million m³ flash flood to the fan apex where c. 70% percolated to the underlying aquifers. Groundwater recharge through the fan is calculated to be a minimum of 200 l/s or 6% of the long‐term catchment rainfall. These figures are supported by hydrochemical data that suggest that recharge may be 9% of long‐term rainfall. Isotopic data suggest groundwater less than 50 years old is transmitted westward through the permeable sheetflood sediments of the fan overlying the main aquifer. Analysis of this and other events shows that the hydrological system is non‐linear with positive feedback. The magnitude of groundwater recharge is dependent on climatic variations, antecedent soil moisture storage and changes in channel characteristics. Long‐term declines in groundwater level may partly result from climatic fluctuations and the causes of such fluctuations are discussed. Copyright © 2002 John Wiley & Sons, Ltd.     

Analytic solutions to transient groundwater flow under time-dependent sources in a heterogeneous aquifer bounded by fluctuating river stage

Analytical solutions for the water table and lateral discharge in a heterogeneous unconfined aquifer with time-dependent source and fluctuating river stage were derived and compared with those in an equivalent homogeneous aquifer. The heterogeneous aquifer considered consists of a number of sections of different hydraulic conductivity values. The source term and river stage were assumed to be time-dependent but spatially uniform. The solutions derived is useful in studying various groundwater flow problems in a horizontally heterogeneous aquifer since the spatially piecewise-constant hydraulic conductivity and temporally piecewise-constant recharge and lateral discharge can be used to quantify variations in these processes commonly observed in reality. Applying the solutions derived to an aquifer of three sections of different hydraulic conductivity values shown that (1) the aquifer heterogeneity significantly increases the spatial variation of the water table and thus its gradient but it has little effect on lateral discharge in the case of temporally and spatially uniform recharge, (2) the time-dependent but spatially uniform recharge increases the temporal variation of groundwater table over the entire aquifer but its effect on lateral discharge is limited in the zone near the river, and (3) the effect of river stage fluctuation on the water table and lateral discharge is limited in the zone near the river and the effect of the heterogeneity is to increase lateral discharge to or recharge from the river.     

Patterns and dynamics of river–aquifer exchange with variably-saturated flow using a fully-coupled model

The parallel physically-based surface–subsurface model PARFLOW was used to investigate the spatial patterns and temporal dynamics of river–aquifer exchange in a heterogeneous alluvial river–aquifer system with deep water table. Aquifer heterogeneity at two scales was incorporated into the model. The architecture of the alluvial hydrofacies was represented based on conditioned geostatistical indicator simulations. Subscale variability of hydraulic conductivities (K) within hydrofacies bodies was created with a parallel Gaussian simulation. The effects of subscale heterogeneity were investigated in a Monte Carlo framework. Dynamics and patterns of river–aquifer exchange were simulated for a 30-day flow event. Simulation results show the rapid formation of saturated connections between the river channel and the deep water table at preferential flow zones that are characterized by high conductivity hydrofacies. Where the river intersects low conductivity hydrofacies shallow perched saturated zones immediately below the river form, but seepage to the deep water table remains unsaturated and seepage rates are low. Preferential flow zones, although only taking up around 50% of the river channel, account for more than 98% of total seepage. Groundwater recharge is most efficiently realized through these zones. Subscale variability of K_sat slightly increased seepage volumes, but did not change the general seepage patterns (preferential flow zones versus perched zones). Overall it is concluded that typical alluvial heterogeneity (hydrofacies architecture) is an important control of river–aquifer exchange in rivers overlying deep water tables. Simulated patterns and dynamics are in line with field observations and results from previous modeling studies using simpler models. Alluvial heterogeneity results in distinct patterns and dynamics of river–aquifer exchange with implications for groundwater recharge and the management of riparian zones (e.g. river channel-floodplain connectivity via saturated zones).     

Estimation of the percentage of annual groundwater recharge with bomb tritium using a cumulative mass balance method

The bomb tritium (³H) distribution patterns in the aquifer beneath an abandoned landfill at the Canadian Forces Base (CFB) Borden, Ontario, and in a sandy aquifer at Whiteshell Nuclear Research Establishments (WNRE) Pinawa, Manitoba, all in Canada, were delineated in great detail. A sampling and monitoring network of multilevel samplers and bundle piezometers were used. The directions of groundwater flow were established, and the boundary between the tritiated and non-tritiated zones of the two aquifers were closely demarcated. Using a cumulative mass balance method, the³H input mass into the aquifers was compared with the³H mass in groundwater storage to estimate the percentages of annual groundwater recharge from 1953 to 1978. Two recharge calculations for theeffective recharge zone and thetotal recharge area of the aquifers as established from the flownet analysis, and the distributions of dissolved geochemical constitutents showed that theeffective recharge zone calculations gave higher values of 30.6 cm/yr for CFB Borden and 20.1 cm/yr for WNRE while thetotal recharge areas gave lower values of 19.1 and 10.1 cm/yr for the Borden and WNRE aquifers respectively. The two recharge values provide possible minimum and maximum recharge estimates for the two study areas.     

Application of an integrated surface water‐groundwater model to multi‐aquifers modeling in Choushui River alluvial fan,Taiwan

This research proposes a combination of SWAT and MODFLOW, MD‐SWAT‐MODFLOW, to address the multi‐aquifers condition in Choushui River alluvial fan, Taiwan. The natural recharge and unidentified pumping/recharge are separately estimated. The model identifies the monthly pumping/recharge rates in multi‐aquifers so that the daily streamflow can be simulated correctly. A multi‐aquifers condition means a subsurface formation composed of at least the unconfined aquifer, the confined aquifer, and an in‐between aquitard. In such a case, the variation of groundwater level is related to pumping/recharge activities in vertically adjacent aquifer and the river‐aquifer interaction. Both factors in turn affect the streamflow performance. Results show that MD‐SWAT‐MODFLOW performs better than SWAT alone in terms of simulated streamflow, especially during low flow period, when pumping/recharge rates are properly estimated. A sensitivity analysis of individual parameter suggests that the vertical leakance may be the most sensitive among all investigated MODFLOW parameters in terms of the estimated pumping/recharge among aquifers, and the Latin‐Hypercube‐One‐factor‐At‐a‐Time sensitivity analysis indicates that the hydraulic conductivity of channel is the most sensitive to the model performance. It also points out the necessity to simultaneously estimate pumping/recharge rates in multi‐aquifers. The estimated net pumping rate can be treated as a lower bound of the actual local pumping rate. As a whole, the model provides the spatio‐temporal groundwater use, which gives the authorities insights to manage groundwater resources. Copyright © 2012 John Wiley & Sons, Ltd.     

Impacts of riparian zone plant water use on temporal scaling of groundwater systems

In this work, we study groundwater system temporal scaling in relation to plant water use and near‐river‐stage fluctuations in riparian zones where phreatophytes exist. Using detrended fluctuation analysis (DFA), we investigate the influence of regular diurnal fluctuations due to phreatophyte water use on temporal scaling properties of groundwater level variations. We found that groundwater use by phreatophytes, at the field site on the Colorado River, USA, results in distinctive crossovers (slope changes when the plots are fitted with straight lines) in the logarithm plots of root‐mean‐square fluctuations of the detrended water level time series versus time scales of groundwater level dynamics. For groundwater levels monitored at wells close to the river, we identified one crossover at ～1 day in the scaling characteristics of groundwater level variations. When time scale exceeds 1 day, the scaling properties decrease from persistent to close to 1/f noise, where f is the frequency. For groundwater levels recorded at wells further away from the river, the slope of the straight line fit (i.e. scaling exponent) is smallest when the time scale is between 1 and 3 days. When the time scale is < 1 day, groundwater variations become persistent. When the time scale is between 1 and 3 days, the variations are close to white noise, but return to persistent when the time scale is > 3 days. Copyright © 2011 John Wiley & Sons, Ltd.     

The role of antecedent groundwater heads in controlling transient aquifer storage and flood peak attenuation in karst watersheds

Transient storage of floodwaters in aquifers is known to attenuate peak flows in rivers and drive subsurface dissolution. Transient aquifer storage could be enhanced in watersheds overlying karst aquifers where caves facilitate surface and groundwater exchange. Few studies, however, have examined controls on, or magnitudes of, transient aquifer storage or flood peak attenuation in karstic watersheds. Here we evaluate flood peak attenuation with multiple linear regression analyses of 10 years of river and groundwater data from the Suwannee River, which flows over the karstic upper Floridan aquifer in north-central Florida and experiences frequent flooding. Regressions show antecedent river stage exerts the dominant control on magnitudes of transient aquifer storage, with recharge and time to peak having secondary controls. Specifically, low antecedent stages result in larger magnitudes of transient aquifer storage and thus greater flood attenuation than conditions of elevated antecedent stage. These findings suggest subsurface weathering, including cave formation and enlargement, caused by transient aquifer storage could occur on a more frequent basis in aquifers where groundwater table elevation is lowered due to anthropogenic or climatic influences. Our work also shows that measures of groundwater table elevation prior to an event could be used to improve predictive flood models. © 2018 John Wiley & Sons, Ltd.     

The effects of climate changes on aquifer storage and river baseflow

Abstract

The effects of changes in climate on aquifer storage and groundwater flow to rivers have been investigated using an idealized representation of the aquifer/river system. The generalized aquifer/river model can incorporate spatial variability in aquifer transmissivity and is applied with parameters characteristic of Chalk and Triassic sandstone aquifers in the United Kingdom, and is also applicable to other aquifers elsewhere. The model is run using historical time series of recharge, estimated from observed rainfall and potential evaporation data, and with climate inputs perturbed according to a number of climate change scenarios. Simulations of baseflow suggest large proportional reductions at low flows from Chalk under high evaporation change scenarios. Simulated baseflow from the slower responding Triassic sandstone aquifer shows more uniform and less severe reductions. The change in hydrological regime is less extreme for the low evaporation change scenario, but remains significant for the Chalk aquifer.     

Quantifying River‐Groundwater Interactions of New Zealand's Gravel‐Bed Rivers: The Wairau Plain

New Zealand's gravel‐bed rivers have deposited coarse, highly conductive gravel aquifers that are predominantly fed by river water. Managing their groundwater resources is challenging because the recharge mechanisms in these rivers are poorly understood and recharge rates are difficult to predict, particularly under a more variable future climate. To understand the river‐groundwater exchange processes in gravel‐bed rivers, we investigate the Wairau Plain Aquifer using a three‐dimensional groundwater flow model which was calibrated using targeted field observations, “soft” information from experts of the local water authority, parameter regularization techniques, and the model‐independent parameter estimation software PEST. The uncertainty of simulated river‐aquifer exchange flows, groundwater heads, spring flows, and mean transit times were evaluated using Null‐space Monte‐Carlo methods. Our analysis suggests that the river is hydraulically perched (losing) above the regional water table in its upper reaches and is gaining downstream where marine sediments overlay unconfined gravels. River recharge rates are on average 7.3 m³/s, but are highly dynamic in time and variable in space. Although the river discharge regularly hits 1000 m³/s, the net exchange flow rarely exceeds 12 m³/s and seems to be limited by the physical constraints of unit‐gradient flux under disconnected rivers. An important finding for the management of the aquifer is that changes in aquifer storage are mainly affected by the frequency and duration of low‐flow periods in the river. We hypothesize that the new insights into the river‐groundwater exchange mechanisms of the presented case study are transferable to other rivers with similar characteristics.     

Radially convergent groundwater flow in sloping terrain

Abstract

The groundwater flow equation governing the elevation (h) of the steady-state phreatic surface in a sloping aquifer fed by constant recharge over a bi-circular sector is rhh′ ? r ² Bh′ + Pr ² ? PR ² = 0, where r is the radial coordinate, P is a constant involving recharge and aquifer properties, and B is the slope of the aquifer—bedrock boundary. The derived flow equation describes radially convergent flow through a sloping aquifer that discharges to a water body of fixed head. One important simplification is that in which the width of the bi-circular sector is constant, and the draining land becomes a rectangular aquifer. The bi-circular sector and rectangular-strip groundwater flow problems are solved in terms of implicit equations. The solutions for the steady-state phreatic surfaces depend on the ratio of recharge to hydraulic conductivity, the slope of the aquifer-bedrock, and the downstream constant-head boundary. Computational examples illustrate the application of the solutions.     

Spatial and temporal analysis of groundwater recharge with application to sampling design

A numerical experiment of flow in variably saturated porous media was performed in order to evaluate the spatial and temporal distribution of the groundwater recharge at the phreatic surface for a shallow aquifer as a function of the input rainfall process and soil heterogeneity. The study focused on the groundwater recharge which resulted from the percolation of the excess rainfall for a 90-days period of an actual precipitation record. Groundwater recharge was defined as the water flux across the moving phreatic surface. The observed spatial non-uniformity of the groundwater recharge was caused by soil heterogeneity and is particularly pronounced during the stage of recharge peak (substantial percolation stage). During that stage the recharge is associated with preferential flow paths defined as soil zones of locally higher hydraulic conductivity. For the periods of low percolation intensity the groundwater recharge was exhibiting more uniform spatial characteristics. The temporal distribution of the recharge was found to be a function of the frequency and intensity of the rainfall events. Application of sampling design demonstrates the joint influence of the spatial and temporal recharge variability on the cost-effective monitoring of groundwater potentiometric surfaces.     

Terrestrial‐originated submarine groundwater discharge through deep multilayered aquifer systems beneath the seafloor

A large quantity of submarine groundwater discharge (SGD) of about 1000 m³ day^?1 m^?1 of the 600‐km‐long shoreline of South Atlantic Bight has been estimated by Moore (Global Biogeochemical Cycles, 2010b, 24, GB4005, doi: 10.1029/2009GB003747 ). However, there is great uncertainty in estimating the percentage of net, land‐originated groundwater recharge of SGD. Moreover, most previous studies considered the homogeneous case for the coastal superficial aquifers. Here, we investigated the terrestrial‐originated SGD through a multilayered submarine aquifer system, which comprises two confined aquifers and two semi‐permeable layers. The inland recharge includes a constant part representing the annual average and a periodical part representing its seasonal variation. An analytical solution was derived and used to analyse the distributions of the terrestrial‐originated SGD from the multilayered aquifers along the Winyah Bay transect, South Atlantic Bight. It is found that the width of the zone of SGD from the upper aquifer ranges from ~0.8 to ~8.0 km depending on the leakance of the seabed semi‐permeable layer. A head of the upper aquifer at a coastline 1.0 m higher than the mean sea level will cause a SGD of 1.82– 18.3 m³ day^?1 m^?1 from that aquifer as the seabed semi‐permeable layer's leakance varies from 0.001 to 0.1 day^?1, providing considerable possibility for considerable land‐originated SGD. Seasonal terrestrial‐originated SGD variations predicted by the analytical model provide consistent explanation of the seasonal variation of ²²⁶Ra observed by Moore (Journal of Geophysics, 2007, 112, C10013, doi: 10.1029/2007JC004199 ). The contribution of the lower aquifer to SGD is only 1.2–12% of that of the upper aquifer. Copyright © 2014 John Wiley & Sons, Ltd.     

Transient Recharge Estimability Through Field‐Scale Groundwater Model Calibration

The estimation of recharge through groundwater model calibration is hampered by the nonuniqueness of recharge and aquifer parameter values. It has been shown recently that the estimability of spatially distributed recharge through calibration of steady‐state models for practical situations (i.e., real‐world, field‐scale aquifer settings) is limited by the need for excessive amounts of hydraulic‐parameter and groundwater‐level data. However, the extent to which temporal recharge variability can be informed through transient model calibration, which involves larger water‐level datasets, but requires the additional consideration of storage parameters, is presently unknown for practical situations. In this study, time‐varying recharge estimates, inferred through calibration of a field‐scale highly parameterized groundwater model, are systematically investigated subject to changes in (1) the degree to which hydraulic parameters including hydraulic conductivity (K) and specific yield (S_y) are constrained, (2) the number of water‐level calibration targets, and (3) the temporal resolution (up to monthly time steps) at which recharge is estimated. The analysis involves the use of a synthetic reality (a reference model) based on a groundwater model of Uley South Basin, South Australia. Identifiability statistics are used to evaluate the ability of recharge and hydraulic parameters to be estimated uniquely. Results show that reasonable estimates of monthly recharge (<30% recharge root‐mean‐squared error) require a considerable amount of transient water‐level data, and that the spatial distribution of K is known. Joint estimation of recharge, S_y and K, however, precludes reasonable inference of recharge and hydraulic parameter values. We conclude that the estimation of temporal recharge variability through calibration may be impractical for real‐world settings.     

Modelling tidal signals enhanced by a submarine spring in a coastal confined aquifer extending under the sea

Submarine springs discharge offshore groundwater from confined aquifers extending under the sea. The effects of these springs on the propagation of tidal oscillations in coastal confined aquifers are not known. This paper presents an approximate analytical solution of tidal head fluctuations in a confined aquifer with one submarine spring. The aquifer is assumed to extend in all directions infinitely. The spring is represented by a permeable round column on the seabed, which penetrates completely the impermeable layer overlying the confined aquifer. The error of the approximate solution is negligible if the distance from the spring to the coastline is much greater than the radius of the permeable column representing the spring. Through a hypothetical example, we demonstrate that it is possible to identify the spring’s location using tidal signals observed from inland wells. Tidal groundwater head fluctuations from three inland observation wells at least are needed to determine the 5 model parameters, including the location (2 parameters), the radius of the permeable column representing the spring, the diffusivity of the aquifer, and the tidal loading efficiency of the system.     

Groundwater mixing between different aquifer types in a complex structural setting discerned by elemental and stable isotope geochemistry

Karst aquifers are well known for their intricate stratigraphy and geologic structures, which make groundwater characterization challenging because flowpaths and recharge sources are complex and difficult to evaluate. Geochemical data, collected from ten closely spaced production wells constructed in two karst aquifers (Bangor Limestone (Mb) and Tuscumbia Limestone/Fort Payne Chert (Mftp)) in Trussville, north‐central Alabama, illustrate two distinctive groundwater end‐members: (1) higher major ion, dissolved inorganic carbon, conductivity, alkalinity concentrations, heavier δ¹³C ratios (max: −10.2 ± 0.2‰ Vienna Pee Dee Belemnite (PDB)) and lower residence times (mean: 19.5 ± 2 years, n = 2) of groundwater in the Mb aquifer and (2) lower constituent concentrations, lighter δ¹³C ratios (min: −13.4 ± 0.2‰ PDB) and longer residence times of groundwater (mean: 23.6 ± 2 years, n = 4) in the Mftp aquifer. Summer and fall data and the binary mixing model show aquifer inter‐flow mixing along solution fractures and confirms the distinctive groundwater geochemistry of the two aquifers. Lowering of static water levels over the summer (drawdown from 2 to 5.2 m) leads to more reducing groundwater conditions (lower Eh values) and slightly enriched δ¹⁸O and δD ratios during the fall [δ¹⁸O: −4.8 ± 0.1 to −5.4 ± 0.1‰ Vienna Standard Mean Oceanic Water (VSMOW), n = 9; δD: −25.4 ± 1 to −27.4 ± 1‰ VSMOW, n = 9] when compared with summer season samples (δ¹⁸O: −5.1 ± 0.1 to −5.7 ± 0.1‰ VSMOW, n = 11; δD: −25.0 ± 1 to −30.6 ± 1‰ VSMOW, n = 11). GIS analyses confirm the localized origin of recharge to the investigated aquifers. The combination of GIS, field parameters and geochemistry analyses can be successfully used to identify recharge sources, evaluate groundwater flow and transport pathways and to improve understanding of how groundwater withdrawals impact the sustainability and susceptibility to contamination of karst aquifers. Copyright © 2015 John Wiley & Sons, Ltd.     

Benzene Dynamics and Biodegradation in Alluvial Aquifers Affected by River Fluctuations

The spatial distribution and temporal dynamics of a benzene plume in an alluvial aquifer strongly affected by river fluctuations was studied. Benzene concentrations, aquifer geochemistry datasets, past river morphology, and benzene degradation rates estimated in situ using stable carbon isotope enrichment were analyzed in concert with aquifer heterogeneity and river fluctuations. Geochemistry data demonstrated that benzene biodegradation was on‐going under sulfate reducing conditions. Long‐term monitoring of hydraulic heads and characterization of the alluvial aquifer formed the basis of a detailed modeled image of aquifer heterogeneity. Hydraulic conductivity was found to strongly correlate with benzene degradation, indicating that low hydraulic conductivity areas are capable of sustaining benzene anaerobic biodegradation provided the electron acceptor (SO₄^2–) does not become rate limiting. Modeling results demonstrated that the groundwater flux direction is reversed on annual basis when the river level rises up to 2 m, thereby forcing the infiltration of oxygenated surface water into the aquifer. The mobilization state of metal trace elements such as Zn, Cd, and As present in the aquifer predominantly depended on the strong potential gradient within the plume. However, infiltration of oxygenated water was found to trigger a change from strongly reducing to oxic conditions near the river, causing mobilization of previously immobile metal species and vice versa. MNA appears to be an appropriate remediation strategy in this type of dynamic environment provided that aquifer characterization and targeted monitoring of redox conditions are adequate and electron acceptors remain available until concentrations of toxic compounds reduce to acceptable levels.     

The response of idealized aquifer/river systems to climate change

Abstract

A study of the effect of changes in climate on aquifer storage and river recharge using a simple model of an idealized aquifer/river system shows the combined influence of aquifer properties and climate change scenario on the system response. The study shows that changes in the seasonal distribution of recharge may have a critical effect on low flows in rivers supported by baseflow. However, rivers supported by slowly responding aquifers may show a considerable delay in response to climate change allowing an opportunity for water resources planning over an extended period.     

Effect of heterogeneity on spatiotemporal variations of groundwater level in a bounded unconfined aquifer

Spatiotemporal variations of groundwater level due to a white noise recharge time series and a random transmissivity field in a bounded unconfined aquifer was studied. The analytical solutions for the variance and covariance of groundwater level were derived with non-stationary spectral analyses and superposition principle. It was found that the fluctuations of groundwater level are spatially non-stationary due to a fixed head boundary condition and temporal non-stationary at early time but gradually became stationary as time progresses due to effect of the initial condition. The variation in groundwater level is mainly caused by the random source/sink in the case of temporally random recharge and spatially random transmissivity. The effect of heterogeneity is to increase the variation of groundwater level and the maximum effect occurs close to the constant head boundary because of the linear mean hydraulic gradient. The heterogeneity also enhances the correlation of groundwater level, especially at large time intervals and small spatial distances.     

Estimating Effective Porosity in Bedrock Aquifers

Flow in many bedrock aquifers is through fracture networks. Point to point tracer tests using applied tracers provide a direct measure of time of travel and are most useful for determining effective porosity. Calculated values from these tests are typically between 10⁻⁴ and 10⁻² (0.01% to 1%), with these low values indicating preferential flow through fracture and channel networks. Tracer tests are not commonly used in site investigations, and specific yield is often used as a proxy for effective porosity. The most popular methods have used centrifuge measurements, water table fluctuations, pumping tests, and packer tests. Specific yield varies substantially with the testing method. No method is as reliable as tracer testing for providing estimates of effective porosity, but all methods provide complementary insights on aquifer structure. Temporal and spatial scaling effects suggest that bedrock aquifers have hierarchical structures, with a network of more permeable fractures and channels, which are connected to less permeable fractures and to the matrix. Consequences of the low effective porosities include groundwater velocities that often exceed 100 m/d and more frequent microbial contamination than in aquifers in unconsolidated sediments. The large uncertainty over the magnitude of effective porosity in bedrock aquifers makes it an important parameter to determine in studies where time of travel is of interest.