Journal of Hydrologic Engineering

As issues of source water protection of drinking water supplies have come to the forefront, the methodology to effectively manage semiconfined aquifers is still unclear. Commonly, the area around the wellhead is considered the most risk sensitive area, but in semiconfined settings the most sensitive areas may be located some distance away from the wellhead. This research employed the use of age-distribution modeling in concert with environmental tracers (tritium/helium-3), geochemical, and other hydrogeologic data. A synthetic test case was developed to determine the suitability of the technique for identifying localized areas of recharge to a wellhead in aquifers where evidence of modern water infiltration exists. Results of the model runs based on the synthetic test case indicate that the technique presented herein is capable of identifying localized areas of recharge contributing to a wellhead, in a semiconfined aquifer setting, with only a limited amount of required data. These results and the relative ease of application make this technique a valuable tool for obtaining a greater understanding of the flow regime at a wellhead, which in turn provides more information for risk assessment of public water supplies.

Source water protection zones are not easily determined for semiconfined aquifers with highly localized areas of leakage from overlying shallow aquifers. This research is a companion case study to a theoretical study detailing the inverse modeling of aquifer mixing zones using age-distribution models. Where the first study detailed the capabilities of inverse age-distribution modeling given various sets of environmental tracer data and prior information, this study demonstrates the successful application of the technique to a real-world problem with a robust conceptual model verified in the current literature. The case study presented here considers a hydrogeologic setting in the northern Mississippi Embayment where highly localized leakage features exist between a shallow alluvial aquifer and the Memphis aquifer. Geochemical analyses, environmental, and radiochemical tracers have been used to develop and verify a conceptual model of the flow system at the Sheahan Wellfield in Memphis, Tenn. This study used inverse age-distribution modeling of tritium and helium-3 at multiple wellheads to determine the most highly probable location of a near field leakage source that is impacting wellheads. The method was used to identify the most likely location of the leakage site, and to identify an area at most risk for wellhead management considerations.

Groundwater travel time is an important criterion for regulating managed aquifer recharge (MAR) operations because of its relationship to water quality. Here, three complementary methods for determining travel times are examined. Sulfur hexafluoride $\left(\mathrm{S}{\mathrm{F}}_6\right)$ , a gas tracer, was injected into 23 spreading basins at the Montebello Forebay MAR operation (Los Angeles County, United States) and monitored at ten monitoring and 18 production wells within $150\mathrm{m}$ . Over $2\text{years}$ , $\mathrm{S}{\mathrm{F}}_6$ was detected at nine monitoring and 11 production wells. Travel times showed a significant relationship with depth, but not with horizontal distance or pumping rate. A pumping influence was apparent as the tracer arrived sooner at production wells then at monitoring wells of similar depth. In the unconfined aquifer, estimated hydrogeologic travel times were $<0.2\text{years}(<10\text{weeks})$ and agree with the $\mathrm{S}{\mathrm{F}}_6$ data. However, in the confined aquifers, estimated travel times were $>4\text{years}$ and the agreement with the $\mathrm{S}{\mathrm{F}}_6$ travel times was poor. At the seven production wells with $\mathrm{S}{\mathrm{F}}_6$ detections, leakage through low permeability layers leading to earlier tracer arrival provides a likely explanation. All tritium/ ${}^3\mathrm{He}$ ages at production wells are greater than $10\text{years}$ ; this data combined with the $\mathrm{S}{\mathrm{F}}_6$ results indicate the wells produce a mixture of young and old groundwater.

This paper describes a study of groundwater characteristics and groundwater dating in the Kern Water Bank, west of Bakersfield, Calif. The paper also presents the results of developing a calibrated groundwater-flow model for the Kern Water Bank’s aquifer. The Kern Water Bank is one of the largest artificial storage and recovery operations in the southwestern United States. This study sheds light on the chemical characteristics of groundwater, on the nature of the recharge water, on the subsequent groundwater movement through the storage aquifer, and on the origin and age of groundwater in the Kern Water Bank. It also produced a calibrated groundwater-flow model that can be used in predicting the effects of future recharge and groundwater extraction operations in the Kern Water Bank aquifer. It was determined that the chemistry of groundwater in the Kern Water Bank is suitable for irrigation following additional purification. Groundwater in the Kern Water Bank originates primarily from western Sierra Nevada runoff and from regional groundwater accretions. Groundwater age shows a clear differentiation into three age ranges. An optimal set of hydrogeologic parameters was identified which, in conjunction with recharge data, boundary-, and initial-condition data, and a hydrogeologically based finite difference grid, were integrated into a groundwater-flow model useful for predicting recharge and stress impacts in the Kern Water Bank.

Using environmental tracers in groundwater dating partly relies on the assumption that groundwater age distribution can be described analytically. To investigate the applicability of age dating in complex multiaquifer systems, a methodology for simulating well specific groundwater age distribution was developed. Using a groundwater model and particle tracking we modeled age distributions at screen locations. By enveloping modeled age distributions and estimated recharge concentrations, environmental tracer breakthroughs were simulated for specific screens. Simulated age distributions are of irregular shapes and sizes without being similar to the assumed age distributions used in the analytical approach. The shape of age distribution to some extent depends on sampling size and on whether the system is modeled in a transient or in a steady state, but shape and size were largely driven by the heterogeneity of the model and by topographical variations as well. Analytically derived groundwater ages are dependent on sampling time. This time dependence relates to the nonlinearity of recharge concentrations and the shape and size of age distribution that has no coherence with the simplified assumptions of traditional approaches. Accordingly, constraining flow models by “age observations” may lead to misrepresentations that are biased depending on sampling time. If environmental tracers are used directly in terms of concentrations instead of ages, spatial as well as temporal variations become useful in constraining models.

Concentrations of halogenated volatile organic compounds (VOCs) were determined by gas chromatography (GC) with an electron-capture detector (GC-ECD) and by gas chromatography with mass spectrometry (GC-MS) in 109 groundwater samples from five study areas in the United States. In each case, the untreated water sample was used for drinking-water purposes or was from a monitoring well in an area near a drinking-water source. The minimum detection levels (MDLs) for 25 VOCs that were identified in GC-ECD chromatograms, typically, were two to more than four orders of magnitude below the GC-MS MDLs. At least six halogenated VOCs were detected in all of the water samples analyzed by GC-ECD, although one or more VOCs were detected in only 43% of the water samples analyzed by GC-MS. In nearly all of the samples, VOC concentrations were very low and presented no known health risk. Most of the low-level VOC detections indicated post-1940s recharge, or mixtures of recharge that contained a fraction of post-1940s water. Concentrations of selected halogenated VOCs in groundwater from natural and anthropogenic atmospheric sources were estimated and used to recognize water samples that are being impacted by nonatmospheric sources. A classification is presented to perform vulnerability assessments at the scale of individual wells using the number of halogenated VOC detections and total dissolved VOC concentrations in samples of untreated drinking water. The low-level VOC detections are useful in vulnerability assessments, particularly for samples in which no VOCs are detected by GC-MS analysis.

In this study, a new stochastic model for the propagation analysis of fluctuations in rainfall to soil water dynamics is proposed. Based on a lumped conceptualization of soil water dynamics with rainfall forcings, which are incorporated by a simple stochastic point rainfall model, a model is derived by using cumulant expansion theory from a stochastic differential equation. The advantage of the model is to provide the probabilistic solution in the form of a probability density function (PDF), from which one can find the ensemble average behavior of the system. Steady-state PDF of soil water is analytically obtained and analyzed for different climate, soil, and vegetation conditions. The city of Daegue in Korea, which represents the driest parts of the Korean, Peninsula, is applied for a case study and the result shows that the analytically derived steady-state soil water PDF can make a good agreement to the numerically obtained steady-state PDF from a lumped conceptualization model of soil water dynamics. From this agreement, the steady-state analysis is thought to be appropriate for the study of soil water dynamics where the seasonality of rainfall is not very significant. It is also shown that the fluctuations in rainfall tend to increase the variance of soil water dynamics, while the change of rainfall amount can shift the mode of PDF. General features for the PDFs as a function of different loss and soil characteristics are the decrease of soil water with loss rate and soil water storage capacity. The major conclusion, however, is that the proposed simplified stochastic soil water dynamic model for dry years in the Korean Peninsula can provide quite a reasonable explanation in the main soil water probabilistic properties when the rainfall variability is the only consideration.

The applicability of the kinematic wave (KW) and diffusive wave (DW) approximations was investigated for steady flow in prismatic channels by using a second-order two-step Lax-Wendroff numerical scheme coupled with the characteristic method at the boundaries. Two types of downstream boundary conditions, critical-flow depth and zero-flow depth gradient, were considered together with the condition of discharge hydrograph reaching the steady state at the upstream end. The role of inertial, pressure, friction, and gravity forces was investigated for 16 test cases defined through the kinematic wave number $K$ and the Froude number ${\mathsf{F}}_0$ , whose range was assumed to be (3–30) and (0.1–1), respectively. Errors were computed by comparing the steady dimensionless profiles of the flow depth with those estimated by the dynamic wave solution. The accuracy of the two approximations was assessed through the mean value $\epsilon$ of the magnitudes of errors computed for the channel region where the solution was not significantly influenced by the boundary conditions. For critical flow at the downstream end and for $\epsilon$ less than 5%, the KW approximation was reasonably accurate for $K{\mathsf{F}}_0^2⩾1.4$ , whereas the DW solution for $K{\mathsf{F}}_0^2>0.6$ . However, close to the downstream end, the KW approximation gave large errors in flow depth, indicating that if an accurate solution there was needed, the KW solution should not be used. For the DW approximation, the maximum error in the flow depth also occurred close to the downstream end; for the lowest $K$ and ${\mathsf{F}}_0$ values it reached 13%. On the other hand, under the steady flow condition and zero-flow depth gradient at the downstream end, both the diffusive solution and the kinematic solution were found reasonably accurate for the $K$ and ${\mathsf{F}}_0$ values investigated. Therefore, the rule adopted for the critical depth during steady flow also holds for the zero-flow depth gradient.

The applicability of the kinematic wave (KW) approximation was investigated for unsteady flow in prismatic channels. Each of the 16 cases analyzed under steady flow conditions by Moramarco et al. (2008) was now perturbed such that synthetic discharge hydrographs varying around the steady value $Q_0$ and characterized by different values of the wave period $T$ and steady wave travel times, $T_0^{\prime }$ , were obtained. Therefore, based on the kinematic wave number $K$ and steady Froude number ${\mathsf{F}}_0$ , a set of 224 experimental tests were carried out and the KW accuracy was investigated by routing synthetic discharge hydrographs. In this case, the dynamic wave solution DYW was also considered as a benchmark and adopting the critical-flow depth at the downstream end. The performance of KW was assessed using different accuracy measures: (a) errors in dimensionless maximum flow depth along the channel ${\epsilon }_{\max }$ ; (b) explained variance ${\mathrm{NS}}_Q$ on discharge hydrographs at the outlet section; and (c) errors in peak discharge ${\epsilon }_{Q_p}$ and water level ${\epsilon }_{h_p}$ at the downstream channel end, and errors in time to peak discharge ${\epsilon }_{t_{Q_p}}$ and water level ${\epsilon }_{t_{h_p}}$ always at the downstream end. Based on these KW accuracy measures, different scenarios for the KW applicability were found as a function of the quantities $K{\mathsf{F}}_0^2$ and $T∕T_0^{\prime }$ . It was found that the KW applicability depended on the accuracy measure of interest and different criteria were accordingly defined. Moreover, the comparison between the proposed KW applicability criteria and the existing ones shows that these latter tend to limit the KW application and, hence, they have to be used with caution. This insight was also inferred from an analysis of flood events that occurred along an equipped branch of the upper Tiber River in central Italy. Therefore, also based on the real case study, it was shown that there is not a single rule for the KW applicability but different criteria can be defined, taking care, however, that their application strictly depends on the selected accuracy measure.

To simulate a runoff hydrograph from an overland plane or from a catchment that is subject to natural rainfall, the use of a computer model is essential. To develop such a model, among other parameters, the modeler is required to specify rainfall interval, rainfall data for that interval, and Manning’s roughness coefficient (Manning’s $n$ ) of the plane or catchment surface. To evaluate Manning’s $n$ for runoff simulation, it is common to use the hydrograph fitting technique. With this technique, the simulated hydrographs are actually dependent on the rainfall data and, hence, the rainfall interval. The Manning’s $n$ is, therefore, also dependent on the rainfall interval. In this technical note, using rainfall and runoff data over a concrete plane, a concrete catchment, and an asphalt plane, the optimum rainfall interval and the corresponding optimum Manning’s $n$ have been evaluated. Five rainfall intervals were used in the evaluation, which ranged from $0.25\min \text{to}4.0\min$ . The evaluation shows that: (1) for cases where the rainfall interval is shorter than the time of concentration, the effect of rainfall interval on the optimum Manning’s $n$ is small in that they share a common optimum Manning’s $n$ . The evaluated optimum Manning’s $n$ are all consistent with the published recommended values. (2) For cases where the rainfall interval is longer than the time of concentration, the evaluated optimum Manning’s $n$ are larger than those for cases where the rainfall interval is shorter than the time of concentration. (3) A comparison of simulated hydrographs with observed hydrographs shows that the simulated hydrographs are significantly closer to the observed hydrographs for cases where the rainfall interval is shorter than the time of concentration. Further, for the cases where the rainfall interval is equal to or longer than the time of concentration, there is a tendency for the simulated hydrographs to reach equilibrium, which never occurs in the observed hydrographs. (4) As a balance between the extra effort and space required to collect and store rainfall data of a shorter interval and the goodness of fit between the simulated and observed hydrographs, a rainfall interval equal to about half of the time of concentration is considered optimum.