Vertical Groundwater Fluxes Research Articles

Analytical solution for estimating transient vertical groundwater flux from temperature-depth profiles

Many studies have developed analytical models for describing the subsurface heat transfer to estimate the infiltration rate, that is, the vertical groundwater flux (VGF). These studies assumed that the VGF was constant in time to acquire mathematical tractability. However, the assumption generally violates the natural system and cannot delineate the transient behavior of the VGF. Such an illogical assumption would contribute to unreliable estimation of the VGF from field-observed temperature-depth (TD) profiles. To accurately estimate VGF based on an analytical model, this study develops a new analytical heat-transfer model and a novel inverse approach to estimate the transient VGF. The analytical model is verified by a numerical model based on the finite-element method. We further perform the sensitivity analysis to the analytical model to examine the temperature response to changes in the thermal parameters. It reveals that thermal dispersion has a minor effect on temperature. The results of the numerical experiment show that the present approach can yield the correct transient VGF. Finally, the present approach is applied to estimate the transient VGF for a field case study. The results show that the predicted VGF and the measured VGF are almost consistent, revealing that our method is feasible for the estimation of VGF in the field.

Inferring Aquitard Hydraulic Conductivity Using Transient Temperature‐Depth Profiles Impacted by Ground Surface Warming

AbstractAquitard hydraulic properties are notoriously difficult to assess, yet accurate aquitard hydraulic conductivity estimates are critical to quantify recharge and discharge to and from semi‐confined aquifer systems via hydraulic head gradients. Such flux quantification is required to evaluate the risks of aquifer exploitation by groundwater abstraction and aquifer vulnerability to surface contamination. In this study, we consider a regionally important aquitard and compare existing hydraulic conductivity estimates obtained through traditional methods to those inferred from long‐term hydraulic head monitoring and thermally derived vertical groundwater fluxes (0.04–0.25 m/y). We estimate the fluxes using numerical modeling to analyze the propagation of decadal climate signals into temperature‐depth profiles and fitting the simulated and observed inflection point depths (location of minimum temperature). Results suggest that climate‐disturbed temperature‐depth profiles paired with multi‐level head data can yield accurate vertical fluxes and aquitard hydraulic conductivities. This approach for characterizing groundwater systems and quantifying flows to and from sedimentary aquifers is more efficient but yields results that are comparable to conventional methods.

Seasonal to Decadal Variability in Focused Groundwater and Contaminant Discharge along a Channelized Stream

AbstractFocused groundwater discharge to streams is problematic at contaminated sites because high fluxes can limit natural attenuation in the hyporheic zone. However, information on location, spatial evolution, and temporal persistence of springs in unlithified sediments over multiyear time scales is limited. We examine discharge at point (~1‐m) to reach (~300‐m) scales along a stream that intercepts trichloroethene and technetium‐99 plumes from a Superfund site. During 2011 to 2012, we seasonally monitored stream and spring flow and contaminant concentrations, along with probing streambed temperatures on a grid in winter and summer, building on prior monitoring during 1999 to 2002. Baseflow measured by both gauging and dye dilution generally increased with distance downstream, and stream and spring discharge varied seasonally, from minima in October to January to maxima in February to June. Thermal anomalies identified by probing occupied approximately 3% to 6% of the reach and typically coincided with visible springs or seeps. Locations of anomalies were similar to those identified in summer 2002, although some orifices disappeared and others emerged. Vertical groundwater fluxes calculated from probing tended to be less than net fluxes calculated from stream discharge, perhaps in part because the assumption of one‐dimensional, steady‐state flow in calculating point fluxes was simplistic. Maximum contaminant concentrations and fluxes decreased between 1999 to 2001 and 2011 to 2012 as a result of partial capture by an upgradient pump‐and‐treat system. Our findings confirm that springs in unlithified sediments can remain stationary within a few meters over decadal time scales, and seasonal variability in discharge can be greater than decadal variability.

Evaluation of vertical groundwater flux from borehole temperatures: a case study in the Leizhou Peninsula, South China

A least-square solver is presented for groundwater flux estimation using the one-dimensional conduction–advection equation, which was numerically solved using the MacCormack scheme. This approach was utilized to estimate groundwater fluxes from observed borehole temperatures under conditions of surface warming in both rural and urban areas in Leizhou Peninsula, China. The estimated groundwater recharge rate is 0.423 m/year, while the discharge rate is 0.269 m/year. The groundwater recharge rates were obtained in the north part of the study area, and the discharge locations were on Nansan, Donghai and Luzhou Islands, which fit favorably with the regional groundwater flow pattern. Relatively high correlations and low root mean square errors were detected between observed and computed borehole temperature–depth profiles, indicating the estimation is reasonable. The misfit between the observed and computed data might be associated with the uneven distribution of ground surface temperature (GST) and vertical soil heterogeneity. The urban heat island effect contributes an increment of 0.006 °C per year to the GST in the study area, which induces a 0.96 °C higher subsurface temperature in both recharge and discharge areas. The utilization of surface air temperature (SAT) as the upper boundary might underestimate groundwater fluxes, which might lead to inaccurate information for regional groundwater resource management.

Using transient temperature–depth profiles to assess vertical groundwater flow across semi-confining layers in the Chianan coastal plain aquifer systeme, southern Taiwan

The quantification of vertical groundwater fluxes across semi-confining layers is fundamental to evaluate groundwater recharge and discharge rates to and from aquifer systems. Methods to estimate vertical groundwater fluxes from temperature–depth profiles have been available since the 1960s. While some methodologies assume steady-state conditions, changes in land-surface temperatures as well as hydrogeological conditions can lead to transient heat flow conditions. Indeed, many studies have indicated that transient temperatures in deeper confined aquifers are widespread. A study is presented that uses transient-temperature–depth curves obtained from groundwater observation wells in the Chianan coastal plain in southern Taiwan. In this area, sedimentary aquifer systems consist of a stack of alternating sand and mud layers, over several hundred meters in thickness. Groundwater has been abstracted from these aquifers for decades, resulting in large hydraulic gradients between the shallow and deeper aquifers. Hence, vertical groundwater flow is likely enhanced across finer-grained, semi-confining units. A set of temperature–depth profiles is available from this area. Constrained by these profiles, numerical models of one-dimensional transient heat transfer were used to infer vertical fluxes of 3.3 × 10−8 to 3.9 × 10−8 m/s using thermal data from 2013 to 2016. An analytical solution was also employed that assumes steady-state conditions. Calculated fluxes using the latter approach were lower, at approximately 1.1 × 10−8 to 1.6 × 10−8 m/s. The study suggests that vertical fluxes derived from using Bredehoeft and Papadopulos’s analytical solutions result in underestimates of actual vertical seepage rates across aquitards.

Vertical groundwater flux estimation from borehole temperature profiles by a numerical model, RFLUX

AbstractWe developed a numerical model, RFLUX, which uses the heat tracer method for vertical groundwater flux estimation, and applied it to the Leizhou Peninsula, South China, to provide information to inform local groundwater resource utilization and management. The temperature–depth (TD) profiles of 24 boreholes, along with the observed ground surface temperature (GST) and surface air temperature (SAT) series in recent decades, were collected in this area. Underground TD data demonstrated the capacity to identify groundwater flow patterns, and local GST and SAT data demonstrated a strong correlation with each other over monthly, seasonal, and annual scales. In the RFLUX model, the average GST and SAT series were applied as an upper boundary condition, and a nonlinear initial condition was set using an analytical solution from the literature. The model results of selected TD profiles demonstrated that the annual vertical groundwater flux was about 0.15 m a−1, which tended to be overestimated if a linear initial condition was used. This model can be easily applied with minor modifications, considering its clear purpose and simplicity.

Hydrogeochemical controls on brook trout spawning habitats in a coastal stream.

Brook trout (Salvelinus fontinalis) spawn in fall and overwintering egg development can benefit from stable, relatively warm temperatures in groundwater-seepage zones. However, eggs are also sensitive to dissolved oxygen concentration, which may be reduced in discharging groundwater (i.e., seepage). We investigated a 2 km reach of the coastal Quashnet River in Cape Cod, Massachusetts, USA, to relate preferred fish spawning habitats to geology, geomorphology, and discharging groundwater geochemistry. Thermal reconnaissance methods were used to locate zones of rapid groundwater discharge, which were predominantly found along the central channel of a wider stream valley section. Pore-water chemistry and temporal vertical groundwater flux were measured at a subset of these zones during field campaigns over several seasons. Seepage zones in open-valley sub-reaches generally showed suboxic conditions and higher dissolved solutes compared to the underlying glacial outwash aquifer. These discharge zones were cross-referenced with preferred brook trout redds and evaluated during 10 years of observation, all of which were associated with discrete alcove features in steep cutbanks, where stream meander bends intersect the glacial valley walls. Seepage in these repeat spawning zones was generally stronger and more variable than in open-valley sites, with higher dissolved oxygen and reduced solute concentrations. The combined evidence indicates that regional groundwater discharge along the broader valley bottom is predominantly suboxic due to the influence of near-stream organic deposits; trout show no obvious preference for these zones when spawning. However, the meander bends that cut into sandy deposits near the valley walls generate strong oxic seepage zones that are utilized routinely for redd construction and the overwintering of trout eggs. Stable water isotopic data support the conclusion that repeat spawning zones are located directly on preferential discharges of more localized groundwater. In similar coastal systems with extensive valley peat deposits, the specific use of groundwater-discharge points by brook trout may be limited to morphologies such as cutbanks, where groundwater flow paths do not encounter substantial buried organic material and remain oxygen-rich.

Tracking the Subsurface Signal of Decadal Climate Warming to Quantify Vertical Groundwater Flow Rates

AbstractSustained ground surface warming on a decadal time scale leads to an inversion of thermal gradients in the upper tens of meters. The magnitude and direction of vertical groundwater flow should influence the propagation of this warming signal, but direct field observations of this phenomenon are rare. Comparison of temperature‐depth profiles in boreholes in the Veluwe area, Netherlands, collected in 1978–1982 and 2016 provided such direct measurement. We used these repeated profiles to track the downward propagation rate of the depth at which the thermal gradient is zero. Numerical modeling of the migration of this thermal gradient “inflection point” yielded estimates of downward groundwater flow rates (0–0.24 m a−1) that generally concurred with known hydrogeological conditions in the area. We conclude that analysis of inflection point depths in temperature‐depth profiles impacted by surface warming provides a largely untapped opportunity to inform sustainable groundwater management plans that rely on accurate estimates of long‐term vertical groundwater fluxes.

Interpreting Repeated Temperature‐Depth Profiles for Groundwater Flow

AbstractTemperature can be used to trace groundwater flows due to thermal disturbances of subsurface advection. Prior hydrogeological studies that have used temperature‐depth profiles to estimate vertical groundwater fluxes have either ignored the influence of climate change by employing steady‐state analytical solutions or applied transient techniques to study temperature‐depth profiles recorded at only a single point in time. Transient analyses of a single profile are predicated on the accurate determination of an unknown profile at some time in the past to form the initial condition. In this study, we use both analytical solutions and a numerical model to demonstrate that boreholes with temperature‐depth profiles recorded at multiple times can be analyzed to either overcome the uncertainty associated with estimating unknown initial conditions or to form an additional check for the profile fitting. We further illustrate that the common approach of assuming a linear initial temperature‐depth profile can result in significant errors for groundwater flux estimates. Profiles obtained from a borehole in the Veluwe area, Netherlands in both 1978 and 2016 are analyzed for an illustrative example. Since many temperature‐depth profiles were collected in the late 1970s and 1980s, these previously profiled boreholes represent a significant and underexploited opportunity to obtain repeat measurements that can be used for similar analyses at other sites around the world.

Ambient groundwater flow diminishes nitrate processing in the hyporheic zone of streams

AbstractModeling and experimental studies demonstrate that ambient groundwater reduces hyporheic exchange, but the implications of this observation for stream N‐cycling is not yet clear. Here we utilize a simple process‐based model (the Pumping and Streamline Segregation or PASS model) to evaluate N‐cycling over two scales of hyporheic exchange (fluvial ripples and riffle‐pool sequences), ten ambient groundwater and stream flow scenarios (five gaining and losing conditions and two stream discharges), and three biogeochemical settings (identified based on a principal component analysis of previously published measurements in streams throughout the United States). Model‐data comparisons indicate that our model provides realistic estimates for direct denitrification of stream nitrate, but overpredicts nitrification and coupled nitrification‐denitrification. Riffle‐pool sequences are responsible for most of the N‐processing, despite the fact that fluvial ripples generate 3–11 times more hyporheic exchange flux. Across all scenarios, hyporheic exchange flux and the Damköhler Number emerge as primary controls on stream N‐cycling; the former regulates trafficking of nutrients and oxygen across the sediment‐water interface, while the latter quantifies the relative rates of organic carbon mineralization and advective transport in streambed sediments. Vertical groundwater flux modulates both of these master variables in ways that tend to diminish stream N‐cycling. Thus, anthropogenic perturbations of ambient groundwater flows (e.g., by urbanization, agricultural activities, groundwater mining, and/or climate change) may compromise some of the key ecosystem services provided by streams.

Uncertainties in vertical groundwater fluxes from 1‐D steady state heat transport analyses caused by heterogeneity, multidimensional flow, and climate change

AbstractSteady state 1‐D analytical solutions to estimate groundwater fluxes from temperature profiles are an attractive option because they are simple to apply, with no complex boundary or initial conditions. Steady state solutions have been applied to estimate both aquifer scale fluxes as well as to estimate groundwater discharge to streams. This study explores the sources of uncertainty in flux estimates from regional scale aquifers caused by sensor precision, aquifer heterogeneity, multidimensional flow and variations in surface temperature due to climate change. Synthetic temperature profiles were generated using 2‐D groundwater flow and heat transport models with homogeneous and heterogeneous hydraulic and thermal properties. Temperature profiles were analyzed assuming temperature can be determined with a precision between 0.1°C and 0.001°C. Analysis of synthetic temperature profiles show that the Bredehoeft and Papadopulos (1965) method can provide good estimates of the mean vertical Darcy flux over the length of the temperature profile. Reliable flux estimates were obtained when the ratio of vertical to horizontal flux was as low as 0.1, and in heterogeneous media, providing that temperature at the upper boundary was constant in time. However, temporal increases in surface temperature led to over‐estimation of fluxes. Overestimates increased with time since the onset of, and with the rate of surface warming. Overall, the Bredehoeft and Papadopulos (1965) method may be more robust for the conditions with constant temperature distributions than previously thought, but that transient methods that account for surface warming should be used to determine fluxes in shallow aquifers.

Performance of different assessment methods to evaluate contaminant sources and fate in a coastal aquifer.

The present study deals with the application of different monitoring techniques and numerical models to characterize coastal aquifers affected by multiple sources of contamination. Specifically, equivalent freshwater heads in 243 monitoring wells were used to reconstruct the piezometric map of the studied aquifer; flow meter tests were carried out to infer vertical groundwater fluxes at selected wells; deuterium and oxygen isotopes were used to identify the groundwater origin, and tritium was analyzed to estimate the residence time; compound-specific isotope analyses and microbial analyses were employed to track different sources of contamination and their degradation; numerical modelling was used to estimate and verify groundwater flow direction and magnitude throughout the aquifer. The comparison of the information level for each technique allowed determining which of the applied approaches showed the best results to locate the possible sources and better understanding of the fate of the contaminants. This study reports a detailed site characterization process and outcomes for a coastal industrial site, where a comprehensive conceptual model of pollution and seawater intrusion has been built using different assessment methods. Information and results from this study encourages combining different methods for the design and implementation of the monitoring activities in real-life coastal contaminated sites in order to develop an appropriate strategy for control and remediation of the contamination.

Combining flux estimation techniques to improve characterization of groundwater–surface-water interaction in the Zenne River, Belgium

The management of urban rivers which drain contaminated groundwater is suffering from high uncertainties regarding reliable quantification of groundwater fluxes. Independent techniques are combined for estimating these fluxes towards the Zenne River, Belgium. Measured hydraulic gradients, temperature gradients in conjunction with a 1D-heat and fluid transport model, direct flux measurement with the finite volume point dilution method (FVPDM), and a numerical groundwater flow model are applied, to estimate vertical and horizontal groundwater fluxes and groundwater–surface-water interaction. Hydraulic gradient analysis, the temperature-based method, and the groundwater flow model yielded average vertical fluxes of –61, –45 and –40 mm/d, respectively. The negative sign indicates upward flow to the river. Changes in exchange fluxes are sensitive to precipitation but the river remained gaining during the examined period. The FVPDM, compared to the groundwater flow model, results in two very high estimates of the horizontal Darcy fluxes (2,600 and 500 mm/d), depending on the depth of application. The obtained results allow an evaluation of the temporal and spatial variability of estimated fluxes, thereby helping to curtail possible consequences of pollution of the Zenne River as final receptor, and contribute to the setup of a suitable remediation plan for the contaminated study site.

Spatial and temporal connections in groundwater contribution to evaporation

Abstract. In climate models, lateral terrestrial water fluxes are usually neglected. We estimated the contribution of vertical and lateral groundwater fluxes to the land surface water budget at a subcontinental scale, by modeling convergence of groundwater and surfacewater fluxes. We present a hydrological model of the entire Danube Basin at 5 km resolution, and use it to show the importance of groundwater for the surface climate. Results show that the contribution of groundwater to evaporation is significant, and can locally be higher than 30 % in summer. We demonstrate through the same model that this contribution also has important temporal characteristics. A wet episode can influence groundwater contribution to summer evaporation for several years afterwards. This indicates that modeling groundwater flow has the potential to augment the multi-year memory of climate models. We also show that the groundwater contribution to evaporation is local by presenting the groundwater travel times and the magnitude of groundwater convergence. Throughout the Danube Basin the lateral fluxes of groundwater are negligible when modeling at this scale and resolution. This suggests that groundwater can be adequately added in land surface models by including a lower closed groundwater reservoir of sufficient size with two-way interaction with surface water and the overlying soil layers.

A numerical model for estimating groundwater flux from subsurface temperature profiles

AbstractA simple numerical model is presented for estimating vertical groundwater flux from transient subsurface temperature profiles obtained from field measurements. The model developed utilizes the MacCormack scheme, which is based on the Finite Difference Method (FDM), for solving the governing partial differential equation of convection–diffusion heat transport with appropriate initial and boundary conditions within the subsurface. In order to validate the model, numerical solutions obtained for the study area located in the Nagoka plain, Japan are compared with the published measured data and results obtained by others. Results obtained show good agreement and fit the observed data with a correlation coefficient, R2, of 0·88. The estimated groundwater flux is 1·85 × 10−7 m s−1. Sensitivity analyses were also carried out to investigate the effect of variations in groundwater fluxes, thermal properties and the annual thermal variability due to climatic changes on the transient subsurface temperature profiles and to have a better understanding of the subsurface thermal dynamics. A substantial effect of annual climatic variability is observed on the temporal distributions of temperature depth profiles, and a better estimate of thermal parameters is required to estimate vertical groundwater flux. The largest change in subsurface temperature depth profiles due to groundwater flux over a year is within ± 4 °C. The influence of groundwater flux on subsurface temperature distributions in space and time may be more pronounced in areas where the top of the saturated layer fluctuates considerably. Variation in thermal diffusivity results in temperature change up to ± 1·5% and may cause change in groundwater flux estimate by ± 18%. The model presented has merits over analytical solutions (type curve matching techniques) in terms of suitability and applicability to real field problems, and can be a good asset to hydrological models as quantifying groundwater recharge or deducing it from other quantities, such as rainfall, evapotranspiration and runoff, is often complicated. Copyright © 2007 John Wiley & Sons, Ltd.

Heat flow and vertical groundwater flux in deep fractured basement rock in Nara Basin, southwest Japan

The temperature measurement in a borehole that intersects the flow zone is one of the effective methods to detect the vertical flow of water. Geothermal gradients, thermal conductivity, and heat flow have been assessed for the crystalline basement and the overlying sedimentary cover in the study area. The geothermal gradient in sedimentary cover ranges from 0.83-3.87 °C/100 m, whereas in the basement rock it ranges from 2.49-3.38 °C/100 m. The heat flow values in sedimentary cover and basement rocks lies between 13.46 and 56.87, and 79.89 and 108.63 mW/m2, respectively. Vertical specific discharge of groundwater flow in the fractured basement rock is estimated for different depth intervals. Groundwater in the unconsolidated sediment and at most places in fractured rocks is moving vertically down. However, at some locations, water is moving upward especially at greater depth intervals. The calculated vertical specific discharges reflect the relative degree of fracturing in the basement rocks at the corresponding depth intervals.

Disturbances of temperature‐depth profiles due to surface climate change and subsurface water flow: 1. An effect of linear increase in surface temperature caused by global warming and urbanization in the Tokyo Metropolitan Area, Japan

A series of type curves is presented for evaluating vertical groundwater fluxes under the condition of a linear increase in surface temperature. The depths of minimum groundwater temperature in the temperature‐depth profiles indicate the magnitude of the downward groundwater flux. The type curve method has been applied to the subsurface thermal regime observed in Tokyo metropolitan area, Japan, to estimate the vertical groundwater fluxes under the condition of surface warming caused by global warming and urbanization. The groundwater fluxes obtained from the type curves and the depths of minimum groundwater temperature agree well with the values obtained from the other studies in the Tokyo metropolitan area. The inversion due to the surface warming could be a good tracer to detect the groundwater flow system.

Disturbances of temperature‐depth profiles due to surface climate change and subsurface water flow: 2. An effect of step increase in surface temperature caused by forest clearing in southwest western Australia

A series of type curves is presented for estimating vertical groundwater fluxes under the condition of a step increase in surface temperature. The depths of minimum groundwater temperature in temperature‐depth profiles are used as an indicator of the magnitude of the downward groundwater fluxes. The type curve method has been applied to the subsurface thermal regime observed in experimental catchments in the Collie River Basin in southwest Western Australia to estimate the vertical groundwater fluxes under the condition of surface warming caused by land cover change from forest to agriculture. The groundwater fluxes obtained from the type curves and the depths of minimum groundwater temperature in temperature‐depth profiles agree well with the values obtained from the other studies.

Mixing and stretching efficiency in steady and unsteady groundwater flows

Mixing is the physical process through which solute is spread into a fluid by the stretching and folding of material lines and surfaces. Mixing, as compared to dilution, is important to solute spreading by groundwater because it operates on much shorter timescales than does dilution, and it provides the increased plume boundary area and high local concentration gradients that promote effective solute dilution. In this paper, the mixing process is investigated theoretically for subsurface tracer plume movement, using as heuristic examples both steady and unsteady groundwater flows in a perfectly stratified aquifer whose properties mimic those of the sand aquifer at the Borden site. It is shown that the stretching efficiency, a parameter that characterizes the effectiveness of mixing, is largest at transitions between regions of highly contrasting hydraulic conductivity and, more broadly, that pronounced spatial variability in the hydraulic conductivity is conducive to good mixing because of the periodic resurgences in material line stretching that it causes. Unsteady groundwater flow resulting from a decrease in vertical groundwater flux with time leads to greater rates of material line stretching than do steady flows, whereas little difference from the steady flow case occurs for unsteady groundwater flow under a time‐varying horizontal hydraulic head gradient. Overall, pronounced spatial variability in the hydraulic conductivity is the most important contributor to good mixing of a tracer solute plume, but highly effective mixing requires additional physical conditions that induce chaotic solute pathlines.

Evaluation of vertical groundwater fluxes and thermal properties of aquifers based on transient temperature‐depth profiles

A series of type curves is presented for estimating vertical groundwater fluxes in relatively shallow aquifers by using seasonal changes in groundwater temperature‐depth profiles. Vertical groundwater fluxes are estimated by fitting a dimensionless parameter to the type curves when the amplitude of annual variations of groundwater temperature at several depths and the thermal diffusivity of the aquifer are known or measured. Both upward and downward groundwater fluxes estimated by fitting temperatures observed in Nagaoka plain, Japan to the type curves agree well with the fluxes calculated from hydraulic conductivity and hydraulic gradient data. Measurements of seasonal changes in groundwater temperature and hydraulic gradients were analyzed to estimate the thermal diffusivity of the aquifer in situ that is close to the value reported in the literature.