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1.
A new method was developed for analysing and delineating streambed water fluxes, flow conditions and hydraulic properties using coiled fibre‐optic distributed temperature sensing or closely spaced discrete temperature sensors. This method allows for a thorough treatment of the spatial information embedded in temperature data by creating a matrix visualization of all possible sensor pairs. Application of the method to a 5‐day field dataset reveals the complexity of shallow streambed thermal regimes. To understand how velocity estimates are affected by violations of assumptions of one‐dimensional, saturated, homogeneous flow and to aid in the interpretation of field observations, the method was also applied to temperature data generated by numerical models of common field conditions: horizontal layering, presence of lateral flow and variable streambed saturation. The results show that each condition creates a distinct signature visible in the triangular matrices. The matrices are used to perform a comparison of the behaviour of one‐dimensional analytical heat‐tracing models. The results show that the amplitude ratio‐based method of velocity calculation leads to the most reliable estimates. The minimum sensor spacing required to obtain reliable velocity estimates with discrete sensors is also investigated using field data. The developed method will aid future heat‐tracing studies by providing a technique for visualizing and comparing results from fibre‐optic distributed temperature sensing installations and testing the robustness of analytical heat‐tracing models. Copyright © 2016 John Wiley & Sons, Ltd.  相似文献   

2.
Management of water resources in alluvial aquifers relies mainly on understanding interactions between hydraulically connected streams and aquifers. Numerical models that simulate this interaction often are used as decision support tools for water resource management. However, the accuracy of numerical predictions relies heavily on unknown system parameters (e.g., streambed conductivity and aquifer hydraulic conductivity), which are spatially heterogeneous and difficult to measure directly. This paper employs an ensemble smoother to invert groundwater level measurements to jointly estimate spatially varying streambed and alluvial aquifer hydraulic conductivity along a 35.6‐km segment of the South Platte River in Northeastern Colorado. The accuracy of the inversion procedure is evaluated using a synthetic experiment and historical groundwater level measurements, with the latter constituting the novelty of this study in the inversion and validation of high‐resolution fields of streambed and aquifer conductivities. Results show that the estimated streambed conductivity field and aquifer conductivity field produce an acceptable agreement between observed and simulated groundwater levels and stream flow rates. The estimated parameter fields are also used to simulate the spatially varying flow exchange between the alluvial aquifer and the stream, which exhibits high spatial variability along the river reach with a maximum average monthly aquifer gain of about 2.3 m3/day and a maximum average monthly aquifer loss of 2.8 m3/day, per unit area of streambed (m2). These results demonstrate that data assimilation inversion provides a reliable and computationally affordable tool to estimate the spatial variability of streambed and aquifer conductivities at high resolution in real‐world systems.  相似文献   

3.
Estimating streambed parameters for a disconnected river   总被引:1,自引:0,他引:1       下载免费PDF全文
Evaluation of stream–aquifer interaction and water balance for a catchment often requires specific information on streambed parameters, such as streambed hydraulic conductivity, seepage flux across the streambed and so on. This paper describes a simple, inexpensive instrument that is used to measure these streambed parameters under the condition of a stream disconnected from groundwater. Our method includes a seepage cylinder for simulation of river water depth. The proposed method was applied to estimate the vertical hydraulic conductivity of a streambed and the changes in vertical seepage rate from stream to groundwater with varied stream water depth in the Manasi River of Xinjiang Uygur Autonomous Region, China. The vertical hydraulic conductivities of the streambed determined from 12 sites along the Manasi River vary from 1.01 to 29.m/day where the stream disconnects from the groundwater. The experimental results suggest that there are two kinds of relations between the vertical seepage rate and the simulated stream water depth. One is a linear relation between the two variables with low Reynolds numbers (less than 10); the other is a nonlinear relation (exponential relation) between the two variables with larger Reynolds numbers (greater than 10). This second relationship is quite different from the traditional model that usually calculates the vertical seepage rate from stream to groundwater under the condition of disconnection using a linear relation (Darcy's Law). Our results suggest that a linear relation can only be used for a limited range of river water depth. This method gives a convenient tool for rapidly estimating the streambed hydraulic conductivity and the changes in the vertical seepage rate across streambed with varied stream water depths for the case of a stream disconnected from groundwater. Copyright © 2013 John Wiley & Sons, Ltd.  相似文献   

4.
This study investigates spatial patterns and temporal dynamics of aquifer–river exchange flow at a reach of the River Leith, UK. Observations of sub‐channel vertical hydraulic gradients at the field site indicate the dominance of groundwater up‐welling into the river and the absence of groundwater recharge from surface water. However, observed hydraulic heads do not provide information on potential surface water infiltration into the top 0–15 cm of the streambed as these depths are not covered by the existing experimental infrastructure. In order to evaluate whether surface water infiltration is likely to occur outside the ‘window of detection’, i.e. the shallow streambed, a numerical groundwater model is used to simulate hydrological exchanges between the aquifer and the river. Transient simulations of the successfully validated model (Nash and Sutcliff efficiency of 0·91) suggest that surface water infiltration is marginal and that the possibility of significant volumes of surface water infiltrating into non‐monitored shallow streambed sediments can be excluded for the simulation period. Furthermore, the simulation results show that with increasing head differences between river and aquifer towards the end of the simulation period, the impact of streambed topography and hydraulic conductivity on spatial patterns of exchange flow rates decreases. A set of peak flow scenarios with altered groundwater‐surface water head gradients is simulated in order to quantify the potential for surface water infiltration during characteristic winter flow conditions following the observation period. The results indicate that, particularly at the beginning of peak flow conditions, head gradients are likely to cause substantial increase in surface water infiltration into the streambed. The study highlights the potential for the improvement of process understanding of hyporheic exchange flow patterns at the stream reach scale by simulating aquifer‐river exchange fluxes with a standard numerical groundwater model and a simple but robust model structure and parameterization. Copyright © 2011 John Wiley & Sons, Ltd.  相似文献   

5.
Interactions of surface water and groundwater (SW–GW) play an important role in the physical, chemical, and ecological processes of riparian zones. The main objective of this study was to describe the two‐dimensional characteristics of riverbank SW–GW interactions and to quantify their influence factors. The SW–GW exchange fluxes for six sections (S1 to S6) of the Qinhuai River, China, were estimated using a heat tracing method, and field hydrogeological and thermodynamic parameters were obtained via inverse modelling. Global sensitivity analysis was performed to compare the effects of layered heterogeneity of hydraulic conductivity and river stage variation on SW–GW exchange. Under the condition of varied river stage, only the lateral exchange fluxes at S1 apparently decreased during the monitoring period, probably resulting from its relatively higher hydraulic conductivity. Meanwhile, the SW–GW exchanges for the other five sections were quite stable over time. The lateral exchange fluxes were higher than the vertical ones. The riverbank groundwater flow showed different spatial variation characteristics for the six sections, but most of the higher exchange fluxes occurred in the lower area of a section. The section with larger hydraulic conductivity has an apparent dynamic response to surface water and groundwater level differences, whereas lower permeabilities severely reduced the response of groundwater flow. The influence of boundary conditions on SW–GW interactions was restricted to a limited extent, and the impact extent will expand with the increase of peak water level and hydraulic conductivity. The SW–GW head difference was the main influence factors in SW–GW interactions, and the influence of both SW–GW head difference and hydraulic conductivity decreased with an increase of the distance from the surface water boundary. For each layer of riverbank sediment, its hydraulic conductivity had greater influence on its groundwater flow than the other layers, whereas it had negligible effects on its overlying/underlying layers. Consequently, the variations in river stage and hydraulic conductivity were the main factors influencing the spatial and temporal characteristics of riverbank groundwater flow, respectively.  相似文献   

6.
Xunhong Chen 《水文研究》2011,25(2):278-287
Characterization of streambed hydraulic conductivity from the channel surface to a great depth below the channel surface can provide needed information for the determination of stream‐aquifer hydrologic connectedness, and it is also important to river restoration. However, knowledge on the streambed hydraulic conductivity for sediments 1 m below the channel surface is scarce. This study describes a method that was used to determine the distribution patterns of streambed hydraulic conductivity for sediments from channel surface to a depth of 15 m below. The method includes Geoprobe's direct‐push techniques and Permeameter tests. Direct‐push techniques were used to generate the electrical conductivity (EC) logs and to collect sequences of continuous sediment cores from river channels, as well as from the alluvial aquifer connected to the river. Permeameter tests on these sediment cores give the profiles of vertical hydraulic conductivity (Kv) of the channel sediments and the aquifer materials. This method was applied to produce Kv profiles for a streambed and an alluvial aquifer in the Platte River Valley of Nebraska, USA. Comparison and statistical analysis of the Kv profiles from the river channel and from the proximate alluvial aquifer indicates a special pattern of Kv in the channel sediments. This depth‐dependent pattern of Kv distribution for the channel sediments is considered to be produced by hyporheic processes. This Kv‐distribution pattern implied that the effect of hyporheic processes on streambed hydraulic conductivity can reach the sediments about 9 m below the channel surface. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

7.
Characterization of groundwater contaminant source using Bayesian method   总被引:2,自引:1,他引:1  
Contaminant source identification in groundwater system is critical for remediation strategy implementation, including gathering further samples and analysis, as well as implementing and evaluating different remediation plans. Such problem is usually solved with the aid of groundwater modeling with lots of uncertainty, e.g. existing uncertainty in hydraulic conductivity, measurement variance and the model structure error. Monte Carlo simulation of flow model allows the input uncertainty onto the model predictions of concentration measurements at monitoring sites. Bayesian approach provides the advantage to update estimation. This paper presents an application of a dynamic framework coupling with a three dimensional groundwater modeling scheme in contamination source identification of groundwater. Markov Chain Monte Carlo (MCMC) is being applied to infer the possible location and magnitude of contamination source. Uncertainty existing in heterogonous hydraulic conductivity field is explicitly considered in evaluating the likelihood function. Unlike other inverse-problem approaches to provide single but maybe untrue solution, the MCMC algorithm provides probability distributions over estimated parameters. Results from this algorithm offer a probabilistic inference of the location and concentration of released contamination. The convergence analysis of MCMC reveals the effectiveness of the proposed algorithm. Further investigation to extend this study is also discussed.  相似文献   

8.
There are many field techniques used to quantify rates of hyporheic exchange, which can vary in magnitude and direction spatially over distances of only a few metres, both within and between morphological features. We used in‐stream mini‐piezometers and heat transport modelling of stream and streambed temperatures to quantify the rates and directions of water flux across the streambed interface upstream and downstream of three types of in‐stream geomorphic features: a permanent dam, a beaver dam remnant and a stream meander. We derived hyporheic flux estimates at three different depths at six different sites for a month and then paired those flux rates with measurements of gradient to derive hydraulic conductivity (K) of the streambed sediments. Heat transport modelling provided consistent daily flux estimates that were in agreement directionally with hydraulic gradient measurements and also identified vertical heterogeneities in hydraulic conductivity that led to variable hyporheic exchange. Streambed K varied over an order of magnitude (1·9 × 10?6 to 5·7 × 10?5 m/s). Average rates of hyporheic flux ranged from static (q < ±0·02 m/day) to 0·42 m/day. Heat transport modelling results suggest three kinds of flow around the dams and the meander. Copyright © 2010 John Wiley & Sons, Ltd.  相似文献   

9.
Heat as a ground water tracer   总被引:40,自引:0,他引:40  
Anderson MP 《Ground water》2005,43(6):951-968
Heat carried by ground water serves as a tracer to identify surface water infiltration, flow through fractures, and flow patterns in ground water basins. Temperature measurements can be analyzed for recharge and discharge rates, the effects of surface warming, interchange with surface water, hydraulic conductivity of streambed sediments, and basin-scale permeability. Temperature data are also used in formal solutions of the inverse problem to estimate ground water flow and hydraulic conductivity. The fundamentals of using heat as a ground water tracer were published in the 1960s, but recent work has significantly expanded the application to a variety of hydrogeological settings. In recent work, temperature is used to delineate flows in the hyporheic zone, estimate submarine ground water discharge and depth to the salt-water interface, and in parameter estimation with coupled ground water and heat-flow models. While short reviews of selected work on heat as a ground water tracer can be found in a number of research papers, there is no critical synthesis of the larger body of work found in the hydrogeological literature. The purpose of this review paper is to fill that void and to show that ground water temperature data and associated analytical tools are currently underused and have not yet realized their full potential.  相似文献   

10.
11.
Including geophysical data in ground water model inverse calibration   总被引:1,自引:0,他引:1  
Dam D  Christensen S 《Ground water》2003,41(2):178-189
A nonlinear regression method is developed that can be used to estimate parameters of a ground waterflow model from a combination of observations of hydrological variables and observations of geophysical properties that are functionally related with the hydraulic conductivity. The procedure estimates: parameters characterizing the hydraulic conductivity field (e.g., zonal or pilot point values); geophysical properties that have been observed and that are functionally related with the hydraulic conductivity parameters; and a few parameters of the function that relates the hydraulic conductivity parameters with the geophysical properties (the type of function is assumed known). A fidelity factor, sigma(r)2, of a term of the minimized objective function reflects the faith one has in the validity of this functional relationship. The estimation methodology has been tested by means of synthetic models. The experimental results demonstrate that the number of estimated hydraulic conductivity parameters can be increased by adding geophysical observations to the set of hydrological observations that are traditionally used for model calibration. The improvement of the estimated hydraulic conductivity field and the simulated hydraulic head field can be significant but is dependent on the number, the locations, and the uncertainty of geophysical observations. The sensitivity of the estimation results to the value of sigma(r) is small for the studied problems except when the uncertainty of geophysical observations is high. In the latter case, a large sigma(r) value was found to be optimal to avoid that hydraulic conductivity estimates are closely tied to corresponding but highly uncertain geophysical observations.  相似文献   

12.
Simultaneous measurement of coupled water, heat, and solute transport in unsaturated porous media is made possible with the multi-functional heat pulse probe (MFHPP). The probe combines a heat pulse technique for estimating soil heat properties, water flux, and water content with a Wenner array measurement of bulk soil electrical conductivity (ECbulk). To evaluate the MFHPP, we conducted controlled steady-state flow experiments in a sand column for a wide range of water saturations, flow velocities, and solute concentrations. Flow and transport processes were monitored continuously using the MFHPP. Experimental data were analyzed by inverse modeling of simultaneous water, heat, and solute transport using an adapted HYDRUS-2D model. Various optimization scenarios yielded simultaneous estimation of thermal, solute, and hydraulic parameters and variables, including thermal conductivity, volumetric water content, water flux, and thermal and solute dispersivities. We conclude that the MFHPP holds great promise as an excellent instrument for the continuous monitoring and characterization of the vadose zone.  相似文献   

13.
We investigated the role of increasingly well‐constrained geologic structures in the subsurface (i.e., subsurface architecture) in predicting streambed flux and hyporheic residence time distribution (RTD) for a headwater stream. Five subsurface realizations with increasingly resolved lithological boundaries were simulated in which model geometries were based on increasing information about flow and transport using soil and geologic maps, surface observations, probing to depth to refusal, seismic refraction, electrical resistivity (ER) imaging of subsurface architecture, and time‐lapse ER imaging during a solute tracer study. Particle tracking was used to generate RTDs for each model run. We demonstrate how improved characterization of complex lithological boundaries and calibration of porosity and hydraulic conductivity affect model prediction of hyporheic flow and transport. Models using hydraulic conductivity calibrated using transient ER data yield estimates of streambed flux that are three orders of magnitude larger than uncalibrated models using estimated values for hydraulic conductivity based on values published for nearby hillslopes (10?4 vs. 10?7 m2/s, respectively). Median residence times for uncalibrated and calibrated models are 103 and 100 h, respectively. Increasingly well‐resolved subsurface architectures yield wider hyporheic RTDs, indicative of more complex hyporheic flowpath networks and potentially important to biogeochemical cycling. The use of ER imaging to monitor solute tracers informs subsurface structure not apparent from other techniques, and helps to define transport properties of the subsurface (i.e., hydraulic conductivity). Results of this study demonstrate the value of geophysical measurements to more realistically simulate flow and transport along hyporheic flowpaths.  相似文献   

14.
Emission tomography used in passive seismic monitoring of hydrocarbon deposits enables regular inspection of development of hydraulic fracturing and relaxation processes in volumes of fracturing, tracing of fluid migration paths, redistribution of stresses due to field development accompanied by seismic emission from volumes of structural defects and stress concentration, and localization of fractured and faulted structures from emission and scattering data. Intensive man-made seismic noise in the areas of oil field development produces a strong screening effect in identification of weak deep seismic sources. On the basis of experiments with simulated and real data of surface seismic arrays in regions of oil deposits in Western Siberia (carried out in the framework of the passive monitoring program of the SYNAPSE Science Center), it is shown that the use of algorithms of adaptive optimal and rejection spatial filtering with the estimation of the spectral density matrix of multichannel observations in the framework of multivariate autoregressive-moving average modeling is effective for eliminating the influence of anthropogenic noise and revealing (in oil production areas) both deep seismic sources supposedly active in scattering regions of the lower part of the sedimentary cover and the crystalline basement. The projection of the scattering regions onto the horizontal plane correlates well with the position of faults in the area of in situ observations.  相似文献   

15.
This study evaluates and compares two methodologies, Monte Carlo simple genetic algorithm (MCSGA) and noisy genetic algorithm (NGA), for cost-effective sampling network design in the presence of uncertainties in the hydraulic conductivity (K) field. Both methodologies couple a genetic algorithm (GA) with a numerical flow and transport simulator and a global plume estimator to identify the optimal sampling network for contaminant plume monitoring. The MCSGA approach yields one optimal design each for a large number of realizations generated to represent the uncertain K-field. A composite design is developed on the basis of those potential monitoring wells that are most frequently selected by the individual designs for different K-field realizations. The NGA approach relies on a much smaller sample of K-field realizations and incorporates the average of objective functions associated with all K-field realizations directly into the GA operators, leading to a single optimal design. The efficacy of the MCSGA-based composite design and the NGA-based optimal design is assessed by applying them to 1000 realizations of the K-field and evaluating the relative errors of global mass and higher moments between the plume interpolated from a sampling network and that output by the transport model without any interpolation. For the synthetic application examined in this study, the optimal sampling network obtained using NGA achieves a potential cost savings of 45% while keeping the global mass and higher moment estimation errors comparable to those errors obtained using MCSGA. The results of this study indicate that NGA can be used as a useful surrogate of MCSGA for cost-effective sampling network design under uncertainty. Compared with MCSGA, NGA reduces the optimization runtime by a factor of 6.5.  相似文献   

16.
This study introduces Bayesian model averaging (BMA) to deal with model structure uncertainty in groundwater management decisions. A robust optimized policy should take into account model parameter uncertainty as well as uncertainty in imprecise model structure. Due to a limited amount of groundwater head data and hydraulic conductivity data, multiple simulation models are developed based on different head boundary condition values and semivariogram models of hydraulic conductivity. Instead of selecting the best simulation model, a variance-window-based BMA method is introduced to the management model to utilize all simulation models to predict chloride concentration. Given different semivariogram models, the spatially correlated hydraulic conductivity distributions are estimated by the generalized parameterization (GP) method that combines the Voronoi zones and the ordinary kriging (OK) estimates. The model weights of BMA are estimated by the Bayesian information criterion (BIC) and the variance window in the maximum likelihood estimation. The simulation models are then weighted to predict chloride concentrations within the constraints of the management model. The methodology is implemented to manage saltwater intrusion in the “1,500-foot” sand aquifer in the Baton Rouge area, Louisiana. The management model aims to obtain optimal joint operations of the hydraulic barrier system and the saltwater extraction system to mitigate saltwater intrusion. A genetic algorithm (GA) is used to obtain the optimal injection and extraction policies. Using the BMA predictions, higher injection rates and pumping rates are needed to cover more constraint violations, which do not occur if a single best model is used.  相似文献   

17.
The hyporheic zone (HZ), which is the region beneath or alongside a streambed, plays an important role in the stream's ecology. The duration that a water molecule or a solute remains within the HZ, or residence time (RT), is one of the most common metrics used to evaluate the function of the HZ. The RT is greatly influenced by the streambed's hydraulic conductivity (K), which is intrinsically difficult to characterize due to its heterogeneity and anisotropy. Many laboratory and numerical studies of the HZ have simplified the streambed K to a constant, thus producing RT values that may differ from those gathered from the field. Some studies have considered the heterogeneity of the HZ, but very few have accounted for anisotropy or the natural K distributions typically found in real streambeds. This study developed numerical models in MODFLOW to examine the influence of heterogeneity and anisotropy, and that of the natural K distribution in a streambed, on the RT of the HZ. Heterogeneity and anisotropy were both found to shorten the mean and median RTs while increasing the range of the RTs. Moreover, heterogeneous K fields arranged in a more orderly pattern had longer RTs than those with random K distributions. These results could facilitate the design of streambed K values and distributions to achieve the desired RT during river restoration. They could also assist the translation of results from the more commonly considered homogeneous and/or isotropic conditions into heterogeneous and anisotropic field situations.  相似文献   

18.
The Beerkan method based on in situ single‐ring water infiltration experiments along with the relevant specific Beerkan estimation of soil transfer parameters (BEST) algorithm is attractive for simple soil hydraulic characterization. However, the BEST algorithm may lead to erroneous or null values for the saturated hydraulic conductivity and sorptivity especially when there are only few infiltration data points under the transient flow state, either for sandy soil or soils in wet conditions. This study developed an alternative algorithm for analysis of the Beerkan infiltration experiment referred to as BEST‐generalized likelihood uncertainty estimation (GLUE). The proposed method estimates the scale parameters of van Genuchten water retention and Brooks–Corey hydraulic conductivity functions through the GLUE methodology. The GLUE method is a Bayesian Monte Carlo parameter estimation technique that makes use of a likelihood function to measure the goodness‐of‐fit between modelled and observed data. The results showed that using a combination of three different likelihood measurements based on observed transient flow, steady‐state flow and experimental steady‐state infiltration rate made the BEST‐GLUE procedure capable of performing an efficient inverse analysis of Beerkan infiltration experiments. Therefore, it is more applicable for a wider range of soils with contrasting texture, structure, and initial and saturated water content. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献   

19.
Xi Chen  Xunhong Chen   《Journal of Hydrology》2003,280(1-4):246-264
During a flood period, stream-stage increases induce infiltration of stream water into an aquifer; subsequent declines in stream stage cause a reverse motion of the infiltrated water. This paper presents the results of the water exchange rate between a stream and aquifer, the storage volume of the infiltrated stream water in the surrounding aquifer (bank storage), and the storage zone. The storage zone is the part of aquifer where groundwater is replaced by stream water during the flood. MODFLOW was used to simulate stream–aquifer interactions and to quantify rates of stream infiltration and return flow. MODPATH was used to trace the pathlines of the infiltrated stream water and to determine the size of the storage zone. Simulations were focused on the analyses of the effects of the stream-stage fluctuation, aquifer properties, the hydraulic conductivity of streambed sediments, regional hydraulic gradients, and recharge and evapotranspiration (ET) rates on stream–aquifer interactions. Generally, for a given stream–aquifer system, larger flow rates result from larger stream-stage fluctuations; larger storage volumes and storage zones are produced by larger and longer-lasting fluctuations. For a given stream-stage hydrograph, a lower-permeable streambed, an aquitard, or an anisotropic aquifer of low vertical hydraulic conductivity can significantly reduce the rate of infiltration and limit the size of the storage zone. The bank storage solely caused by the stage fluctuation differs slightly between gaining and losing streams. Short-term rainfall recharge and ET loss in the shallow groundwater slightly influence on the flow rate, but their effects on bank storage in a larger area for a longer period can be considerable.  相似文献   

20.
Depth-discrete aquifer in formal ion was obtained using recently developed adaptations and improvements to conventional characterization techniques. These improvements included running neutron porosity and hulk density geophysical logging tools through a cased hole, performing an enhanced point-dilution tracer test for monitoring tracer concentration as a function of Lime and depth, and using pressure derivatives for diagnostic and quantitative analysis of constant rate discharge lest data. Data results from the use of these techniques were used to develop a conceptual model of a heterogeneous aquifer. Depth-discrete aquifer information was required to effectively design field-scale deployment and monitoring of an in situ bioremediation technology.
Geophysical logging and point-dilution tracer test results provided the relative distribution of porosity and horizontal hydraulic conductivity, respectively, with depth and correlated well. Hydraulic pumping tests were conducted to estimate mean values for transmissivity and effective hydraulic conductivity, Tracer lest and geophysical logging results indicated that ground water flow was predominant in the upper approximate 10 feet of the aquifer investigated. These results were used to delineate a more representative interval thickness for estimating effective hydraulic conductivity. Hydraulic conductivity, calculated using this representative interval, was estimated lo be 73 ft/d, approximately three limes higher than that calculated using the full length of the screened test interval.  相似文献   

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