Skeletal Specific Storage Research Articles

Characterization of Changes in Groundwater Storage in the Lachlan Catchment, Australia, Derived From Observations of Surface Deformation and Groundwater Level Data

AbstractGlobal Positioning System (GPS) deformation measurements were combined with groundwater level data to examine the spatiotemporal variability of groundwater storage in the Lachlan catchment located in central New South Wales (Australia). After correcting for effects of glacial isostatic adjustment, non‐tidal oceanic and atmospheric loading as well as hydrologic loading using existing models, we show that the seasonal and interannual variability of ground deformation and hydraulic head level data, extracted using wavelet time‐frequency analysis, exhibits an in‐phase behavior, indicating that the observed surface deformation is the poroelastic response to groundwater pressure change in aquifer system. Combination of GPS displacement and groundwater level change enables the estimation of elastic skeletal specific storage coefficients, which were then used for estimating groundwater storage changes. The estimated groundwater storage changes clearly reflect the four climate events of the Lachlan catchment since 1996: (a) the Millennium drought over 1996–2009, (b) the 2011–2012 La Nina and two significant floods in 2012 and 2016, (c) the drought conditions from mid‐2017 to late‐2019, and (d) the return of La Nina conditions since early 2020. We also found annual and long‐term groundwater storage variations of respectively and over the period 2012–2021. Moreover, we show that groundwater level fluctuations can be predicted from GPS displacement measurements and storage coefficients with sufficient accuracy (80% correlation and 70% RMS reduction when compared in terms of seasonal cycle). This study provides essential information that can contribute to future groundwater planning, management, and control over the Australian continent.

Estimation of aquitard hydraulic conductivity and skeletal specific storage considering non-Darcy flow

Darcy's law has been widely used to study the groundwater drainage process within an aquitard. However, non-Darcy flow is frequently encountered in laboratory and in situ investigations. With consideration of a sudden drop in boundary hydraulic heads, aquitard compaction characteristics and their sensitivities to the non-Darcy flow control variables were analyzed. The non-Darcy flow was found to retard groundwater drainage, and the retardation effects were much more significant at early-to-intermediate time points. Under this specific boundary condition, the time–compaction curve in a log–log graph at early time points was found to be close to a straight line, whose slope can be used to indirectly evaluate the extent of the non-Darcy effect. A non-Darcy flow-based type curve method was developed for estimating aquitard hydraulic conductivity (K) and skeletal specific storage (Ss), and this method was used to interpret the time–compaction data recorded in a laboratory experiment. The tested aquitard was determined to be associated with non-Darcy flow due to the fact that the time–compaction curve deviated from the Darcy's law-based theoretical curve. Darcy's law resulted in an underestimated K. In contrast, the estimated Ss was almost unaffected by the flow state, if the observation lasted long enough to reach final steady compaction.

Parameter estimation of a multiple aquifer-aquitard system from a single extensometer record: Las Vegas, Nevada, USA

Abstract. The purpose of this investigation is to develop a semi-analytical procedure for quantifying aquifer and aquitard properties from a single extensometer record in lieu of the time-consuming development of more complex numerical models to quantify and constrain these parameter values. Despite a limited 12-year record and the fact that water levels both decline and increase on an annual basis, estimates of both aquifer and aquitard parameters have been reasonably estimated at the Lorenzi extensometer site in Las Vegas Valley, Nevada when compared to the estimates developed numerically. The key factors that allow for accurate estimates of elastic and inelastic skeletal specific storage and hydraulic conductivity of the aquitards and elastic specific storage and hydraulic conductivity of the intervening aquifers is the presence of pumping cycles at multiple frequencies, and measured heads at all the aquifer units covered in the extensometer record and the inherent assumption that the aquitards have identical hydrologic characteristics and are homogeneous and isotropic. This latter assumption is also a usual limitation in numerical modelling of these settings because of the complex temporal head relationships occurring within the aquitards that are rarely, if ever, measured.

Parameter estimation of an overconsolidated aquitard subjected to periodic hydraulic head variations within adjacent aquifers

Extensometers provide long-term records of deformation over a depth interval of interest. An overconsolidated aquitard usually undergoes elastic deformation if the hydraulic head within adjacent aquifers remains higher than the preconsolidation head within the aquitard. The vertical hydraulic conductivity Kv and elastic skeletal specific storage Sske are two critical parameters that control the deformation behavior of an overconsolidated aquitard, and they could be interpreted from valuable extensometer data. An analytical solution for the elastic aquitard deformation caused by periodic hydraulic head variations (PHHV) within adjacent aquifers is derived using the separation of variables method based on Euler’s formula. The phase difference in PHHV between adjacent aquifers is found to reduce the amplitude of periodic aquitard deformation. Meanwhile, the phase difference is found to cause no influence on the growth pattern of the phase shift, which is between the periodic aquitard deformation and PHHV, versus the period. A new parameter estimation method is further proposed to interpret aquitard Kv and Sske from periodic aquitard deformation data. This new method yields robust Kv and Sske estimates of a moderately thick aquitard, whose deformation history has been recorded by an extensometer, located in Shanghai, China. The field study confirms that the phase difference in PHHV between the aquifers adjacent to the overconsolidated aquitard of interest cannot be ignored.

Extensometer forensics: what can the data really tell us?

Extensometer data have an advantage over satellite-based data for monitoring land subsidence in that extensometer data provide continuous measurements (hourly or better temporal resolution) at very high precision (several tens of microns) over a known depth interval; the latter is important for isolating groundwater pumping from other causes of land subsidence attributed to tectonics or eustatic adjustments in the Earth’s crust. This investigation aims to identify a semi-analytical procedure for quantifying aquifer and aquitard properties from a single extensometer record in lieu of the time-consuming development of more complex numerical models to quantify and constrain these parameter values. In spite of a limited 12-year record and the fact that water levels both decline and increase on an annual basis, this study successfully and reasonably estimated both aquifer and aquitard parameters at the Lorenzi extensometer site in Las Vegas Valley, Nevada (USA), when compared to the estimates developed numerically. The key factors that allow for estimates of elastic and inelastic skeletal-specific storage and hydraulic conductivity of the aquitards and elastic specific storage and hydraulic conductivity of the intervening aquifers is the presence of pumping cycles at multiple frequencies, and measured heads at all the aquifer units covered in the extensometer record. There is an inherent assumption that the aquitards possess the same hydrologic characteristics and are homogeneous and isotropic. This assumption is also a usual limitation in numerical modeling of these settings because of the complex temporal head relationships occurring within the aquitards that are rarely, if ever, measured.

Coupled Stress-Dependent Groundwater Flow-Deformation Model to Predict Land Subsidence in Basins with Highly Compressible Deposits

In this study, a stress-dependent groundwater model, MODFLOW-SD, has been developed and coupled with the nonlinear subsidence model, NDIS, to predict vertical deformation occurring in basins with highly compressible deposits. The MODFLOW-SD is a modified version of MODFLOW (the USGS Modular Three-Dimensional Groundwater Flow Model) with two new packages, NONK and NONS, to update hydraulic conductivity and skeletal specific storage due to change in effective stress. The NDIS package was developed based on Darcy–Gersevanov Law and bulk flux to model land subsidence. Results of sample simulations run for a conceptual model showed that hydraulic heads calculated by MODFLOW significantly overestimated for confining units and slightly underestimated for aquifer ones. Moreover, it showed that applied stress due to pumping changed initially homogeneous layers to be heterogeneous ones. Comparison of vertical deformations calculated by NDIS and MODFLOW-SUB showed that neglecting horizontal strain and stress-dependency of aquifer parameters can overestimate future subsidence. Furthermore, compared to the SUB (Subsidence and Aquifer-System Compaction) package, NDIS is more likely to provide a more accurate compaction model for a complex aquifer system with vertically variable compression (Cc), recompression (Cr), and hydraulic conductivity change (Ck) indices.

A Joint Analytic Method for Estimating Aquitard Hydraulic Parameters.

The vertical hydraulic conductivity (Kv ), elastic (Sske ), and inelastic (Sskv ) skeletal specific storage of aquitards are three of the most critical parameters in land subsidence investigations. Two new analytic methods are proposed to estimate the three parameters. The first analytic method is based on a new concept of delay time ratio for estimating Kv and Sske of an aquitard subject to long-term stable, cyclic hydraulic head changes at boundaries. The second analytic method estimates the Sskv of the aquitard subject to linearly declining hydraulic heads at boundaries. Both methods are based on analytical solutions for flow within the aquitard, and they are jointly employed to obtain the three parameter estimates. This joint analytic method is applied to estimate the Kv , Sske , and Sskv of a 34.54-m thick aquitard for which the deformation progress has been recorded by an extensometer located in Shanghai, China. The estimated results are then calibrated by PEST (Doherty 2005), a parameter estimation code coupled with a one-dimensional aquitard-drainage model. The Kv and Sske estimated by the joint analytic method are quite close to those estimated via inverse modeling and performed much better in simulating elastic deformation than the estimates obtained from the stress-strain diagram method of Ye and Xue (2005). The newly proposed joint analytic method is an effective tool that provides reasonable initial values for calibrating land subsidence models.

A modified inverse procedure for calibrating parameters in a land subsidence model and its field application in Shanghai, China

Land-subsidence prediction depends on an appropriate subsidence model and the calibration of its parameter values. A modified inverse procedure is developed and applied to calibrate five parameters in a compacting confined aquifer system using records of field data from vertical extensometers and corresponding hydrographs. The inverse procedure of COMPAC (InvCOMPAC) has been used in the past for calibrating vertical hydraulic conductivity of the aquitards, nonrecoverable and recoverable skeletal specific storages of the aquitards, skeletal specific storage of the aquifers, and initial preconsolidation stress within the aquitards. InvCOMPAC is modified to increase robustness in this study. There are two main differences in the modified InvCOMPAC model (MInvCOMPAC). One is that field data are smoothed before diagram analysis to reduce local oscillation of data and remove abnormal data points. A robust locally weighted regression method is applied to smooth the field data. The other difference is that the Newton-Raphson method, with a variable scale factor, is used to conduct the computer-based inverse adjustment procedure. MInvCOMPAC is then applied to calibrate parameters in a land subsidence model of Shanghai, China. Five parameters of aquifers and aquitards at 15 multiple-extensometer sites are calibrated. Vertical deformation of sedimentary layers can be predicted by the one-dimensional COMPAC model with these calibrated parameters at extensometer sites. These calibrated parameters could also serve as good initial values for parameters of three-dimensional regional land subsidence models of Shanghai.

Predictability of hydraulic head changes and characterization of aquifer‐system and fault properties from InSAR‐derived ground deformation

AbstractWe evaluate the benefits of space‐derived ground deformation measurements for basin‐wide characterization of aquifer‐system properties and groundwater levels. We use Interferometric Synthetic Aperture Radar (InSAR) time series analysis of ERS, Envisat, and ALOS SAR data to resolve 1992–2011 ground deformation in the Santa Clara Valley, California. T‐mode principal component analysis successfully isolates temporally variable deformation patterns embedded in the multidecadal time series. The data reveal uplift at 0.4 cm/yr between 1992 and 2000 and < 0.1 cm/yr during 2000–2011, illustrating the end of the aquifer‐system's poroelastic rebound following recovery of hydraulic heads after the 1960s low stand. In addition, seasonal elastic deformation with amplitude of up to 3 cm, in phase with head fluctuations, is observed over the confined aquifer sharply partitioned by the Quaternary Silver Creek Fault (SCF). Integration of this deformation with hydraulic head data enables characterization of the aquifer‐system storativity and elastic skeletal specific storage. Modeling of the deformation partitioning across the SCF constrains the fault's last tectonic activity, hydraulic conductivity, and material composition. The SCF likely cuts the shallow confining clays and was last active since ~140 ka, it has a horizontal hydraulic conductivity several orders of magnitude lower than the surrounding aquifer‐system, and is likely composed of clays, making it an effective barrier to across‐fault fluid flow. Finally, we show that after a period of calibration, InSAR can be used to characterize basin‐wide water level changes without well measurements with an accuracy of 70%, which demonstrates that it provides useful data for groundwater management.

A New Zonation Algorithm with Parameter Estimation Using Hydraulic Head and Subsidence Observations

Parameter estimation codes such as UCODE_2005 are becoming well-known tools in groundwater modeling investigations. These programs estimate important parameter values such as transmissivity (T) and aquifer storage values (Sa ) from known observations of hydraulic head, flow, or other physical quantities. One drawback inherent in these codes is that the parameter zones must be specified by the user. However, such knowledge is often unknown even if a detailed hydrogeological description is available. To overcome this deficiency, we present a discrete adjoint algorithm for identifying suitable zonations from hydraulic head and subsidence measurements, which are highly sensitive to both elastic (Sske) and inelastic (Sskv) skeletal specific storage coefficients. With the advent of interferometric synthetic aperture radar (InSAR), distributed spatial and temporal subsidence measurements can be obtained. A synthetic conceptual model containing seven transmissivity zones, one aquifer storage zone and three interbed zones for elastic and inelastic storage coefficients were developed to simulate drawdown and subsidence in an aquifer interbedded with clay that exhibits delayed drainage. Simulated delayed land subsidence and groundwater head data are assumed to be the observed measurements, to which the discrete adjoint algorithm is called to create approximate spatial zonations of T, Sske , and Sskv . UCODE-2005 is then used to obtain the final optimal parameter values. Calibration results indicate that the estimated zonations calculated from the discrete adjoint algorithm closely approximate the true parameter zonations. This automation algorithm reduces the bias established by the initial distribution of zones and provides a robust parameter zonation distribution.

Modeling aquifer-system compaction and predicting land subsidence in central Taiwan

Changhua is a county in central Taiwan that will house several major economic development projects. Extracting groundwater has caused large-scale land subsidence in Changhua, with the largest cumulative subsidence being 210cm over 1992–2010. A multi-sensor monitoring system consisting of continuous GPS stations, a leveling network, multi-layer compaction monitoring wells and groundwater wells is deployed to monitor land subsidence and its mechanism in Changhua. Data from the monitoring well CGSG in Dacheng Township of Changhua show a cumulative compaction of 110.6cm over 1997–2010, occurring mainly at two aquifers and one aquitard. A novel combination of GPS and monitoring well data was used to determine the stress–strain relations. The stratum compaction turns from plasticity to elastoplasticity after a long-term compaction at the second aquifer below the surface. Four hydrogeological parameters of the three sediment layers in Dacheng, vertical hydraulic conductivity, elastic skeletal specific storage, inelastic skeletal specific storage, and the initial maximum preconsolidation stress, in the one‐dimensional compaction model COMPAC, are estimated using the genetic algorithm. With the parameters, COMPAC predicts compactions to an accuracy consistent with in situ measurements, and the mean absolute percentage errors of prediction are below 10%. The result provides a key reference for water management in central Taiwan.

Simulating pumping-induced regional land subsidence with the use of InSAR and field data in the Toluca Valley, Mexico

A multidisciplinary approach is presented here for quantifying land subsidence in a heavily pumped aquifer system with complex stratigraphy. The methodology consists in incorporating Terzaghi’s 1D instantaneous compaction principle into a 3D groundwater flow model that is then applied and calibrated to reproduce observed hydraulic heads and compaction for the Toluca Valley, Mexico. Differential Interferometric Synthetic Aperture Radar (D-InSAR), a generated 3D-geological model, extensometers, monitoring wells, and available literature are used to constrain the model. The D-InSAR measured subsidence, extensometers, and numerical simulations of subsidence agree relatively well. Simulations show that since regional subsidence began in the mid 1960s there has been up to 2 m of subsidence in the industrial corridor, where heavy pumping and thick clay layers are found. This study shows that an approach using various sources of data is useful in estimating and constraining the vertical component of the inelastic skeletal specific storage.

Inverse procedure for calibrating parameters that control land subsidence caused by subsurface fluid withdrawal: 1. Methods

Land subsidence prediction depends on a selected theoretical model and the calibration of its parameter values. An inverse model is developed that calibrates five parameters of a compacting confined aquifer system: K′v (vertical hydraulic conductivity of the aquitards), S′skv (aquitard nonrecoverable skeletal specific storage), S′ske (aquitard recoverable skeletal specific storage), Ssk (skeletal specific storage of the aquifer), and p′max 0 (initial preconsolidation stress within the aquitards). This inverse model combines a procedure for finding an initial set of parameter values and an inverse adjustment procedure. Initial values are estimated by using a new graphic method for the analysis of field data. The follow‐up inverse procedure is a computer algorithm that combines the Newton‐Raphson method with Helm's one‐dimensional finite difference subsidence model (COMPAC). COMPAC offers two options: a constant‐parameter simulation and a stress‐dependent parameter simulation. The classical least squares criterion is employed as the objective function of this inverse procedure. Three characteristics of the objective function are considered. This inverse model is applied to calculations of an idealized compacting confined aquifer system using Helm's model. This investigation shows that the final values for the five parameters lead to simulated compaction error of less than 1%. This contrasts to the initial error of more than 60%. These results indicate that the proposed inverse procedure (model) can be applied to actual field data.

The Value of Subsidence Data in Ground Water Model Calibration

The accurate estimation of aquifer parameters such as transmissivity and specific storage is often an important objective during a ground water modeling investigation or aquifer resource evaluation. Parameter estimation is often accomplished with changes in hydraulic head data as the key and most abundant type of observation. The availability and accessibility of global positioning system and interferometric synthetic aperture radar data in heavily pumped alluvial basins can provide important subsidence observations that can greatly aid parameter estimation. The aim of this investigation is to evaluate the value of spatial and temporal subsidence data for automatically estimating parameters with and without observation error using UCODE-2005 and MODFLOW-2000. A synthetic conceptual model (24 separate cases) containing seven transmissivity zones and three zones each for elastic and inelastic skeletal specific storage was used to simulate subsidence and drawdown in an aquifer with variably thick interbeds with delayed drainage. Five pumping wells of variable rates were used to stress the system for up to 15 years. Calibration results indicate that (1) the inverse of the square of the observation values is a reasonable way to weight the observations, (2) spatially abundant subsidence data typically produce superior parameter estimates under constant pumping even with observation error, (3) only a small number of subsidence observations are required to achieve accurate parameter estimates, and (4) for seasonal pumping, accurate parameter estimates for elastic skeletal specific storage values are largely dependent on the quantity of temporal observational data and less on the quantity of available spatial data.

Inverse procedure for calibrating parameters that control land subsidence caused by subsurface fluid withdrawal: 2. Field application

The inverse procedure (InvCOMPAC) that was developed in part 1 of this two‐part paper is applied to two aquifer systems at two sites in Shanghai. The present part 2 illustrates how to calibrate transient land subsidence parameter values on the basis of in situ data. The new graphic‐analytic method yields initial parameter values for use in the inverse procedure. For the upper and lower confined aquifer systems at multiple‐extensometer sites F09 and F16 in Shanghai, their final parameter values are calibrated further by InvCOMPAC, a computer‐based inverse model. The simulation error of transient subsidence over a period of 13 and 20 years, respectively, at sites F09 and F16 is decreased to 11.8 and 13.9%, respectively, from an initial graphic‐analytic result of 72.1 and 415.3%. This demonstrates that InvCOMPAC is applicable to complex field conditions. The new graphic‐analytic method is necessary in order to find a realistic set of initial parameter values. Calibrated parameter values are used to predict future subsidence in the field. Predictions indicate that a large amount of ongoing residual nonrecoverable compaction will occur and will not equilibrate with the anticipated decline of groundwater levels at these sites. The reason is that the vertical nonrecoverable skeletal specific storage of the aquitards is 2−3 orders of magnitude larger than the vertical recoverable skeletal specific storage of both the aquitards and the aquifer. The vertical hydraulic conductivity is too small for the aquitards to drain sufficiently quickly for them to reach a new equilibrium in response to water level declines. It is recommended that groundwater levels be kept above the past maximum preconsolidation pressure levels within the aquitards. This will prevent continued nonrecoverable compaction from occurring.

Three-dimensional deformation and strain induced by municipal pumping, Part 2: Numerical analysis

Summary Field measurements consisting of water levels from a municipal well and three-dimensional surface deformations and strains from high-precision GPS measurements at various radial distances from the well were collected as part of a 62-day controlled aquifer test at Mesquite, NV. These measurements were used as observations in several numerical models and a parameter estimation code to characterize and constrain hydraulic and mechanical properties of a 400 m thick basin-fill aquifer. A parsimonious approach was used in conceptualizing the aquifer system. Nonetheless, results from the calibrated deformation and flow models accurately reproduced the observed head and deformations during the first 20 days of pumping, the time at which a new equilibrium was achieved. Surface deformations were shown to reflect hydraulic anisotropy and direction of principal conductivity. In addition, the radius of influence and cone of depression from pumping was approximated in spite of the fact that no monitoring well data existed at the site. Sensitivity analysis indicates that cyclical head values are most sensitive to changes in horizontal hydraulic conductivity, while time-dependent vertical deformations are most sensitive to changes in skeletal specific storage. This investigation shows that GPS monitoring can be used in place of costly monitoring wells to characterize aquifers for water-management purposes where skeletal deformation tends to be elastic.

Use of time–subsidence data during pumping to characterize specific storage and hydraulic conductivity of semi-confining units

A new graphical technique is developed that takes advantage of time–subsidence data collected from either traditional extensometer installations or from newer technologies such as fixed-station global positioning systems or interferometric synthetic aperture radar imagery, to accurately estimate storage properties of the aquifer and vertical hydraulic conductivity of semi-confining units. Semi-log plots of time–compaction data are highly diagnostic with the straight-line portion of the plot reflecting the specific storage of the semi-confining unit. Calculation of compaction during one-log cycle of time from these plots can be used in a simple analytical expression based on the Cooper–Jacob technique to accurately calculate specific storage of the semi-confining units. In addition, these semi-log plots can be used to identify when the pressure transient has migrated through the confining layer into the unpumped aquifer, precluding the need for additional piezometers within the unpumped aquifer or within the semi-confining units as is necessary in the Neuman and Witherspoon method. Numerical simulations are used to evaluate the accuracy of the new technique. The technique was applied to time–drawdown and time–compaction data collected near Franklin Virginia, within the Potomac aquifers of the Coastal Plain, and shows that the method can be easily applied to estimate the inelastic skeletal specific storage of this aquifer system.

Stress‐Strain Analyses for Aquifer‐System Characterization

AbstractSubsidence data historically have been collected using costly extensometers. Recent advances in InSAR and GPS technology may provide noninvasive methods for collecting these data, which can be used in conjunction with hydrograph information to estimate the skeletal specific storage and hydraulic conductivity values of compressible units. Numerical analysis is used to evaluate the conditions affecting nonrecoverable (inelastic) and recoverable (elastic) skeletal specific storage and to investigate the affects of horizontal strain on the extensometer record. Stress‐strain diagrams represented as subsidence‐drawdown plots are one‐dimensional in scope, yet are typically used for estimating specific storage. Simulation results indicate that nonrecoverable specific can be estimated from these diagrams even when the storage contribution from horizontal strain is significant. Hysteresis effects are common during recovery and recompression of cyclically pumped confined aquifers. Several factors were found to affect the shape of the hysteresis loops; these include (a) the hydraulic diffusivity of the confining unit, (b) the distance from the pumped well, (c) length of the recovery cycle, (d) the ratio of confined aquifer to confining unit hydraulic conductivities, and (e) the thickness of the confining unit. Stress‐strain analyses can supplement classical time‐drawdown data to yield valuable parameter estimation of the confining unit that would be otherwise difficult to quantify.