Groundwater Recharge Rate and Zone Structure Estimation Using PSOLVER Algorithm

The quantification of groundwater recharge is an important but challenging task in groundwater flow modeling because recharge varies spatially and temporally. The goal of this study is to present an innovative methodology to estimate groundwater recharge rates and zone structures for regional groundwater flow models. Here, the unknown recharge field is partitioned into a number of zones using Voronoi Tessellation (VT). The identified zone structure with the recharge rates is associated through a simulation‐optimization model that couples MODFLOW‐2000 and the hybrid PSOLVER optimization algorithm. Applicability of this procedure is tested on a previously developed groundwater flow model of the Tahtal? Watershed. Successive zone structure solutions are obtained in an additive manner and penalty functions are used in the procedure to obtain realistic and plausible solutions. One of these functions constrains the optimization by forcing the sum of recharge rates for the grid cells that coincide with the Tahtal? Watershed area to be equal to the areal recharge rate determined in the previous modeling by a separate precipitation‐runoff model. As a result, a six‐zone structure is selected as the best zone structure that represents the areal recharge distribution. Comparison to results of a previous model for the same study area reveals that the proposed procedure significantly improves model performance with respect to calibration statistics. The proposed identification procedure can be thought of as an effective way to determine the recharge zone structure for groundwater flow models, in particular for situations where tangible information about groundwater recharge distribution does not exist.     

A hybrid framework for improving recharge and discharge estimation for a three-dimensional groundwater flow model

We employed the ArcGIS plug-in package PRO-GRADE (Lin et al. 2009), developed for zonation of recharge/discharge (R/D) for modeling two-dimensional aquifer systems, to develop alternative R/D zonations for an existing three-dimensional groundwater flow model of a complex hydrogeologic setting. Our process began by intersecting PRO-GRADE output with the existing model's 4-zone R/D representation to develop a model having 12 R/D zones (R12) and then calibrating the resulting model using PEST. We then revised the R12 zonation using supplementary GIS data to develop a 51-zone R/D zonation (R51). From R51, we developed a series of daughter models having 40, 30, 28, and 18 R/D zones by removing zones from R51 if calibration resulted in little change in the zone's starting R/D rate and/or if the model was insensitive to the zone's R/D rate. For these models (R40N, R30N, R28N, and R18N), we used the ArcGIS Nibble tool to rapidly and consistently reassign model cells within eliminated zones of R51 to the zone of the nearest model cell in a retained zone having the same starting value. R12, R51, R40N, R30N, R28N, and R18N are all more accurate than the original model (R4), although improvements relative to stream discharge targets exceeded improvements relative to head targets. The models also executed with better numerical stability and less mass balance discrepancy than R4. These improvements demonstrate that R/D estimation in a complex shallow three-dimensional steady-state model can be improved with PRO-GRADE estimates of R/D when guided by calibration statistics and supplemental geographic data.     

Hydrological modelling of Ethiopian catchments using limited data

The hydrological component of the soil and water assessment tool (SWAT) model is adapted for two Ethiopian catchments based on primary knowledge of the coherence spectrum between rainfall and stream flow data. Spectrum analysis using the available nearby climatic data is made to limit the temporal and spatial scales (inverse rate coefficients) subject to the calibration of compartmentalized runoff models. The exclusion of unwarranted time scales in the calibration implies that the model efficiency (r² values) decrease only moderately between calibration and validation, and the optimization is focused on warranted problems. On the basis of the available data for the two Ethiopian catchments, the implication is that only periods longer than about 50 days can be reliably evaluated in the model. The model structure of SWAT for the surface runoff and groundwater flow response is modified to make the time scales consistent with the results of the spectrum analysis. An optimization algorithm is developed to constrain and combine the model parameters with the spectrum analysis results. Copyright © 2009 John Wiley & Sons, Ltd.     

On the use of multi‐algorithm,genetically adaptive multi‐objective method for multi‐site calibration of the SWAT model

With the availability of spatially distributed data, distributed hydrologic models are increasingly used for simulation of spatially varied hydrologic processes to understand and manage natural and human activities that affect watershed systems. Multi‐objective optimization methods have been applied to calibrate distributed hydrologic models using observed data from multiple sites. As the time consumed by running these complex models is increasing substantially, selecting efficient and effective multi‐objective optimization algorithms is becoming a nontrivial issue. In this study, we evaluated a multi‐algorithm, genetically adaptive multi‐objective method (AMALGAM) for multi‐site calibration of a distributed hydrologic model—Soil and Water Assessment Tool (SWAT), and compared its performance with two widely used evolutionary multi‐objective optimization (EMO) algorithms (i.e. Strength Pareto Evolutionary Algorithm 2 (SPEA2) and Non‐dominated Sorted Genetic Algorithm II (NSGA‐II)). In order to provide insights into each method's overall performance, these three methods were tested in four watersheds with various characteristics. The test results indicate that the AMALGAM can consistently provide competitive or superior results compared with the other two methods. The multi‐method search framework of AMALGAM, which can flexibly and adaptively utilize multiple optimization algorithms, makes it a promising tool for multi‐site calibration of the distributed SWAT. For practical use of AMALGAM, it is suggested to implement this method in multiple trials with relatively small number of model runs rather than run it once with long iterations. In addition, incorporating different multi‐objective optimization algorithms and multi‐mode search operators into AMALGAM deserves further research. Copyright © 2009 John Wiley & Sons, Ltd.     

Multi-Constrained Catchment Scale Optimization of Groundwater Abstraction Using Linear Programming

Due to increasing water demands globally, freshwater ecosystems are under constant pressure. Groundwater resources, as the main source of accessible freshwater, are crucially important for irrigation worldwide. Over-abstraction of groundwater leads to declines in groundwater levels; consequently, the groundwater inflow to streams decreases. The reduction in baseflow and alteration of the streamflow regime can potentially have an adverse effect on groundwater-dependent ecosystems. A spatially distributed, coupled groundwater–surface water model can simulate the impacts of groundwater abstraction on aquatic ecosystems. A constrained optimization algorithm and a simulation model in combination can provide an objective tool for the water practitioner to evaluate the interplay between economic benefits of groundwater abstractions and requirements to environmental flow. In this study, a holistic catchment-scale groundwater abstraction optimization framework has been developed that allows for a spatially explicit optimization of groundwater abstraction, while fulfilling a predefined maximum allowed reduction of streamflow (baseflow [Q95] or median flow [Q50]) as constraint criteria for 1484 stream locations across the catchment. A balanced K-Means clustering method was implemented to reduce the computational burden of the optimization. The model parameters and observation uncertainties calculated based on Bayesian linear theory allow for a risk assessment on the optimized groundwater abstraction values. The results from different optimization scenarios indicated that using the linear programming optimization algorithm in conjunction with integrated models provides valuable information for guiding the water practitioners in designing an effective groundwater abstraction plan with the consideration of environmental flow criteria important for the ecological status of the entire system.     

The role of prior model calibration on predictions with ensemble Kalman filter

This paper, based on a real world case study (Limmat aquifer, Switzerland), compares inverse groundwater flow models calibrated with specified numbers of monitoring head locations. These models are updated in real time with the ensemble Kalman filter (EnKF) and the prediction improvement is assessed in relation to the amount of monitoring locations used for calibration and updating. The prediction errors of the models calibrated in transient state are smaller if the amount of monitoring locations used for the calibration is larger. For highly dynamic groundwater flow systems a transient calibration is recommended as a model calibrated in steady state can lead to worse results than a noncalibrated model with a well-chosen uniform conductivity. The model predictions can be improved further with the assimilation of new measurement data from on-line sensors with the EnKF. Within all the studied models the reduction of 1-day hydraulic head prediction error (in terms of mean absolute error [MAE]) with EnKF lies between 31% (assimilation of head data from 5 locations) and 72% (assimilation of head data from 85 locations). The largest prediction improvements are expected for models that were calibrated with only a limited amount of historical information. It is worthwhile to update the model even with few monitoring locations as it seems that the error reduction with EnKF decreases exponentially with the amount of monitoring locations used. These results prove the feasibility of data assimilation with EnKF also for a real world case and show that improved predictions of groundwater levels can be obtained.     

Groundwater recharge estimation in arid hardrock‐alluvium aquifers using combined water‐table fluctuation and groundwater balance approaches

This paper proposes an approach to estimate groundwater recharge using an optimization‐based water‐table fluctuation method combined with a groundwater balance model in an arid hardrock‐alluvium region, located at the Oman–United Arab Emirates border. We introduce an “effective hardrock thickness” term to identify the percentage of the considered hardrock thickness in which effective groundwater flow takes place. The proposed method is based upon a Thiessen polygon zoning approach. The method includes subpolygons to represent specific geologic units and to enhance the confidence of the estimated groundwater recharge. Two linear and 1 nonlinear submodels were developed to evaluate the model components for the calibration (October 1996 to September 2008) and validation (October 2008 to September 2013) periods. Long‐term annual groundwater recharge from rainfall and return flow over the model domain are estimated as 24.62 and 5.71 Mm³, respectively, while the effective groundwater flow circulation is found to occur in the upper 7% of the known hardrock thickness (42 m), confirming conclusions of previous field studies. Considering a total difference in groundwater levels between eastern and western points of the study area of the order of 220 m and a 12‐year monthly calibration period, a weighted root mean squared error in predicted groundwater elevation of 2.75 m is considered quite reasonable for the study area characterized by remarkable geological and hydrogeological diversity. The proposed approach provides an efficient and robust method to estimate groundwater recharge in regions with a complex geological setting in which interaction between fractured and porous media cannot be easily assessed.     

Advantages of the analytic element method for the solution of groundwater management problems

In the simulation‐optimization approach, a coupled optimization and groundwater flow/transport model is used to solve groundwater management problems. The efficiency of the numerical method, which is used to simulate the groundwater flow, is one the major reason to obtain the best solution for a management problem. This study was carried out to examine the advantages of the analytic element method (AEM) in the simulation‐optimization approach, for the solution of groundwater management problems. For this study, the AEM and finite difference method (FDM) based flow models were developed and coupled with the particle swarm optimization (PSO)‐based optimization model. Furthermore, the AEM‐PSO and FDM‐PSO models developed were applied in hypothetical as well as real field conditions to address groundwater management problems and the results were compared. For the real field situation, the models developed were applied to the Dore River basin in France to minimize the installation and operational cost of new pumping wells taking the location and discharge of the pumping wells as decision variables. The constraints of the problem were identified with the help of stakeholders and water authority officials. The AEM flow model was developed to facilitate the management model particularly when at each iteration, the optimization model calls for a simulation model to calculate the values of groundwater heads. The results show that, at some points, the AEM‐PSO model is efficient in identifying the optimal location of wells and consequently results in optimal costs, sometimes difficult when using the FDM. Copyright © 2011 John Wiley & Sons, Ltd.     

Combination of FEM and CMA‐ES algorithm for transmissivity identification in aquifer systems

In this paper, we propose a coupling of a finite element model with a metaheuristic optimization algorithm for solving the inverse problem in groundwater flow (Darcy's equations). This coupling performed in 2 phases is based on the combination of 2 codes: This is the HySubF‐FEM code (hydrodynamic of subsurface flow by finite element method) used for the first phase allowing the calculation of the flow and the CMA‐ES code (covariance matrix adaptation evolution strategy) adopted in the second phase for the optimization process. The combination of these 2 codes was implemented to identify the transmissivity field of groundwater by knowing the hydraulic head in some point of the studied domain. The integrated optimization algorithm HySubF‐FEM/CMA‐ES has been validated successfully on a schematic case offering an analytical solution. As realistic application, the integrated optimization algorithm HySubF‐FEM/CMA‐ES was applied to a complex groundwater in the north of France to identify the transmissivity field. This application does not use zonation techniques but solves an optimization problem at each internal node of the mesh. The obtained results are considered excellent with high accuracy and fully consistent with the hydrogeological characteristics of the studied aquifer.However, the various numerical simulations performed in this paper have shown that the CMA‐ES algorithm is time‐consuming. Finally, the paper concludes that the proposed algorithm can be considered as an efficient tool for solving inverse problems in groundwater flow.     

Enhancing gradient-based parameter estimation with an evolutionary approach

Traditionally, the calibration of groundwater models has depended on gradient-based local optimization methods. These methods provide a reasonable degree of success only when the objective function is smooth, second-order differentiable, and satisfies the Lipschitz's condition. For complicated and highly nonlinear objective functions it is almost impractical to satisfy these conditions simultaneously. Research in the calibration of conceptual rainfall-runoff models, has shown that global optimization methods are more successful in locating the global optimum in the region of multiple local optima. In this study, a global optimization technique, known as shuffle complex evolution (SCE), is coupled to the gradient-based Lavenberg–Marquardt algorithm (GBLM). The resultant hybrid global optimization algorithm (SCEGB) is then deployed in parallel testing with SCE and GBLM to solve several inverse problems where parameters of a nonlinear numerical groundwater flow model are estimated. Using perfect (i.e. noise-free) observation data, it is shown SCEGB and SCE are successful at identifying the global optimum and predicting all model parameters; whereas, the commonly applied GBLM fails to identify the optimum. In subsequent inverse simulations using observation data corrupted with noise, SCEGB and SCE again outperform GBLM by consistently producing more accurate parameter estimates. Finally, in all simulations the hybrid SCEGB is seen to be equally effective as SCE but computationally more efficient.     

Modeling the spatial distribution of landslide‐prone colluvium and shallow groundwater on hillslopes of Seattle,WA

Landslides in partially saturated colluvium on Seattle, WA, hillslopes have resulted in property damage and human casualties. We developed statistical models of colluvium and shallow‐groundwater distributions to aid landslide hazard assessments. The models were developed using a geographic information system, digital geologic maps, digital topography, subsurface exploration results, the groundwater flow modeling software VS2DI and regression analyses. Input to the colluvium model includes slope, distance to a hillslope–crest escarpment, and escarpment slope and height. We developed different statistical relations for thickness of colluvium on four landforms. Groundwater model input includes colluvium basal slope and distance from the Fraser aquifer. This distance was used to estimate hydraulic conductivity based on the assumption that addition of finer‐grained material from down‐section would result in lower conductivity. Colluvial groundwater is perched so we estimated its saturated thickness. We used VS2DI to establish relations between saturated thickness and the hydraulic conductivity and basal slope of the colluvium. We developed different statistical relations for three groundwater flow regimes. All model results were validated using observational data that were excluded from calibration. Eighty percent of colluvium thickness predictions were within 25% of observed values and 88% of saturated thickness predictions were within 20% of observed values. The models are based on conditions common to many areas, so our method can provide accurate results for similar regions; relations in our statistical models require calibration for new regions. Our results suggest that Seattle landslides occur in native deposits and colluvium, ultimately in response to surface‐water erosion of hillslope toes. Regional groundwater conditions do not appear to strongly affect the general distribution of Seattle landslides; historical landslides were equally dispersed within and outside of the area potentially affected by regional groundwater conditions. Published in 2007 by John Wiley & Sons, Ltd.     

Inverse methods for subsurface flow: A critical review of stochastic techniques

The development of stochastic methods for groundwater flow representation has undergone enormous expansion in recent years. The calibration of groundwater models, the inverse problem, has lately received comparable attention especially and almost exclusively from the stochastic perspective. In this review we trace the evolution of the methods to date with a specific view toward identifying the most important issues involved in the usefulness of the approaches. The methods are critiqued regarding practical usefulness, and future directions for requisite study are discussed.     

Parameter Estimation for Groundwater Models under Uncertain Irrigation Data

The success of modeling groundwater is strongly influenced by the accuracy of the model parameters that are used to characterize the subsurface system. However, the presence of uncertainty and possibly bias in groundwater model source/sink terms may lead to biased estimates of model parameters and model predictions when the standard regression‐based inverse modeling techniques are used. This study first quantifies the levels of bias in groundwater model parameters and predictions due to the presence of errors in irrigation data. Then, a new inverse modeling technique called input uncertainty weighted least‐squares (IUWLS) is presented for unbiased estimation of the parameters when pumping and other source/sink data are uncertain. The approach uses the concept of generalized least‐squares method with the weight of the objective function depending on the level of pumping uncertainty and iteratively adjusted during the parameter optimization process. We have conducted both analytical and numerical experiments, using irrigation pumping data from the Republican River Basin in Nebraska, to evaluate the performance of ordinary least‐squares (OLS) and IUWLS calibration methods under different levels of uncertainty of irrigation data and calibration conditions. The result from the OLS method shows the presence of statistically significant (p < 0.05) bias in estimated parameters and model predictions that persist despite calibrating the models to different calibration data and sample sizes. However, by directly accounting for the irrigation pumping uncertainties during the calibration procedures, the proposed IUWLS is able to minimize the bias effectively without adding significant computational burden to the calibration processes.     

Post Processing of Zone Budgets to Generate Improved Groundwater Influx Estimates Associated with Longwall Mining

Impacts of underground longwall mining on groundwater systems are commonly assessed using numerical groundwater flow models that are capable of forecasting changes to strata pore pressures and rates of groundwater seepage over the mine life. Groundwater ingress to a mining operation is typically estimated using zone budgets to isolate relevant parts of a model that represent specific mining areas, and to aggregate flows at nominated times within specific model stress periods. These rates can be easily misinterpreted if simplistic averaging of daily flow budgets is adopted. Such misinterpretation has significant implications for design of underground dewatering systems for a new mine site or it may lead to model calibration errors where measured mine water seepage rates are used as a primary calibration constraint. Improved estimates of groundwater ingress can be made by generating a cumulative flow history from zone budget data, then differentiating the cumulative flow history using a low order polynomial convolved through the data set.     

Constraining water table depth simulations in a land surface model using estimated baseflow

Several recent studies have shown the significance of representing groundwater in land surface hydrologic simulations. However, optimal methods for model parameter calibration in order to realistically simulate baseflow and groundwater depth have received little attention. Most studies still use globally constant groundwater parameters due to the lack of available datasets for calibration. Moreover, when models are calibrated, various parameter combinations are found to exhibit equifinality in simulated total runoff due to model parameter interactions. In this study, a simple lumped groundwater model is incorporated into the Community Land Model (CLM), in which the water table is interactively coupled to soil moisture through the groundwater recharge fluxes. The coupled model (CLMGW) is successfully validated in Illinois using a 22-year (1984–2005) monthly observational dataset. Baseflow estimates from the digital recursive filter technique are used to calibrate the CLMGW parameters. The advantage obtained from incorporating baseflow calibration in addition to traditional calibration based on measured streamflow alone is demonstrated by a Monte Carlo-type simulation analysis. Using the optimal parameter sets identified from baseflow calibration, flow partitioning and water table depth simulations using CLMGW are improved, and the equifinality problem is alleviated. For other regions that lack observations of water table depth, the baseflow calibration approach can be used to enhance parameter estimation and constrain water table depth simulations.     

Simple automatic time-stepping for improved simulation of groundwater hydrographs

An automatic time-stepping algorithm is presented, based on the intensity of driving groundwater recharge, that improves the simulation of groundwater level fluctuations in regional models while maintaining model run-times. The algorithm is implemented in the ZOOMQ3D finite difference groundwater flow code and controls the discretization of time using two user-defined criteria: a maximum time-step length and a maximum recharge per time-step. Daily recharge is accumulated in time until either of these criteria is violated when the model then calculates a solution. The efficiency and accuracy of the algorithm is tested using an idealized groundwater model and an existing regional groundwater model of a UK aquifer. The approach is illustrated using simulations of high groundwater levels and associated groundwater flood events in a responsive, high-diffusivity aquifer. Simulations using the automatic time-stepping technique are presented that reduce the maximum absolute error in groundwater level by 45% and the run-time by 51% compared to models using conventional, a priori defined stress-periods and time-steps.     

Induced Temperature Gradients to Examine Groundwater Flowpaths in Open Boreholes

Techniques for characterizing the hydraulic properties and groundwater flow processes of aquifers are essential to design hydrogeologic conceptual models. In this study, rapid time series temperature profiles within open‐groundwater wells in fractured rock were measured using fiber optic distributed temperature sensing (FO‐DTS). To identify zones of active groundwater flow, two continuous electrical heating cables were installed alongside a FO‐DTS cable to heat the column of water within the well and to create a temperature difference between the ambient temperature of the groundwater in the aquifer and that within the well. Additional tests were performed to examine the effects of pumping on hydraulic fracture interconnectivity around the well and to identify zones of increased groundwater flow. High‐ and low‐resolution FO‐DTS cable configurations were examined to test the sensitivities of the technique and compared with downhole video footage and geophysical logging to confirm the zones of active groundwater flow. Two examples are presented to demonstrate the usefulness of this new technique for rapid characterization of fracture zones in open boreholes. The combination of the FO‐DTS and heating cable has excellent scope as a rapid appraisal tool for borehole construction design and improving hydrogeologic conceptual models.     

Effects of Linking a Soil‐Water‐Balance Model with a Groundwater‐Flow Model

A previously published regional groundwater‐flow model in north‐central Nebraska was sequentially linked with the recently developed soil‐water‐balance (SWB) model to analyze effects to groundwater‐flow model parameters and calibration results. The linked models provided a more detailed spatial and temporal distribution of simulated recharge based on hydrologic processes, improvement of simulated groundwater‐level changes and base flows at specific sites in agricultural areas, and a physically based assessment of the relative magnitude of recharge for grassland, nonirrigated cropland, and irrigated cropland areas. Root‐mean‐squared (RMS) differences between the simulated and estimated or measured target values for the previously published model and linked models were relatively similar and did not improve for all types of calibration targets. However, without any adjustment to the SWB‐generated recharge, the RMS difference between simulated and estimated base‐flow target values for the groundwater‐flow model was slightly smaller than for the previously published model, possibly indicating that the volume of recharge simulated by the SWB code was closer to actual hydrogeologic conditions than the previously published model provided. Groundwater‐level and base‐flow hydrographs showed that temporal patterns of simulated groundwater levels and base flows were more accurate for the linked models than for the previously published model at several sites, particularly in agricultural areas.     

Automated calibration applied to watershed‐scale flow simulations

Complexity in simulating the hydrological response in large watersheds over long times has prompted a significant need for procedures for automatic calibration. Such a procedure is implemented in the basin‐scale hydrological model (BSHM), a physically based distributed parameter watershed model. BSHM simulates the most important basin‐scale hydrological processes, such as overland flow, groundwater flow and stream–aquifer interaction in watersheds. Here, the emphasis is on estimating the groundwater parameters with water levels in wells and groundwater baseflows selected as the calibration targets. The best set of parameters is selected from within plausible ranges of parameters by adjusting the values of hydraulic conductivity, storativity, groundwater recharge and stream bed permeability. The baseflow is determined from stream flow hydrographs by using an empirical scheme validated using a chemical approach to hydrograph separation. Field studies determined that the specific conductance for components of the composite hydrograph were sufficiently unique to make the chemical approach feasible. The method was applied to the Big Darby Creek Watershed, Ohio. The parameter set selected for the groundwater system provides a good fit with the estimated baseflow and observed water well data. Copyright © 1999 John Wiley & Sons, Ltd.