Incorporating subjective and stochastic uncertainty in an interactive multi-objective groundwater calibration framework

The interactive multi-objective genetic algorithm (IMOGA) combines traditional optimization with an interactive framework that considers the subjective knowledge of hydro-geological experts in addition to quantitative calibration measures such as calibration errors and regularization to solve the groundwater inverse problem. The IMOGA is inherently a deterministic framework and identifies multiple large-scale parameter fields (typically head and transmissivity data are used to identify transmissivity fields). These large-scale parameter fields represent the optimal trade-offs between the different criteria (quantitative and qualitative) used in the IMOGA. This paper further extends the IMOGA to incorporate uncertainty both in the large-scale trends as well as the small-scale variability (which can not be resolved using the field data) in the parameter fields. The different parameter fields identified by the IMOGA represent the uncertainty in large-scale trends, and this uncertainty is modeled using a Bayesian approach where calibration error, regularization, and the expert’s subjective preference are combined to compute a likelihood metric for each parameter field. Small-scale (stochastic) variability is modeled using a geostatistical approach and added onto the large-scale trends identified by the IMOGA. This approach is applied to the Waste Isolation Pilot Plant (WIPP) case-study. Results, with and without expert interaction, are analyzed and the impact that expert judgment has on predictive uncertainty at the WIPP site is discussed. It is shown that for this case, expert interaction leads to more conservative solutions as the expert compensates for some of the lack of data and modeling approximations introduced in the formulation of the problem.     

Transient Recharge Estimability Through Field‐Scale Groundwater Model Calibration

The estimation of recharge through groundwater model calibration is hampered by the nonuniqueness of recharge and aquifer parameter values. It has been shown recently that the estimability of spatially distributed recharge through calibration of steady‐state models for practical situations (i.e., real‐world, field‐scale aquifer settings) is limited by the need for excessive amounts of hydraulic‐parameter and groundwater‐level data. However, the extent to which temporal recharge variability can be informed through transient model calibration, which involves larger water‐level datasets, but requires the additional consideration of storage parameters, is presently unknown for practical situations. In this study, time‐varying recharge estimates, inferred through calibration of a field‐scale highly parameterized groundwater model, are systematically investigated subject to changes in (1) the degree to which hydraulic parameters including hydraulic conductivity (K) and specific yield (S_y) are constrained, (2) the number of water‐level calibration targets, and (3) the temporal resolution (up to monthly time steps) at which recharge is estimated. The analysis involves the use of a synthetic reality (a reference model) based on a groundwater model of Uley South Basin, South Australia. Identifiability statistics are used to evaluate the ability of recharge and hydraulic parameters to be estimated uniquely. Results show that reasonable estimates of monthly recharge (<30% recharge root‐mean‐squared error) require a considerable amount of transient water‐level data, and that the spatial distribution of K is known. Joint estimation of recharge, S_y and K, however, precludes reasonable inference of recharge and hydraulic parameter values. We conclude that the estimation of temporal recharge variability through calibration may be impractical for real‐world settings.     

Estimating River Conductance from Prior Information to Improve Surface‐Subsurface Model Calibration

Most groundwater models simulate stream‐aquifer interactions with a head‐dependent flux boundary condition based on a river conductance (CRIV). CRIV is usually calibrated with other parameters by history matching. However, the inverse problem of groundwater models is often ill‐posed and individual model parameters are likely to be poorly constrained. Ill‐posedness can be addressed by Tikhonov regularization with prior knowledge on parameter values. The difficulty with a lumped parameter like CRIV, which cannot be measured in the field, is to find suitable initial and regularization values. Several formulations have been proposed for the estimation of CRIV from physical parameters. However, these methods are either too simple to provide a reliable estimate of CRIV, or too complex to be easily implemented by groundwater modelers. This paper addresses the issue with a flexible and operational tool based on a 2D numerical model in a local vertical cross section, where the river conductance is computed from selected geometric and hydrodynamic parameters. Contrary to other approaches, the grid size of the regional model and the anisotropy of the aquifer hydraulic conductivity are also taken into account. A global sensitivity analysis indicates the strong sensitivity of CRIV to these parameters. This enhancement for the prior estimation of CRIV is a step forward for the calibration and uncertainty analysis of surface‐subsurface models. It is especially useful for modeling objectives that require CRIV to be well known such as conjunctive surface water‐groundwater use.     

Estimation of anisotropic hydraulic conductivity using geophysical data in a coastal aquifer of Karnataka,India

Estimation of hydraulic parameters is essential to understand the interaction between groundwater flow and seawater intrusion. Though several studies have addressed hydraulic parameter estimation, based on pumping tests as well as geophysical methods, not many studies have addressed the problem with clayey formations being present. In this study, a methodology is proposed to estimate anisotropic hydraulic conductivity and porosity values for the coastal aquifer with unconsolidated formations. For this purpose, the one-dimensional resistivity of the aquifer and the groundwater conductivity data are used to estimate porosity at discrete points. The hydraulic conductivity values are estimated by its mutual dependence with porosity and petrophysical parameters. From these estimated values, the bilinear relationship between hydraulic conductivity and aquifer resistivity is established based on the clay content of the sampled formation. The methodology is applied on a coastal aquifer along with the coastal Karnataka, India, which has significant clayey formations embedded in unconsolidated rock. The estimation of hydraulic conductivity values from the established correlations has a correlation coefficient of 0.83 with pumping test data, indicating good reliability of the methodology. The established correlations also enable the estimation of horizontal hydraulic conductivity on two-dimensional resistivity sections, which was not addressed by earlier studies. The inventive approach of using the established bilinear correlations at one-dimensional to two-dimensional resistivity sections is verified by the comparison method. The horizontal hydraulic conductivity agrees with previous findings from inverse modelling. Additionally, this study provides critical insights into the estimation of vertical hydraulic conductivity and an equation is formulated which relates vertical hydraulic conductivity with horizontal. Based on the approach presented, the anisotropic hydraulic conductivity of any type aquifer with embedded clayey formations can be estimated. The anisotropic hydraulic conductivity has the potential to be used as an important input to the groundwater models.     

Improving Groundwater Model Calibration with Repeat Microgravity Measurements

Groundwater-flow models depend on hydraulic head and flux observations for evaluation and calibration. A different type of observation—change in storage measured using repeat microgravity—can also be used for parameter estimation by simulating the expected change in gravity from a groundwater model and including the observation misfit in the objective function. The method is demonstrated using new software linked to MODFLOW input and output files and field data from the vicinity of the All American Canal in southeast California, USA. Over a 10-year period following lining of the previously highly permeable canal with concrete, gravity decreased by over 100 μGal (equivalent to about 2.5 m of free-standing water) at some locations as seepage decreased and the remnant groundwater mound dissipated into the aquifer or was removed by groundwater pumping. Simulated gravity from a MODFLOW model closely matched observations, and repeat microgravity data proved useful for constraining both hydraulic conductivity and specific yield estimates. Specific yield estimated using the infinite-horizontal slab approximation agreed well with model-derived values, and the departure from the linear, flat-water-table approximation was small, less than 2%, despite relatively large and dynamic water-table slope. First-order second-moment parameter uncertainty analysis shows reduction in uncertainty for all hydraulic conductivity and specific yield parameter estimates with the addition of repeat microgravity data, as compared to drawdown data alone.     

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.     

AN EXERCISE IN GROUND-WATER MODEL CALIBRATION AND PREDICTION

Abstract. For a classroom exercise, nine groups of graduate students calibrated a numerical ground-water flow model to a set of perfectly observed hydraulic head data for a hypothetical phreatic aquifer. All groups used exactly the same numerical model and identical sets of observed data. After calibration, the students predicted the hydraulic head distribution in the aquifer resulting from a modification in one boundary condition. A quantitative analysis of the results of this calibration-prediction exercise vividly demonstrates some of the difficulties in parameter identification for ground-water flow models. Group predictions differed significantly. Successful prediction was strongly correlated with successful estimation of conductivity values, and was essentially unrelated to successful estimation of aquifer bottom elevations or with the number of trial-and-error simulations required for calibration. Most importantly, success in prediction was unrelated to success in matching observed heads under premodification conditions. In this sense, good calibration did not lead to good prediction.     

Incorporating multiple observations for distributed hydrologic model calibration: An approach using a multi-objective evolutionary algorithm and clustering

The use of distributed data for model calibration is becoming more popular in the advent of the availability of spatially distributed observations. Hydrological model calibration has traditionally been carried out using single objective optimisation and only recently has been extended to a multi-objective optimisation domain. By formulating the calibration problem with several objectives, each objective relating to a set of observations, the parameter sets can be constrained more effectively. However, many previous multi-objective calibration studies do not consider individual observations or catchment responses separately, but instead utilises some form of aggregation of objectives. This paper proposes a multi-objective calibration approach that can efficiently handle many objectives using both clustering and preference ordered ranking. The algorithm is applied to calibrate the MIKE SHE distributed hydrologic model and tested on the Karup catchment in Denmark. The results indicate that the preferred solutions selected using the proposed algorithm are good compromise solutions and the parameter values are well defined. Clustering with Kohonen mapping was able to reduce the number of objective functions from 18 to 5. Calibration using the standard deviation of groundwater level residuals enabled us to identify a group of wells that may not be simulated properly, thus highlighting potential problems with the model parameterisation.     

Steady state flow with hydraulic conductivity change around large diameter wells

Darcian flow law in aquifers assumes that the aquifer hydraulic conductivity is constant and the groundwater movement is due only to the piezometric level changes through hydraulic gradient. In practice, after the well development the aquifer just around the well has comparatively larger hydraulic conductivity and gradient. Patchy aquifer solutions in the literature consider sudden hydraulic conductivity changes with distance for the steady state flow. The change of transmissivity is demonstrated by the application of slope‐matching procedure to actual field data. It is the main purpose of this paper to derive simple analytical expressions for aquifer parameter evaluations with steadily decreasing hydraulic conductivity around the well. Spatial nonlinear hydraulic conductivity changes around a large‐diameter well within the depression cone of a confined aquifer are considered as exponentially decreasing functions of the radial distance. Copyright © 2010 John Wiley & Sons, Ltd.     

Including prior information in the estimation of effective soil parameters in unsaturated zone modelling

In this paper we propose a methodology to include prior information in the estimation of effective soil parameters for modelling the soil moisture content in the unsaturated zone. Laboratory measurements on undisturbed soil cores were used to estimate the moisture retention curve and hydraulic conductivity curve parameters. The soil moisture content was measured at 25 locations along three transects and at three different depths (surface, 30 and 60 cm) on an 80×20 m hillslope for the year 2001. Soil cores were collected in 84 locations situated in three profile pits along the hillslope. For the estimation of the effective soil hydraulic parameters the joint probability distribution of measured parameter values was used as prior information. A two-horizon single column 1D MIKE SHE model based on Richards' equation was set-up for nine soil moisture measurement locations along the middle transect of the hillslope. The goal of the model is to simulate the soil moisture profile at each location. The shuffled complex evolution (SCE) algorithm has been applied to estimate effective model parameters using either wide parameter ranges, referred to as the ‘no-prior’ case, or the joint probability distribution of measured parameter values as prior information (‘prior’ case). When the prior information is incorporated in the SCE optimisation the goodness-of-fit of the model predictions is only slightly worse compared to when no-prior information is incorporated. However, the effective parameter estimates are more realistic when the prior information is incorporated. For both the no-prior and prior case the generalised likelihood uncertainty estimation procedure (GLUE) was subsequently used to estimate the uncertainty bounds (UB) on the model predictions. When incorporating the prior information more parameter sets were accepted for the estimation of the predictive uncertainty and the parameter values were more realistic. Moreover, UB better enclosed the observations. Thus, incorporating prior information in GLUE reduces the amount of model evaluations needed to obtain sufficient behavioural parameter sets. The results indicate the importance of prior information in the SCE and GLUE parameter estimation strategies.     

Simulation of groundwater flow in a crystalline rock aquifer system in Southern Ghana – An evaluation of the effects of increased groundwater abstraction on the aquifers using a transient groundwater flow model

Monitored groundwater level data, well logs, and aquifer data as well as the relevant surface hydrological data were used to conceptualise the hydrogeological system of the Densu Basin in Southern Ghana. The objective was to numerically derive the hydraulic conductivity field for better characterization of the aquifer system and for simulating the effects of increasing groundwater abstraction on the aquifer system in the basin. The hydraulic conductivity field has been generated in this study through model calibration. This study finds that hydraulic conductivity ranges between a low of 2 m/d in the middle sections of the basin and about 40 m/d in the south. Clear differences in the underlying geology have been indicated in the distribution of aquifer hydraulic conductivities. This is in consonance with the general assertion that the hydrogeological properties of the aquifers in the crystalline basement terrains are controlled by the degree of fracturing and/or weathering of the country rock. The transient model suggest aquifer specific storage values to range between 6.0 × 10^?5 m^?1 and 2.1 × 10^?4 m^?1 which are within acceptable range of values normally quoted for similar lithologies in the literature. There is an apparent subtle decrease in groundwater recharge from about 13% of the annual precipitation in 2005 to about 10.3% of the precipitation in 2008. The transient model was used to simulate responses of the system to annual increment of groundwater abstraction by 20% at the 2008 recharge rates for the period 2009 – 2024. The results suggest that the system will not be able to sustain this level of abstraction as it would lead to a basin wide drawdown in the hydraulic head by 4 m by the end of the prediction period. It further suggests a safe annual increment in groundwater abstraction by 5% under business as usual recharge conditions. Identification and protection of groundwater recharge areas in the basin are recommended in order to safeguard the integrity of the resource under the scenario of increased abstraction for commercial activities in the basin. Copyright © 2012 John Wiley & Sons, Ltd.     

Identification of Groundwater Parameters Using an Adaptative Multiscale Method

The identification of groundwater parameters in heterogeneous systems is a major challenge in groundwater modeling. Flexible parameterization methods are needed to assess the complexity of the spatial distributions of these parameters in real aquifers. In this article, we introduce an adaptative parameterization to identify the distribution of hydraulic conductivity within the large‐scale (4400 km²) Upper Rhine aquifer. The method is based on adaptative multiscale triangulation (AMT) coupled with an inverse problem procedure that identifies the parameters' distributions by reducing the error between measured and simulated heads. The AMT method has the advantage of combining both zonation and interpolation approaches. The AMT method uses area‐based interpolation rather than an interpolation based on stochastic features. The method is applied to a standard 2D groundwater model that takes into account the interactions between the aquifer and surface water bodies, groundwater recharge, and pumping wells. The simulation period covers 204 months, from January 1986 to December 2002. Recordings at 109 piezometers are used for model calibration. The simulated heads are globally quite accurate and reproduce the main dynamics of the system. The local hydraulic conductivities resulting from the AMT method agree qualitatively with existing local experimental observations across the Rhine aquifer.     

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.     

Assimilation of historical head data to estimate spatial distributions of stream bed and aquifer hydraulic conductivity fields

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.     

The Effect of Modeled Recharge Distribution on Simulated Groundwater Availability and Capture

Simulating groundwater flow in basin‐fill aquifers of the semiarid southwestern United States commonly requires decisions about how to distribute aquifer recharge. Precipitation can recharge basin‐fill aquifers by direct infiltration and transport through faults and fractures in the high‐elevation areas, by flowing overland through high‐elevation areas to infiltrate at basin‐fill margins along mountain fronts, by flowing overland to infiltrate along ephemeral channels that often traverse basins in the area, or by some combination of these processes. The importance of accurately simulating recharge distributions is a current topic of discussion among hydrologists and water managers in the region, but no comparative study has been performed to analyze the effects of different recharge distributions on groundwater simulations. This study investigates the importance of the distribution of aquifer recharge in simulating regional groundwater flow in basin‐fill aquifers by calibrating a groundwater‐flow model to four different recharge distributions, all with the same total amount of recharge. Similarities are seen in results from steady‐state models for optimized hydraulic conductivity values, fit of simulated to observed hydraulic heads, and composite scaled sensitivities of conductivity parameter zones. Transient simulations with hypothetical storage properties and pumping rates produce similar capture rates and storage change results, but differences are noted in the rate of drawdown at some well locations owing to the differences in optimized hydraulic conductivity. Depending on whether the purpose of the groundwater model is to simulate changes in groundwater levels or changes in storage and capture, the distribution of aquifer recharge may or may not be of primary importance.     

Effective hydraulic conductivity of nonstationary aquifers

Assuming that the ln hydraulic conductivity in an aquifer is mathematically approximated by a spatial deterministic surface, or trend, plus a stationary random noise, we treat the problem of finding what the effective hydraulic conductivity of that aquifer is. This problem is tackled by spectral methods applied to a type of diffusion equation of groundwater flow, together with suitable coordinate transformations. Analytical (exact) solutions in terms of elementary functions are presented for one- and three-dimensional finite and infinite domains. Stability criteria are obtained for the solutions, in terms of a critical parameter, that turns out to involve the product of correlation scale and trend gradient. For the case of finite and symmetrical domains, additional provisions to insure the stability of numerical calculations of effective hydraulic conductivity are provided. Effective hydraulic conductivity is an important property, with potential applications in the calibrations of groundwater and transport numerical models.     

Effective hydraulic conductivity of nonstationary aquifers

Assuming that the ln hydraulic conductivity in an aquifer is mathematically approximated by a spatial deterministic surface, or trend, plus a stationary random noise, we treat the problem of finding what the effective hydraulic conductivity of that aquifer is. This problem is tackled by spectral methods applied to a type of diffusion equation of groundwater flow, together with suitable coordinate transformations. Analytical (exact) solutions in terms of elementary functions are presented for one- and three-dimensional finite and infinite domains. Stability criteria are obtained for the solutions, in terms of a critical parameter, that turns out to involve the product of correlation scale and trend gradient. For the case of finite and symmetrical domains, additional provisions to insure the stability of numerical calculations of effective hydraulic conductivity are provided. Effective hydraulic conductivity is an important property, with potential applications in the calibrations of groundwater and transport numerical models.     

Some relationships between lithology,basin form and hydrology: a case study from the Thames basin,UK

The role of lithology in influencing basin form and function is explored empirically by investigating correlations between a range of catchment variables, where the spatial unit of analysis is not surface catchments but lithologically coherent groundwater units. Using the Thames basin, UK, as a case study, nine groundwater units have been identified. Values for 11 hydrological and geomorphological variables, including rainfall, drainage density, Baseflow Index, aquifer porosity, storage coefficient and log‐hydraulic conductivity, aquifer and drainage elevation, river incision, and hypsometric integral have been estimated for each of the groundwater units in the basin, and Pearson correlation coefficients calculated for all pairs of variables. Seven of the correlation coefficients are found to be significant at a confidence level of > 99%. Negative correlations between drainage density and log aquifer hydraulic conductivity, and between drainage density and river incision, and positive correlations between log‐hydraulic conductivity and river incision, log‐hydraulic conductivity and Baseflow Index, and between Baseflow Index and river incision are inferred to have consistent causal explanations. For example, incision of rivers into aquifers leads to relative increases in hydraulic gradients in the vicinity of rivers which, in turn, promotes the development of secondary porosity increasing both aquifer hydraulic conductivity and, hence, Baseflow Index. The implication of this interpretation is that the geomorphological evolution of basins is intimately linked to the evolution of hydraulic conductivity of the underlying aquifers. This is consistent with, and supports the notion of a coupled complexly evolving surface water‐groundwater system. Copyright © 2011 John Wiley & Sons, Ltd.     

Influence of Groundwater Hydraulic Gradient on Bank Storage Metrics

The hydraulic gradient between aquifers and rivers is one of the most variable properties in a river/aquifer system. Detailed process understanding of bank storage under hydraulic gradients is obtained from a two‐dimensional numerical model of a variably saturated aquifer slice perpendicular to a river. Exchange between the river and the aquifer occurs first at the interface with the unsaturated zone. The proportion of total water exchanged through the river bank compared to the river bed is a function of aquifer hydraulic conductivity, partial penetration, and hydraulic gradient. Total exchange may be estimated to within 50% using existing analytical solutions provided that unsaturated zone processes do not strongly influence exchange. Model‐calculated bank storage is at a maximum when no hydraulic gradient is present and increases as the hydraulic conductivity increases. However, in the presence of a hydraulic gradient, the largest exchange flux or distance of penetration does not necessarily correspond to the highest hydraulic conductivity, as high hydraulic conductivity increases the components of exchange both into and out of an aquifer. Flood wave characteristics do not influence ambient groundwater discharge, and so in large floods, hydraulic gradients must be high to reduce the volume of bank storage. Practical measurement of bank storage metrics is problematic due to the limitations of available measurement technologies and the nested processes of exchange that occur at the river‐aquifer interface. Proxies, such as time series concentration data in rivers and groundwater, require further development to be representative and quantitative.     

A stochastic optimization framework for the restoration of an over-exploited aquifer

ABSTRACT

This study investigates the impact of hydraulic conductivity uncertainty on the sustainable management of the aquifer of Lake Karla, Greece, using the stochastic optimization approach. The lack of surface water resources in combination with the sharp increase in irrigation needs in the basin over the last 30 years have led to an unprecedented degradation of the aquifer. In addition, the lack of data regarding hydraulic conductivity in a heterogeneous aquifer leads to hydrogeologic uncertainty. This uncertainty has to be taken into consideration when developing the optimization procedure in order to achieve the aquifer’s sustainable management. Multiple Monte Carlo realizations of this spatially-distributed parameter are generated and groundwater flow is simulated for each one of them. The main goal of the sustainable management of the ‘depleted’ aquifer of Lake Karla is two-fold: to determine the optimum volume of renewable groundwater that can be extracted, while, at the same time, restoring its water table to a historic high level. A stochastic optimization problem is therefore formulated, based on the application of the optimization method for each of the aquifer’s multiple stochastic realizations in a future period. In order to carry out this stochastic optimization procedure, a modelling system consisting of a series of interlinked models was developed. The results show that the proposed stochastic optimization framework can be a very useful tool for estimating the impact of hydraulic conductivity uncertainty on the management strategies of a depleted aquifer restoration. They also prove that the optimization process is affected more by hydraulic conductivity uncertainty than the simulation process.

Editor Z.W. Kundzewicz; Guest editor S. Weijs