Groundwater quality management under uncertainty: stochastic programming approaches and the value of information

Abstract

A stochastic optimization model for containment of a plume of groundwater contamination through the installation and operation of pumping wells is developed. It considers explicitly uncertainty about hydraulic conductivity in the aquifer and seeks to minimize the expected total cost of operating the pumping wells plus the recourse cost incurred when containment of the contaminant plume is not achieved. Four different formulations of the model are examined, ranging from simply replacing all uncertain parameters by their expected values to a full stochastic programming with recourse model involving nonsymmetric linear quadratic penalty functions. The full stochastic programming with recourse model, which minimizes the expected total costs over a number of realizations of outcomes of the random parameters, is nonlinear and possibly nonconvex and is solved by an extension of the finite generation algorithm. The value of information about the uncertain parameters is defined through the differences between the values of the optimal solutions to the different formulations. A sample problem is solved using all four formulations. The results indicate that the explicit incorporation of uncertainty does make a difference in the solutions obtained. The work indicates that stochastic programming with recourse is a useful tool in management under uncertainty, and that it can be used with reasonable computational resources for problems of moderate size.

A Quantitative Groundwater Resource Management under Uncertainty Using a Retrospective Optimization Framework

“…The typical number of realizations range between a few tens and thousands, meaning more computer time, and hence high expenses [3]. For instance, van Leeuwen et al [24] used 1000 realizations; Wagner et al [25] used 100 realizations; while Wagner and Gorelick [26], Wagner et al [27], Ndambuki et al [14], and Ndambuki [3] used a total of 30 realizations. In this example, a total of 30 realizations of uncertain hydraulic conductivity fields (which leads to different aquifer water system responses (i.e., hydraulic heads/water table level drawdowns)) were generated for the heterogeneous aquifer system.…”

Monitoring and Modelling of Water Quality

“…This type of models answers "what if" question and finds the solution which is best according to a specified objective and satisfying physical, technical, legal and other constraints (Wagner, 1992). Groundwater quality models can analyse possibilities for removing a plume of polluted water or control its flow away from wells, streams, lakes.…”

“…Groundwater quality models can analyse possibilities for removing a plume of polluted water or control its flow away from wells, streams, lakes. For such purpose models can simulate scenarios including: inserting curtain walls, removing polluted soil, in situ (bio)chemical remediation or installing pumping/recharge wells (Wagner, 1992). For surface waters this type of models is used for development of long-time management scenarios for river basins or lakes and for assessment of the results of planned land use changes and investments (Kardaetz et al, 2008;Thebault & Qotbi, 1999;Yoshimura et al, 2009).…”

A methodology to determine optimal transmissivity measurement locations in groundwater quality management models with scarce field information

“…In order to overcome this difficulty, stochastic models have been used to deal with the spatial variability. In such models the Monte Carlo simulation approach is widely used where the real (unknown) function T(x) is assumed to be represented by a single realization of a random field (RF) of possible transmissivity values [Wagner et al, 1992].…”