Applied Soft Computing 28 (2015) 541–549 Contents lists available at ScienceDirect Applied Soft Computing j ournal homepage: www.elsevier.com/locate/asoc Evaluation of methods for estimating aquifer hydraulic parameters b c d a,e,∗ f S.M. Bateni , M. Mortazavi-Naeini , B. Ataie-Ashtiani , D.S. Jeng , R. Khanbilvardi a Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang, Jiangsu, 212013, China b Department of Civil and Environmental Engineering, and Water Resources Research Center, University of Hawaii at Manoa, Honolulu, HI, 96822, USA c Department of Civil, Surveying and Environmental Engineering, University of Newcastle, Callaghan, NSW, Australia d Department of Civil Engineering, Sharif University of Technology, Tehran, Iran e Griffith School of Engineering, Griffith University, Gold Coast Campus, Queensland, QLD 4222, Australia f NOAA-Cooperative Remote Sensing Science & Technology Center (NOAA-CREST), City University of New York, NY, USA a r t i c l e i n f o a b s t r a c t Article history: An accurate estimation of aquifer hydraulic parameters is required for groundwater modeling and proper Received 16 August 2013 management of vital groundwater resources. In situ measurements of aquifer hydraulic parameters are Received in revised form 30 July 2014 expensive and difficult. Traditionally, these parameters have been estimated by graphical methods that Accepted 17 December 2014 are approximate and time-consuming. As a result, nonlinear programming (NLP) techniques have been Available online 24 December 2014 used extensively to estimate them. Despite the outperformance of NLP approaches over graphical meth- ods, they tend to converge to local minima and typically suffer from a convergence problem. In this study, Keywords: Genetic Algorithm (GA) and Ant Colony Optimization (ACO) methods are used to identify hydraulic Aquifer hydraulic parameters parameters (i.e., storage coefficient, hydraulic conductivity, transmissivity, specific yield, and leakage Ant Colony Optimization (ACO) factor) of three types of aquifers namely, confined, unconfined, and leaky from real time–drawdown Genetic Algorithm (GA) Nonlinear programming (NLP) pumping test data. The performance of GA and ACO is also compared with that of graphical and NLP Pumping test techniques. The results show that both GA and ACO are efficient, robust, and reliable for estimating var- ious aquifer hydraulic parameters from the time–drawdown data and perform better than the graphical and NLP techniques. The outcomes also indicate that the accuracy of GA and ACO is comparable. Compar- ing the running time of various utilized methods illustrates that ACO converges to the optimal solution faster than other techniques, while the graphical method has the highest running time. © 2014 Elsevier B.V. All rights reserved. 1. Introduction variables. Pumping test is the most commonly used and standard technique for inverse modeling of groundwater parameters. In this In many parts of the world, groundwater has been used as a test, time–drawdown measurements are analyzed via the analyt- reliable source of water for numerous purposes such as irrigation, ical solutions such as Theis, corrected Theis, and Hantush models and domestic and industrial uses. Therefore, it is necessary to depending on the aquifer type in which the test is performed [8]. appropriately model the complex groundwater system in order to Several approaches have been proposed to solve the above- properly manage this vital resource. To do so, an accurate specifi- mentioned inverse problem and obtain aquifer hydraulic param- cation of aquifer hydraulic parameters such as transmissivity (T), eters. The first group of approaches is graphical. The aquifer hydraulic conductivity (K), storage coefficient (S), leakage factor (B), hydraulic parameters estimated by the graphical technique are of and specific yield (Sy) is needed since these parameters are com- questionable reliability since a perfect curve matching is not antic- monly required in groundwater/aquifer flow modeling [1–7]. These ipated and the match is typically approximate [1]. The traditional parameters can be measured by laboratory experiments or in situ graphical technique is time-consuming, burdensome, and subjec- tests; however, the former is inaccurate, and the latter is expensive. tive [8]. The second group of approaches attempts to estimate An alternative option for the estimation of the aquifer parame- aquifer parameters using nonlinear programming (NLP) techniques ters is through inverse modeling. In this procedure, some variables such as the steepest descent method, conjugate gradient method, that can be obtained more accurately (e.g., hydraulic head); then, Gauss–Newton method, Marquardt algorithm, etc. Although NLP the aquifer parameters are inversely estimated from the measured methods often outperform the graphical approaches, they suf- fer from a number of shortcomings. Aquifer models are typically non-convex and nonlinear, and for such models, classical gradient- ∗ based optimization techniques may result in local optimum values Corresponding author. Tel.: +61 755528590. E-mail address: d.jeng@griffith.edu.au (D.S. Jeng). rather than global ones. The gradient based techniques may cause http://dx.doi.org/10.1016/j.asoc.2014.12.022 1568-4946/© 2014 Elsevier B.V. All rights reserved. 542 S.M. Bateni et al. / Applied Soft Computing 28 (2015) 541–549 instability and convergence problems due to the numerical dif- observing the response of aquifer (drawdown) in observation wells. ficulties. Moreover, their convergence to a global optima highly The hydraulic-head drawdowns from the pumping test can be used depends on the selection of initial search points. Furthermore, these for aquifer characterization and the estimate of parameters such techniques cannot find the local gradient for the problems with as transmissivity (T), storage coefficient (S), hydraulic conductivity discontinuous objective function [4,9]. (K), leakage factor (B) and specific yield (Sy). Herein, the theoretical To overcome the aforementioned shortcomings, the non- models for response of idealized aquifers to pumping are presented. traditional methods such as evolutionary algorithms can be applied as they can handle highly nonlinear, even non-smooth problems 2.1. Theis model and converge to the global rather than local optimum. In this study, two well-known evolutionary algorithms namely, Genetic The well-known Theis [34] solution describes radial flow to a Algorithm (GA) and Ant Colony Optimization (ACO) are proposed fully penetrated pumping well in a homogeneous, isotropic con- to estimate the hydraulic parameters of three major types of fined aquifer of infinite horizontal extent which is pumped at aquifers (i.e., confined, unconfined, and leaky). An objective func- a constant rate Q. Theis solution that is considered as one of tion is formulated for the inverse estimation using the observed the fundamental breakthroughs in the development of hydrologic hydraulic heads from pumping tests. Thereafter, GA and ACO are modeling can be shown as follows, utilized to minimize the objective function by tuning the aquifer Q = hydraulic parameters. These techniques have several advantages s(r, t) W(U) (1) 4T over gradient-based methods [10,11]: (1) They do not require where s(r, t) is the drawdown at a radial distance r from the a continuous objective function; (2) They often can find a near pumping well at time t since the beginning of pumping, T is the global optima and do not get trapped in a local-optimal solution; 2 transmissivity, S is the storage coefficient, U = r S/4Tt, and W(U) (3) They provide a number of near global optima solutions and is the Theis well function, which is given by hence give users the ability to assess the solutions and make a ∞ decision. e−x W(U) = dx (2) GA has been applied in a number of groundwater optimiza- x U tion problems. El Harrouni et al. [12] used GA to manage pumping from wells and to estimate hydraulic parameters in heterogeneous In this study, the Theis well function W(U) is calculated via the ≤ aquifers. In a similar effort, Lingireddy [13] integrated GA and neu- Taylor series expansion for small values of U(0 < U 1) and the ral network to obtain aquifer hydraulic parameters. Samuel and Gauss–Laguerre quadrature for large values of U(U > 1) [35]. Jha [8] and Jha et al. [4] examined effectiveness of GA in esti- Unconfined aquifers have a different response to the pumping mating aquifer parameters. They showed that GA is a viable and test compared to confined aquifers. Therefore, the Theis model efficient technique that often overcomes the subjectivity, high com- should be corrected in order to be used for unconfined aquifers. putational burden and ill-posedness of traditional optimization The corrected Theis model replaces s(r, t) on the left hand side of 2 − methods. In a more recent attempt, Rajesh et al. [14] utilized GA, Eq. (2) with s (r, t), where s is equal to s (s /2D0), and D0 is the graphical, and sequential unconstrained minimization approaches initial saturated thickness of the unconfined aquifer [36,37]. Theis to retrieve unconfined aquifer hydraulic parameters. Their results and corrected Theis models are used in this study for confined and revealed that GA outperforms the other two methods. unconfined case studies, respectively. ACO has been successfully used in water resources optimiza- tion problems such as minimizing the capital costs associated with 2.2. Hantush model water distribution systems [15–18], design of irrigation networks [19], optimal groundwater monitoring design [20], multi-purpose The leaky-aquifer theory has been evolved from the Theis equa- reservoir operation [21,22], optimal design of open channels [23], tion. In two sets of papers, Hantush and Jacob [38] and later Hantush underground seepage flow [24], and saltwater intrusion in the [39,40], the original differentiation between the Theis response for coastal aquifers [25]. To the best knowledge of the authors, the confined aquifers and the one for leaky aquifers was discussed. The only study on the estimation of aquifer parameters with ACO was analytical solution of Hantush and Jacob [38] can be couched in the conducted by Li et al.