69©Copyright The Korean Society of Environmental Engineers http://www.eer.or.kr

http://dx.doi.org/10.4491/eer.2012.17.S1.S69pISSN 1226-1025 eISSN 2005-968X

Environ. Eng. Res. 2012 December,17(S1) : S69-S74

Research Paper

Predicting Groundwater Level Using the Soft Computing Tool: An Approach for Precision Enhancement

Pagadala Damodaram Sreedevi1†, Pagadala Damodaram Sreekanth2, Shakeel Ahmed1

1National Geophysical Research Institute, Council of Scientific and Industrial Research, Hyderabad 500007, Andhra Pradesh, India2National Academy of Agricultural Research Management, Indian Council of Agricultural Research, Rajendranagar, Hyderabad 500407, Andhra Pradesh, India

AbstractMonitoring a non-linear phenomenon—such as the groundwater levels in an aquifer—by cost-effective techniques is quite a difficult

task. To overcome these limitations, soft computing tools are increasingly being used to predict groundwater levels with high accuracy. In the present study, a soft computing tool called support vector machine (SVM) was employed for predicting the groundwater levels jointly using weather parameters, at Maheshwaram watershed, Hyderabad, Andhra Pradesh, India. The accuracy of this approach was established based on statistical tools termed the regression coefficient, root mean square error, Nash-Sutcliffe coefficient, and error variation. For performance evaluation, the model outputs were compared with traditional statistical multiple regression (SMR) model outputs, and it was found that the SVR method offers better prediction than does SMR.

Keywords: Groundwater levels prediction, Statistical multiple regression analysis, Support vector machine

1. Introduction

Groundwater is indispensable to all life in semi-arid regions, particularly in hard rock terrenes that lack large and perennial surface water bodies, because in most of these places surface water resources are scarce, and in some places it is disappearing Over the last three decades, groundwater resources have been over-exploited, particularly for meeting the requirements of the agricultural and industrial sectors. Large-scale installation of deep bore wells has resulted in a serious decline in groundwater levels in many parts of the country, especially in hard rock areas.

Prediction of Groundwater levels is vital to help water manag-ers optimize groundwater use, and to protect this vital resource. Physically based numerical models have been used during the past several years for simulation and analysis of groundwater flows. They have been applied to problems ranging from aqui-fer safe yield analysis, to groundwater environmental issues. Regarding the diversity of available user-friendly groundwater flow models, the most challenging part of the flow modeling is the parameter estimation and definition of boundary condi-tions for models [1]. Since most of the flow models need to be discretized in the space and time domain, parameters involving aquifer characteristics and boundary conditions are required to be simulated [2].

For large-scale management problems, for which accurate simulation of localized behavior is not essential, numerical mod-

els are extensively used. There are some situations where more precise simulation is needed; therefore, we have to avoid simpli-fying the physical and mathematical assumptions of numerical models. Moreover, field data are typically not accessible for ap-plying to numerical modeling of localized problems [2, 3]. Thus, the problems of inherent complexity and data uncertainty of groundwater systems are the most limiting factors on physical-based modeling simulation accuracy.

In this article, we investigate a state of the art modeling tool, namely support vector machine (SVM), which offers an im-proved and simplified approach to a physical-based model, by applying it to predict the water levels of a specific monitoring well. SVMs are developed based on statistical learning theory (SLT). The most advantageous aspect of these learning machines is their employment of the structural risk minimization (SRM) principle, from which SVMs are able to generalize well to unseen data. According to this principle, SVM has two outstanding fea-tures, which lead to it being a promising prediction method. The first one is its excellent generalization; and the second one is its sparse representation. SVM can be used both for classification and regression problems, as it is a classifier derived from SLT, and were first introduced by Vapnik [4] in 1998. In regression prob-lems, a linear learning machine in a kernel induced feature space learns a non-linear function, while the capacity of the system is controlled by a parameter that does not depend on the dimen-sionality of the space. The process of employing SVMs in regres-

Received September 03, 2012 Accepted October 10, 2012†Corresponding AuthorE-mail: pd_sreedevi@yahoo.co.inTel: +91-4023434700(2641) Fax: +91-4027171564

This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

70http://dx.doi.org/10.4491/eer.2012.17.S1.S69

Pagadala Damodaram Sreedevi, Pagadala Damodaram Sreekanth, Shakeel Ahmed

elevation ranges from 600 to 670 m above mean sea level (amsl) Hot/dry summers and cool/dry winters characterize the area, with a distinct rainy season from June to September. The temper-ature ranges from 22°C to 44°C, with an average rainfall of about 573 mm (an average of 25 years data at Maheshwaram mandal). The region receives more than 80% of its rainfall from the south-west monsoon, but also significant rainfall from the Bay of Ben-gal [8]. In general, the topography in the watershed dips gently from south to north.

The area comprises granites of Archean age, with a thin soil cover of sandy loam and clay (Fig. 2). These granites are medium to coarse grained, pink and gray in color, and have undergone a variable degree of weathering. One hundred fifty dug-wells (defunct dry wells) were examined, and the nature of the weath-ering was studied. The weathered-zone profiles range in thick-ness from 1 to 5 m below ground level (bgl). They are followed by semi-weathered and fractured zones that reach down to 20 m bgl (Fig. 3). The groundwater flow system is local, i.e., with its recharge area at a topographic high and its discharge area at a topographic low, adjacent to each other (Fig. 4) [9].

Maheshwaram is a closed watershed, with no major streams in the area. A network of 1st and 2nd order streams culminates in a large tank known as Mankal Cheruvu, which forms the dis-charge area. The area in general is undulating, and the majority of the area has a slope of 2%. The weathered zone has become completely dry, due to over-exploitation. The existing wells tap the fractured bedrock with groundwater under semi-confined conditions [10]. In general, the water striking level is around 25–30 m bgl whereas the water levels are at depths ranging from 15–23 m. The water-striking surface is always found to be at a deeper

sion problems is referred to as support vector regression (SVR). Since then, there have been a growing number of researches on the SVMs applications. Recently, SVMs have been used in water resources and hydrological areas as a novel approach of learning. Asefa et al. [3, 5] applied SVMs for various water resources mod-elings, including optimal design of groundwater monitoring net-works for both the head observation and contamination detec-tion networks. Many workers have demonstrated the prediction capability of SVMs, compared to that of artificial neural networks (ANNs), in forecasting aquifer water level elevation [2, 6, 7].

In all of the aforementioned applications, SVMs presented overall superior performance, when compared with other data-driven models, such as ANNs. This encouraging performance is because of the high generalization property of SVMs, and it motivates the researcher to work on further applications. In the present study, the results of a statistical multiple regression (SMR) models are used to examine the performance of a SVR model in predicting groundwater levels.

2. Materials and Methods

2.1. Study Area

The Maheshwaram watershed is situated in the Ranga Reddy district of Andhra Pradesh, India, at a distance of about 35 km from Hyderabad. The watershed has an area of 53 km2 (Fig. 1). The study area is situated between longitude 78°24΄30˝E to 78°29΄00˝E and latitude 17°06΄20˝N to 17°11΄00˝N, and forms part of the Survey of India toposheet no. 56K/8. The topographic

Fig. 1 . Location map of Maheshwaram watershed. Fig. 2. Geological map.

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Predicting the Groundwater Levels Using SVM

data for the model training, and three years (2004-2006) of data for the validation.

2.2. SVMs in Regression

In regression problems, a linear learning machine in a kernel induced feature space learns a non-linear function, while the ca-pacity of the system is controlled by a parameter that does not depend on the dimensionality of the space. In SVR, the basic idea is to map the input space x to the high dimensional feature space Φ xin a non-linear manner. This relationship is depicted in Eq. (1), where ‘b’ is the threshold.

ƒ(x) = (w. Φ(x)) + b (1)

Both ‘b’ and the constant ‘w’ are estimated by minimizing the sum of the empirical risk and a complexity term. In Eq. (2), the first term denotes the empirical risk, and the second term de-notes the complexity term.

[ ] [ ] ( )( ) 2

1

2wfCwff

z

iiiempreg yxRR λλ +−=+= ∑

= (2)

Where, ‘z’ denotes the size of the sample, C (.) is a cost function, and λ is the regularization constant. The kernels provide the flex-ibility of the high dimensional feature space for low computa-tional costs, and are a crucial part of SVR. No analytical method is currently available to determine the most suitable kernel for a particular data set, which determination must be done by trial and error. In this study, mainly linear kernel, RBF and MLP ker-nels were applied for predicting the groundwater level, by using SVR. There are many types of kernel functions, such as linear kernels, polynomial kernels, sigmoid kernels, MLP kernels, RBF kernels, etc. Each kernel function is suitable for some tasks, and it must be chosen for the tasks under consideration by hand, or by using prior knowledge [12].

depth than the static water level, supporting that the aquifers are in semi-confined condition. The groundwater is exploited for ir-rigation (mostly through bore wells/submersible pumps), where the discharges are in the range of 100 to 300 m3/day. The ground-water flow is from southwest to north-east (main drainage), and from south to north in other parts of the watershed.

Monthly water levels have been collected from 22 Indo-French Project (IFP) wells fairly distributed in the study area (Fig. 1), during the study period of 2000–2006 [11]. The monitor-ing wells are all non-pumping bore wells, and water levels were monitored using a graded tape that provides sound and light signals when it touches water in the well, with an accuracy of 2 mm. Care has been taken to record the water level in all of the wells in the minimum possible time, and also when surrounding wells were not being pumped (so the water level could reach its natural condition). The data on weather parameters, viz., evapo-ration, rainfall, relative humidity, and temperatures (minimum and maximum), were collected from the local hydro-meteoro-logical station (HM), which was established in 1999 at the center of the Maheshwaram watershed by the Andhra Pradesh Ground Water Department.

The above-mentioned area was selected for developing a model for predicting groundwater levels. In this model, a total of 8 variables (including initial well points along with evaporation, rainfall, relative humidity, minimum and maximum tempera-ture-dry and wet) are independent variables for one dependent variable, i.e., groundwater levels. The applied transfer functions for SVR are linear, radial basis function (RBF) and multilayer per-ceptron (MLP) kernels. This iteration was done for 22 wells.

For this study, we used three years (2000-2003) of monthly

Fig. 3. Vertical sub-surface profile of the study area.

Fig. 4. Groundwater flow map.

72http://dx.doi.org/10.4491/eer.2012.17.S1.S69

Pagadala Damodaram Sreedevi, Pagadala Damodaram Sreekanth, Shakeel Ahmed

ent sets, each with randomly chosen respective well points for training and testing of the above SVR and SMR models (Table 1).

3.1. SVR-Linear Kernel

Based on the statistical analysis, the root mean square error (RMSE) of the SVR-linear across the different sets, viz., set 1, 2, 3, and 4 was found to be 2.07, 2.76, 2.02, and 2.39, respectively. The regression coefficient (R2) for all of the four sets, viz., set 1, 2, 3, and 4 was found to be 0.98, 0.97, 0.98, and 0.98, respectively, with the linear kernel. The error variation was also found to be at its minimum for all of the sets tried, i.e., -1.02 to 0.50 (for set 1), -1.03 to 0.88 (for set 2), -0.74 to 0.49 (for set 3), and -0.91 to 0.59 (for set 4) (Table 2).

3.2. SVR-RBF Kernel

All of the four sets, viz., set 1, 2, 3, and 4, when analyzed with SVM-RBF, recorded error variation in the range of -0.92 to 1.23, -0.93 to 1.15, -0.90 to 1.18, -0.91 to 1.18, respectively. The RMSE was calculated to be 4.87, 5.11, 4.55, and 4.83 for set 1, 2, 3, and 4, respectively. The R2 was found to be comparatively lesser than the SVR-linear analysis, i.e., 0.93 (for sets 1, 2, and 4), and 0.94 (for set 3) (Table 2).

3.3. SVR-MLP Kernel

The error variation between the actual and calculated values using SVR-MLP was found to range from -6.54 to 4.97 (for set 1), -8.39 to 5.27 (for set 2), -3.67 to 2.85 (for set 3), and -5.76 to 1.63 (for set 4). However, the RMSE and R2 were found to be non-sig-nificant for all four sets (Table 2).

The accuracy of each model was tested with Nr efficiencies. Nr efficiencies can range from −∞ to 1. An efficiency of 1 (Nr = 1) corresponds to a perfect match of modeled discharge to the ob-served data. The efficacy coefficients of SVR-linear, SVR-RBF and SVR-MLP are 0.83, -0.03, and -4.15, respectively.

3.4. SMR

All of the four sets, viz., set 1, 2, 3, and 4, when analyzed with SMR, recorded error variation in the range of -1.48 to 1.26, -2.25 to 2.18, -1.42 to 1.06, and -2.25 to 2.18, respectively. The RMSE was calculated to be 2.07, 2.78, 2.03, and 2.31 for set 1, 2, 3, and 4, respectively. The R2 was found to be comparatively lesser than

2.3. Linear Kernel

The Linear kernel is the simplest kernel function. It is given by the common inner product <x,y> plus an optional constant c.

K(x,y) = xTy + c (3)

2.4. RBF Kernel

The Gaussian RBF kernel is a most successful kernel in many problems, but still has restrictions in some complex problems. This kernel is widely used in many problems. It uses the Euclid-ean distance between two points in the original space, to find the correlation in the augmented space [13].

K(x,y) = exp(-γ || x-y ||2) (4)

2.5. MLP Kernel

The MLP kernel representation is,

K(x, y) = tanh(ρ (x,y) + ∂) (5)

The value of the kernel will depend on certain values of the scale, ρ, and offset, ∂, parameters.

Nash-Sutcliffe coefficient (Nr) is a measure of statistical asso-ciation, which indicates the percentage of the observed variance that is explained by the predicted data. The Nash-Sutcliffe coeffi-cient, also known as the efficiency criterion, is perhaps the most common measurement mentioned in the hydrological literature for evaluating the performance of a model [14, 15].

3. Results and Discussion

The whole data set was arbitrarily grouped into four differ-

Table 1. Data set distribution

Data set Observations (well no.)

Set 1 1, 6, 11, 18, 20

Set 2 2, 5, 7, 9, 13, 15, 16, 22

Set 3 3, 4, 8, 10, 12, 14, 17, 19, 21

Set 4 1 to 22

Table 2. Statistical values of SVR models

Data set

SVR-linear SVR-RBF SVR-MLP

R2 RMSEError

R2 RMSEError

R2 RMSEError

Min. Max. Min. Max. Min. Max.

Set 1 0.98 2.07 -1.02 0.50 0.93 4.87 -0.92 1.23 NS NS -6.54 4.97

Set 2 0.97 2.76 -1.03 0.88 0.93 5.11 -0.93 1.15 NS NS -8.39 5.27

Set 3 0.98 2.02 -0.74 0.49 0.94 4.55 -0.90 1.18 NS NS -3.67 2.85

Set 4 0.98 2.39 -0.91 0.59 0.93 4.83 -0.91 1.18 NS NS -5.76 1.63

SVR: support vector regression, RBF: radial basis function, MLP: multilayer perceptron, R2: regression coefficient, RMSE: root mean square error, NS: not significant.

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Predicting the Groundwater Levels Using SVM

between SVM and SVR parameters is shown in Fig. 6.An accurate prediction of groundwater levels is needed to de-

sign sustainable water management strategies in the study area, because this aquifer is under a stressed condition. The use of physical based flow models in groundwater management, how-ever, is often jeopardized by data and parameter availability. By using soft computing prediction models like SVR in this study, it shows that very good accuracy and the selection of variables (input variables) is very easy.

The present study suggests that SVR would be a better choice in predicting groundwater levels. Further, the main advantages of SVR [18] are: 1) the architecture of the system need not be de-termined before training. Input data of any arbitrary dimension can be treated only linearly, regarding the relation of cost to the number of input dimensions; 2) SVM treats regression as a qua-dratic programming problem of minimizing the data fitting error plus generalization, which produces a global solution having a minimum fitting error, while high generalization of the estimat-ed model can be obtained. The present approach also includes multiple parameters, mainly the meteorological ones that influ-ence the groundwater levels, and hence the prediction becomes more realistic and useful.

4. Conclusions

In this study, a better forecasting model using SVR has been developed for predicting monthly groundwater level fluctua-tions for 22 wells in the Maheshwaram watershed. For this study, we used three years (2000–2003) of monthly groundwater level data for the model training, and three years (2004–2006) of monthly groundwater level data for the validation. The most suitable configuration for this task proved to be the SVR-linear kernel method, as it showed the most accurate prediction. Fur-ther, a significant advantage of this model is that it can also pro-vide satisfactory predictions with limited groundwater level re-cords. Earlier, many researchers also proved that SVR models are the best tools for predicting groundwater levels. Future research efforts should be envisaged towards exploring the use of soft computing tools for predicting ground water levels with more accuracy and stability than the conventional methods.

the SVM-linear analysis, i.e., 0.90 for set 1, 0.85 for set 2, 0.79 for set 3, and 0.84 for set 4 (Table 3).

3.5. Comparison between SVR and SMR Models

In the present study a comparison was made between one of the soft computing tools, i.e., SVR models, and SMR. A close perusal of the data clearly indicated that the SVR-linear model performance is better than that of the SMR model. This suggests that SVR would be a better choice in predicting groundwater lev-els than a statistical model. The performance of the SVR model is shown in Fig. 5. The SVR-linear kernel prediction trend followed the actual data more closely. This again shows the superiority of SVR in predicting the ground water levels more accurately and consistently over other techniques. Kanevski et al. [16] also showed the promising performance of SVR in spatial mapping tasks. As described by Vapnik [17], SVR exploits the idea of map-ping input data into a high dimensional (often infinite) repro-ducing kernel Hilbert space (RKHS), where a linear regression is performed. One reason that SVR performs better than other methods is that SVR is designed to minimize the structural risk, whereas the other techniques are usually based on the minimi-zation of empirical risk. In other words, SVR seeks to minimize an upper bound of the generalization error, rather than minimiz-ing training error. So SVR is usually less vulnerable to the over-fitting problem. A graphical representation of the error variation

Table 3. Statistical values of SMR model

Data set

SMR

R2 RMSEError variation

Min. Max.

Set 1 0.90 2.07 -1.48 1.26

Set 2 0.85 2.78 -2.25 2.18

Set 3 0.79 2.03 -1.42 1.06

Set 4 0.84 2.31 -2.31 2.18

SMR: statistical multiple regression, R2: regression coefficient, RMSE: root mean square error.

Fig. 5. Trend between observed and support vector regression-linear model.

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

May

-04

Aug

-04

Nov

-04

Feb-

05

May

-05

Aug

-05

Nov

-05

Feb-

06

May

-06

Erro

r var

iatio

n

Month

SVM errorSMR error

Fig. 6. Error variation between support vector machine (SVM) and support vector regression (SVR).

74http://dx.doi.org/10.4491/eer.2012.17.S1.S69

Pagadala Damodaram Sreedevi, Pagadala Damodaram Sreekanth, Shakeel Ahmed

RD, Veith TL. Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans. ASABE 2007;50:885-900.

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10. Subrahmanyam K, Ahmed S, Dhar RL. Geological and hydro-geological investigations in the Maheshwaram watershed, Andhra Pradesh, India. Hyderabad: National Geophysical Research Institute; 2000. Technical report no. NGRI-2000-GW-292.

11. Ahmed S, Sreedevi PD. Simulation of flow in weathered-frac-tured aquifer in a semi-arid and over-exploited region. In: Ahmed S, Jayakumar R, Salih A, eds. Groundwater dynamics in hard rock aquifers. Dordrecht: Springer; 2008. p. 219-233.

12. Sreekanth PD, Sreedevi PD, Ahmed S, Geethanjali N. Com-parison of FFNN and ANFIS models for estimating ground-water level. Environ. Earth Sci. 2011;62:1301-1310.

13. Sreekanth PD, Geethanjali N, Sreedevi PD, Ahmed S, Ravi Ku-mar N, Kamala Jayanthi PD. Forecasting groundwater level using artificial neural networks. Curr. Sci. 2009;96:933-939.

14. Daliakopoulos IN, Coulibaly P, Tsanis IK. Groundwater level forecasting using artificial neural networks. J. Hydrol. 2005;309:229-240.

15. Nash JE, Sutcliffe JV. River flow forecasting through con-ceptual models. Part I. A discussion of principles. J. Hydrol. 1970;10:282-290.

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Acknowledgments

The authors are grateful to the Director of the National Geo-physical Research Institute (CSIR) for his kind permission and encouragement to publish this work. The first author gratefully acknowledges the Department of Science and Technology New Delhi, for financial assistance in the form of a Fast Track Young Scientist Project grant (No. SR/FTP/ES-49/2009).

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