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Water Resources Management

, Volume 32, Issue 15, pp 4985–5005 | Cite as

A Framework for Ground Water Management Based on Bayesian Network and MCDM Techniques

  • Abbas RoozbahaniEmail author
  • Ebrahim Ebrahimi
  • Mohammad Ebrahim Banihabib
Article
  • 97 Downloads

Abstract

Groundwater resources are steadily subjected to increasing water demands. The aquifers are considered as the most accessible source of fresh water. In recent years, they have been faced with severe water withdrawal in arid and semi-arid countries like Iran and thus some aquifers was considered as forbidden aquifers that it means the water withdrawal from these aquifers is unauthorized. Given a critical situation, groundwater resources management in the form of tools such as monitoring the level of the aquifers and developing the restoring scenarios is essential. Therefore, for this purpose, a framework has been developed based on prediction of groundwater level using Bayesian Networks (BNs) model. Furthermore, Multi Criteria Decision Making methods (MCDM) techniques proposed and employed for ranking of proposed groundwater management scenarios. This framework was evaluated for restoring the Birjand aquifer in Iran in different hydrological conditions. A probabilistic Dynamic BN was proposed for groundwater level prediction under uncertainties. After analyzing the obtained results, the applicable short term scenarios for groundwater management as well as appropriate economic, social and technical criteria were defined for decision making procedure. Then, using elicitation of decision makers’ opinions on the relative importance and performance of criteria, SAW, TOPSIS and PROMETHEE-II techniques were applied to rank the scenarios and the obtained results were aggregated by Borda method for final ranking of the scenarios. Lastly, the final results demonstrates the capability of the proposed framework for groundwater resources planning and management which can be employed for reducing the risk of aquifer level declining.

Keywords

Bayesian network Groundwater management PROMETHEE-II TOPSIS Borda 

1 Introduction

The water tension impacts the aquifers and make critical situation in most of arid and semi-arid countries especially in Iran. Although groundwater contain low percentage of water on the earth, but often have high quality water resources and easy accessible which can lead to excess water withdrawal and declining groundwater level. As a result, some plain was considered as forbidden plains which means the water withdrawal from these aquifers is illegal. This made the serious tensions in water management. Thus, it is necessary to develop decision support system for groundwater resources along with monitoring the aquifer level and evaluating the effective variables. .

During the recent years some statistical, simulation and optimization methods have been applied for groundwater management (e.g. Fawen et al. 2013; Molina et al. 2013; Thomas and Famiglietti 2015; Ashwell et al. 2018; Rossetto et al. 2018). One of the approaches to aquifer level monitoring is to employ prediction tools for future periods. Today, various tools are used to predict the surface of the aquifer, including mathematical models, Artificial Neural Networks (ANN), Fuzzy Inference Systems (FIS), Bayesian Networks (BN) and time series analysis.

In the last decade, there has been an increasing use of probabilistic assessment, risk assessment, and practices for prediction issues. In recent years, Bayesian Networks have been applied to forecast the hydrological variables due to its flexible and simple structure. BNs are powerful tools for predicting consequences of water management scenarios and uncertain factors (Molina et al. 2013). Bayesian Networks have a lot of advantages as an integrated framework such as their ability to combine quantitative and qualitative data, their capability in the investigation of uncertainties, their provision of a conceptual system, even when the whole process is not present in a system. Moreover, they can also be easily updated with new data (Castelletti and Soncini-Sessa 2007).

In the recent years, due to the flexible and simple structure of Bayesian Network, it has been applied in variant water related issues, especially for the hydrological predictions. Many researchers use it as an artificial intelligence to simulate the complex engineering and managerial issues (Heckerman et al. 1995; Jensen 1996); Groundwater management (Henriksen et al. 2007; Olalla et al. 2007; Farmani et al. 2009; Fienen et al. 2013; Roozbahani et al. 2017); Irrigation systems modelling (Batchelor and Cain 1999); Integrated natural resource management (Borsuk et al. 2004; Hamilton et al. 2007; Johnson et al. 2009; Alameddine et al. 2010); River basins modelling (Kragt et al. 2009; Merritt et al. 2010; Holzkämper et al. 2012; Madadgar and Moradkhani 2014, Shin et al. 2016) and urban water supply (Babovic et al. 2002; Anbari et al. 2017; Tabesh et al. 2018).

The application of management tools and decision support tools is essential for exhausting the plains from the water resources stresses and for managing water resources. For this purpose, one of decision support tools are Multi criteria Decision Making (MCDM) techniques. Considering conditions of forbidden aquifers, different management strategies can be evaluated and ranked based on their effectiveness by using these decision support tools. Several researches have been reported the application of these technique in water resources management. For example, Roozbahani et al. (2012) introduced a new group Multi-Criteria-Decision-Making (MCDM) method by combining of PROMETHEE1 and Multi-attribute decision making with dominance in the criteria methods for Urban Water Supply Management and applied it to the case study of Melbourne water supply system. Geng and Wardlaw (2013) used a MCDM approach in a river basin management in China, in order to consider the different objectives for decision making process. They ranked a set of different management scenarios such as reductions in irrigated areas, improvement in irrigation efficiencies and changes in cropping pattern by Compromise Programming (CP) technique. Dabral et al. (2014) employed spatial MCDM approach in India and determined the suitable locations for artificial recharge of aquifers. Azarnivand et al. (2015) and Azarnivand and Banihabib (2017) presented ranking of strategic options based on sustainable development criteria to restore Lake Urmia in Iran, by using Fuzzy Analytic Hierarchy Process (FAHP) and Strength - Weakness - Opportunity – Threat (SWAT) analysis. Banihabib et al. (2017) and Banihabib and Shabestari (2017) developed integration of MCDMs and Fuzzy AHP-TOPSIS, respectively, for strategic management of water resources in arid regions.

These reports deliberate the developing capability of MCDMs in surface water resources managements which should also be addressed in groundwater management. Research studies about applying the integration of Bayesian network for prediction purpose and MCDM techniques for decision making in groundwater management, are still relatively scarce. Therefore, this research aims to propose an integrated decision support system for groundwater systems and its capability is evaluated in one of Iran’s most important aquifers.

Birjand aquifer as one of the forbidden aquifers in Iran recently has been faced with a sharp dropping in groundwater level which requires management practices, and thus has been selected as the case study to evaluate the proposed framework. Given the critical situation of water resources and lack of effective management scenario for Birjand aquifer, it is necessary to apply MCDM techniques to propose appropriate restoring strategy for it. By using these techniques, the best management scenario can be proposed based on the socioeconomic status of this region. Consequently, in this study, the short term and practical scenarios were employed to decrees the water stress in Birjand aquifer by applying Bayesian Network model. The proposed management scenarios include alteration of current surface irrigation to pressurized irrigation systems, unauthorized wells removal, and construction of artificial recharge projects and installation of smart water meters.These scenarios are evaluated usingthree MCDM techniques, namely, SAW,2 TOPSIS3 and PROMETHEE-II and then final ranking is obtained by application of Borda group decision making method. According to the description provided, the main steps of the proposed framework are as follows:
  • Development of Dynamic Bayesian Networks model for prediction of groundwater level,

  • Development of integrated decision support system by taking into account the technical, social and economic criteria for ranking scenarios to recover the Birjand aquifer by integration of the practical MCDM techniques and decision makers’ opinions under group decision making environment.

2 Methodology

As mentioned in introduction, in this research, a framework is proposed for groundwater resources management by integration of Bayesian Network approach and Multi Criteria Decision Making models. Accordingly, the Bayesian Network model was used to predict and evaluate the effectiveness of management scenarios on the groundwater level of Birjand aquifer plain, Iran. MCDM techniques were also used to rank groundwater management scenarios. The flowchart of the research steps is shown in Fig. 1. The various stages of this flowchart will be discussed further.
Fig. 1

Flowchart of proposed framework in this research

2.1 Bayesian Networks

Bayesian Networks are used to simulate the systems which consist of uncertain conditions through incomplete understanding or insufficient knowledge of a system (Pearl 1988). They are graphical models to express probabilistic relationships between uncertain variables. BNs have been developed based on conditional probabilities and Bayes theory. Bayes theory is mentioned in the following equation (Neapolitan 2003):

$$ P\left(E|F\right)=\frac{P\left(F|E\right)P(E)}{P(F)} $$
(1)
Similarly, for n events of E1, E2,...,En, Eq. (2) can be applied:
$$ P\left({E}_i|F\right)=\frac{P\left(F|{E}_i\right)P\left({E}_i\right)}{P\left(F|{E}_1\right)P\left({E}_1\right)+P\left(F|{E}_2\right)P\left({E}_2\right)+\dots P\left(F|{E}_n\right)P\left({E}_n\right)} $$
(2)
Where P(E) is the probability of event E; P(F)is the probability of event F; P(E|F) and P(F|E) are conditional probability of E given F and conditional probability of F given E, respectively.

A BN is a network of nodes which are connected using direct links and also a probability function is assigned to each node. A node represents a discrete or a continuous random variable, and a link represents causal relationship between nodes (Anbari et al. 2017). If a node has no parent, the node will have a marginal probability table. However, if a node has one parent or more parents, the node has a Conditional Probability Table (CPT). CPT in the case of continuous variables indicates the mean and variance data for each node (variable).This table, in the case of discrete variables, denotes the probability of belonging each node (variable) to different clusters, so that the sum of probabilities is equal to 100 %.

After designing a network, it can be used to determine the probability of all variables using observed data for nodes with known status. Calculating the conditional probability of some variables based on available data of other variables in BNs is called inference (Hugin Expert A/S 2012). using BNs has some advantages such as integrating different types of variables and data within a framework, describing uncertainty, and the updating ability when new information and knowledge become available (Cinar and Kayakutlu 2010).

2.1.1 Bayesian Network Modeling

  1. Step 1:

    Preparing input variables

     
In this stage, the type and quantity of variables used in the validation of the model are determined. According to the data in the database, the data were divided into two categories of calibration data (data used in Bayesian network training) and validation data (to examine the accuracy of the trained network). Data related to input variables can include continues data and discrete or classified data.
  1. Step 2:

    Calibration of Bayesian Network

     
Bayesian Network training using observed data includes two stages of network structure and network’s parameters training that are arranged in a sequential manner. Structure calibration of the network means identifying dependent and independent variables and finding possible relationships between variables whose causal relationships are detectable based on observed data. But the training of parameters means estimating conditional probabilities between two nodes of the network. In this research, for the training of network structure, the method of Necessary Path Condition (NPC) algorithm is recommended. The procedure of this algorithm is to use the concept of “ambiguous regions” which provides the context for the selection of unknown arcs between nodes. Furthermore, in this study Estimation-Maximization algorithm (EM) algorithm is utilized to train the network parameters. This method is a flexible tool for estimating the conditional probabilities even in the case of incomplete data.
  1. Step 3:

    Validation of Bayesian Network

     

After performing the training of the network, predictions’ accuracy of the model should be investigated using preselected data. Validation of the model is one of the most important stages in the development of a model, which it indicates the reliability of the model.

2.1.2 Dynamic Bayesian Network

This research is focused on a specific model that belongs to the class of BNs, namely, Dynamic Bayesian Networks (DBNs) (Dean and Kanazawa 1989). A BN can be run as a standalone network, but it is possible to link together a number of networks to produce an Object Oriented Bayesian Network (OOBN) model (Koller and Pfeffer 1997). OOBNs are based on the Object-Oriented Programming paradigm (OOP) and thus adopt the same attributes used in OOP languages. OOBNs can be utilized in two ways. First, they can be used for time slicing for problems in which processes take place over multiple time periods (Kjaerulff 1995). This is how DBNs are performed. DBN model is a stationary Markov process under the influence of components and changes that are repeated over time. Because BNs are not intended for transient analysis, time slicing provides one way to generate predictive simulations. This method has been adopted for the current study where networks representing different time domains are linked to outputs nodes to produce a dynamic probabilistic network for monthly groundwater level prediction. Figure 2 is shows the concept of different types of Bayesian Networks including DBNs.
Fig. 2

Top left: Simple Bayesian Network. Top right: Network with two feedbacks that they interact with each other; this is not a Bayesian Network. Bottom: time-dependent dynamic Bayesian Networks

DBN is defined as a pair of BNs (B1, B), where B1 is a BN represents the initial distribution of Z1 and B is two time slice BN (2TBN), that defines the transition distribution P(Zt| Zt − 1) using a Directed Acyclic Graph (DAG) as follows (Murphy 2002):
$$ P\left({Z}_t|{Z}_{t-1}\right)=\prod \limits_{i=1}^NP\left({Z}_t^i|{P}_a\left({Z}_t^i\right)\right) $$
(3)
Where \( {Z}_t^i \) is ith node in time of t and \( {P}_a\left({Z}_t^i\right) \) is parent of \( {Z}_t^i \) in the graph.

2.2 MCDM Techniques

The first stage in MCDM problems includes the following items (Roozbahani et al. 2012):
  • Identification of decision makers and stakeholders

  • Selection of criteria and their relative weights

  • Selection of alternatives

After that, selection of appropriate techniques to rank these alternatives is necessary. As it was mentioned before, three techniques of SAW, TOPSIS and PROMETHEE-II were selected in this researchfor purpose of groundwater management. These techniques belong to the scoring, compromising and outranking MCDM groups, respectively and indeed they are different in nature. For this reason, they are used for sensitivity analysis of the ranking results which may vary for each MCDM method. These techniques are described in the following sections:

2.2.1 SAW Method

SAW uses linear combinations of weighted criteria for each alternative to represent and compare the overall score of the alternative, as shown in following equation:
$$ {\mathrm{A}}^{\ast }=\left\{\mathrm{A}\mathrm{i}|\max \frac{\sum_j{w}_j.{r}_{ij}}{\sum_j{w}_j}\right\} $$
(4)
where rij is the normalized value of ith alternative against jth criteria in the normalized decision matrix for i = 1, 2,…, m and j = 1, 2,…, n, wj is the value of normalized weight for jth criteria for j = 1, 2,…, n. In this method, firstly weighted summation of criteria for each of the alternatives is acquired; then, the alternatives are ranked on the basis of these values (Zamani-Sabzi et al. 2016). The fundamental concept of a method of saw is looking for a weighted sum of performance rating of each alternative on all attributes (criteria).

2.2.2 TOPSIS method

TOPSIS was initially presented by Hwang and Yoon (1981). The TOPSIS method selects the best alternatives based on the shortest distance from the ideal solution, as well as the farthest distance from the non-ideal solution. The first step in this approach is to normalize the decision matrix, which means that the matrix is unbalanced. Each rij of the matrix is normalized as follows:
$$ {n}_{ij}=\frac{r_{ij}}{\sum_{i=1}^m{r}_{ij}^2} $$
(5)
Following, the weighted normalized decision matrix can be conducted base on:
$$ V={N}_D.{W}_{n\times n}=\mid {\displaystyle \begin{array}{ccc}{V}_{11},\dots & {V}_{1j},\dots & {V}_{1n}\\ {}\vdots & \vdots & \vdots \\ {}{V}_{m1},\dots & {V}_{mj},\dots & {V}_{mn}\end{array}}\mid $$
(6)

As N is a matrix whose index scores are non-scalable and comparable, and W is a matrix of diagonals that only the elements of its main diameter are non-zero.

Subsequently, the positive and negative ideal solutions, which are characterized by A+and A, are obtained as follows:
$$ {S}^{+}=\left\{\left({\mathit{\max}}_i{V}_{ij}|j\in J\right),\left({\mathit{\min}}_i{V}_{ij}|j\in {J}^{\prime}\right)|i=1,2,\dots, m\right\}=\left\{{V}_1^{+},{V}_2^{+},\dots, {V}_j^{+},\dots, {V}_n^{+}\right\} $$
(7)
$$ {S}^{-}=\left\{\left({\mathit{\min}}_i{V}_{ij}|j\in J\right),\left({\mathit{\max}}_i{V}_{ij}|j\in {J}^{\prime}\right)|i=1,2,\dots, m\right\}=\left\{{V}_1^{-},{V}_2^{-},\dots, {V}_j^{-},\dots, {V}_n^{-}\right\} $$
(8)
Then the distance of each alternative from positive (\( {d}_i^{+} \)) and negative ideal (\( {d}_i^{-} \)) solutions is computed as:
$$ {d}_i^{+}={\left\{{\sum}_{j=1}^n{\left({V}_{ij}-{V}_j^{+}\right)}^2\right\}}^{0.5};i=1,2,\dots, m $$
(9)
$$ {d}_i^{-}={\left\{{\sum}_{j=1}^n{\left({V}_{ij}-{V}_j^{-}\right)}^2\right\}}^{0.5};i=1,2,\dots, m $$
(10)
At the end, the relative closeness is calculated and scenario ranking is performed by following equation:
$$ {cl}_i^{+}=\frac{d_i^{-}}{\left({d}_i^{+}+{d}_i^{-}\right)};0\le {cl}_i^{+}\le 1;i=1,2,\dots, m $$
(11)

It is obvious that the alternative Si is closer to S+ and farther from Sas the closeness coefficient approaches to 1. Accordingly, the ranking order of all alternatives can be obtained according to their closeness coefficients.

2.2.3 PROMETHEE-II Method

The PROMETHEE family of outranking methods is one of the recently developed MCDM techniques, which allow interactive learning. In this paper, method of PROMETHEE-II has been used. This method is based on pair-wise comparison of alternatives and aggregating the decision makers’ preferences in terms of each criterion. PROMETHEE-II is also a quite simple ranking method in the concept and application compared with the other methods for multi criteria analysis (Brans et al. 1986). In addition to elicitation of criteria’s relative importance, the implementation of the PROMETHEE-II needs an additional type of information which is named preference functions. This function translates the difference between the evaluations of two alternatives into a preference degree ranging from zero to one for each criterion. To facilitate the association of a preference function to each criterion, the developers of this technique have proposed six types of preference functions (Fig. 3) which have performed satisfactorily for many real world applications. Each shape depends on up to two main thresholds: indifference threshold (q) and preference threshold (p).
Fig. 3

Preference function types of PROMETHEE method (Brans and Vincke 1985)

PROMETHEE-II consists of the following steps:
  1. Step 1:

    Determination of deviations based on pair-wise comparison between each set of two alternatives a and b:

     
$$ d={g}_j(a)-{g}_j(b) $$
(12)
Where gj(a) and gj(b) are the values of criterion j for alternatives a and b, respectively.
  1. Step 2:

    Determination of preference functions pj(a, b) (as shown in Fig. 3):

     
$$ {p}_j\left(a,b\right)=H\left({d}_j\left(a,b\right)\right) $$
(13)
The choice of the type of priority functions can also be general or specific; that is, all decision makers use the same priority functions, or specifically, each decision maker has its own function.
  1. Step 3:

    Calculation of an overall preference index as follows:

     
$$ \pi \left(a,b\right)=\sum \limits_{j=1}^n{w}_j{p}_j\left(a,b\right) $$
(14)
Where π(a, b) varies from 0 to 1 and expresses the degree of which alternative a is preferred over b based on all the criteria (n). wj is the relative weight of jth criterion.
  1. Step 4:

    Calculation of outranking flows:

     
The leaving flow:
$$ {\phi}^{+}(a)=\sum \limits_{b\in A}\frac{\pi \left(a,b\right)}{n-1} $$
(15)
The entering flow:
$$ {\phi}^{-}(a)=\sum \limits_{b\in A}\frac{\pi \left(a,b\right)}{n-1} $$
(16)
Step 5: Calculation of net outranking flow for each scenario as follows:
$$ \phi (a)={\phi}^{+}(a)-{\phi}^{-}(a) $$
(17)

Where ϕ(a) denotes the net outranking flow for each alternative. A scenario with highest value of net flow represents the best scenario.

2.2.4 Weighing of Criteria

In this research, weighting measures were applied based on direct weighing and pairwise comparison matrix by preparing specialized questionnaire to reduce the uncertainty of decision making. The number of experts who completed the questionnaires included 30 people, including water authorities and experienced experts.

Direct Weighing

In this method, weights of criteria are allocated with qualitative expressions by decision makers through the questioner. So that decisions made by decision makers on scenarios can easily be taken. Equivalent scores for linguistic importance expressions (very low, low, moderate, high and very high) are shown in Table 1. To calculate the final weights, arithmetic mean of individual weights is estimated and normalized.
Table 1

Scoring the weight of criteria in direct method

Importance

Score

Very Low

1

Low

3

Moderate

5

High

7

Very High

7

Pairwise Comparison Matrix Method

Another weighting method is the pairwise comparison matrix. It is a part of Analytic Hierarchy Process (AHP), a famous decision-making framework developed by Saaty (1980). AHP is based on the way a human thinks logically and furnishes a hierarchical structure to analyze complex decision-making problems. It adopts the pairwise comparisons method in order to elicit the weights of criteria and alternatives. For this purpose, Saaty (1980) suggested using the scale presented in Table 1. It is assumed that decision makers give a numerical answer to the question ‘How many times is the ith alternative more important/better/favorable than the jth?‘After constructing the pairwise comparison matrices, it must be ensured that there is a reasonable degree of coherence between judgments. To aggregate the opinions of individuals about the weights in the form of group decision making, the geometric mean for the elements of the decision matrix is used. (Table 2).
Table 2

Saaty’s scale for pairwise comparisons (Saaty 1980)

Definition

Intensity of importance

Equal importance

1

Moderate importance

3

Strong importance

5

Very strong Importance

7

Extreme importance

9

Intermediate values

2,4,6, 8

2.2.5 Borda Count Method

In decision making by MCDM such as current research, a set of rankings is often produced; hence, a method is required to combine different rankings for achieving a final ranking. Borda count is a simple MCDM in which the best scenario obtains N point; the second best alternative obtains N-1 point, and so on, all the way up to the least point for the alternative which is obtained (Borda 1994). If the number of alternatives is K, N is usually considered equal to K. The alternative (scenario) with the largest sum of points is considered as the best alternative. In this paper, if the number of ranking modes – which is obtained from the three MCDM techniques (SAW, TOPSIS, PROMETHEE-II) as well as two weighting methods – is considered equal to n, Eq. 17 can be applied to calculate the final score of each scenario and subsequently the final ranking of each scenario (Srdjevic 2007):
$$ {R}_G=\sum \limits_{i=1}^n{s}_i.{R}_i $$
(18)

In which si is the assigned score to the ith rank, Ri is the number where the scenario obtains the ith rank and RG is the final score of the scenario. Scenario with the highest value is the superior choice of the group resulting from the combination of different MCDM models.

3 Case Study & Results

3.1 Study Area

Birjand basin is located in the Loot Desert and 485 km south of Mashhad and in the East of Iran. The climate of this region is dry and in recent years because of over pumping of water from aquifers, the region has been faced with declining groundwater levels. According to the observations, during last 50 years, the average water level drawdown in this aquifer has been 0.4 m per year and aquifer deficit volume is about 10.75 million cubic meters. The general direction of groundwater flow is from East to West and from the North and South toward the center of the plain. Study area and current piezometric network can be seen in Fig. 4.
Fig. 4

Thiessen network of Birjand aquifer

3.2 Dynamic Bayesian Network Results

BN models can be built using several accessible commercial software packages such as Analytica, Netica, Hugin, and GeNie. In this study, Hugin software (Hugin Expert A/S 2012) was employed to build, learn and validate the Bayesian Network. For DBN modeling regarding the continues input data, NPC method with 5% confidence level as well as EM method was used for calibration of BN’s structure and parameters, respectively. The calibration period includes 12 years of historical data record (1997 to 2008) and validation data contains a period of 5 years (2009 to 2013) with monthly time step. In this paper, six predictors were used to predict the groundwater level in the next month (WTT): Rainfall (Rain), Recharge, Discharge, Temperature (T), Evaporation (ET) as well as groundwater Table (WT) in the current month. Also through defining 10 different scenarios for sensitivity analysis of groundwater level prediction in the next month, uncertainties related to the effect of predictor parameters were evaluated. The final selected DBN structure is shown in Fig. 5.
Fig. 5

Selected BN structure for the prediction of groundwater level

Values of the coefficient of determination (R2) and Root Mean Square Error (RMSE) for the best prediction scenario (Fig. 5) per 13 piezometers were obtained and their accuracy is shown in Table 3. Since groundwater hydrograph is an appropriate tool to evaluate the prediction accuracy, it can be used in demonstrating the efficiency of DBN Model. Therefore, the groundwater hydrograph was calculated and drawn during the validation period.
Table 3

Water level prediction accuracy in 13 piezometers

Piezometer No.

R2

RMSE

1

0.12

1.43

2

0.43

0.44

3

0.06

0.41

4

0.97

1.94

5

0.96

2.66

6

0.99

0.77

7

0.99

0.82

8

0.87

0.84

9

0.98

0.63

10

0.98

0.20

11

0.18

3.58

12

0.79

2.09

13

0.16

2.13

As can be seen in Fig. 6, Bayesian Network was able to predict with high and reasonable accuracy as the values of R2 and RMSE are 0.9925 and 0.2654, respectively. Therefore, due to the precision of the presented approach in the prediction of aquifer hydrograph, this approach is preferred as a superior approach to investigate of the effect of different management scenarios on the enhancement of this aquifer.
Fig. 6

Comparison of observed and predicted groundwater in Birjand aquifer

3.3 Decision Making Scenarios for Groundwater Restoration

The scenarios proposed to help improve the status of water resources should be comprehensive and have the best impact in resolving water resource crises. Also the proposed scenarios must be operational based on climate, economic, geographic and social conditions of the studied area. Therefore, the proposed scenarios in this study were obtained by researching and using the views of local managers and decision makers regarding the condition of water resources. These scenarios are as follows:

3.3.1 S1: Changing Current Surface Irrigation to Pressurized Irrigation Systems

Unlike the fact that efficiency of surface irrigation in Birjand plain is about 30%, the irrigation efficiency in two well-known pressurized irrigation systems of sprinkler Irrigation and drip irrigation methods is up to 75% and 85%, respectively. Therefore changing the current irrigation system is suggested as a management scenario.

3.3.2 S2: Removal of Unauthorized Wells

There are 305 deep and semi-deep wells in the Birjand plain, and its unauthorized wells are 42 wells. Therefore, by eliminating unauthorized wells, it is possible to stop a large part of excessive water withdrawal from the aquifer, which this saved volume of water can be allocated to improve the groundwater level of the aquifer.

3.3.3 S3: Improvement of Artificial Recharge Projects

Due to the lack of attention to artificial recharge plans in the Birjand Plain in recent years, the significant contribution of these plans in restoring the groundwater level has been neglected. It is necessary to implement this measure to control floods and to recharge Birjand aquifer.

3.3.4 S4: Installation of Smart Water Meters

Controlled water allocation using intelligent metering scheme leads to logical management and sustainable productivity of agricultural water resources and provides a framework for legal water consumption. Thus, applying this scenario is tested in this study.

3.4 Decision Making Criteria

To evaluate the decision making scenarios in this study, a number of criteria have been defined which are described below:

3.4.1 C1: Socio-Cultural Acceptance and Participation of Stakeholders

This criterion is one of the most important criteria that evaluates the role of social factors in advancing the process of a project. For fast and desirable management plans, the desired attitude of the society toward those plans is very important and the related values are qualitative, which were obtained by expert questionnaires.

3.4.2 C2: Efficiency of Applying of Scenarios in Improvement of the Aquifer’s Water Level

As it was discussed, the purpose of the proposed scenarios is to help improve the status of aquifer water level. Therefore, it is necessary to obtain the level of improvement of the aquifer level due to the implementation of various management scenarios. To estimate the improvement of aquifer level in different proposed scenarios, groundwater level was predicted using the trained Bayesian model (Fig. 5) under two wet and dry hydrological periods. For this purpose, due to lack of future meteorological information, for extraction of wet and dry years, time series of the annual precipitation was drawn from 1997 to the 2013, with the fitting of the Long-term mean precipitation. According to Fig. 7, for the dry period, years 2007 and 2008 and for the wet period, the years 2009 and 2010 were selected for testing the scenarios. These years and their relative predictors were the basis for calculating the groundwater level of aquifer improvement by applying the restoration scenarios in two years after the last year that predictors’ information are available and groundwater level were also measured.
Fig. 7

Annual precipitation in Birjand Meteorological Station

The groundwater level improvement of aquifer due to the application of the management scenarios for both of wet and dry hydrological periods is equal to the difference between mean groundwater level while the current trend continues with the implementation of management scenarios and mean groundwater level without applying any management scenario in the studied area at the end of next two-years. The impact of changing the irrigation system (the first scenario) was simulated based on the improvement of water use efficiency and the monthly reductions in water consumption from aquifer using Bayesian Network model.

In the scenario of removal of unauthorized wells, the monthly volume of water that would be saved by applying this scenario was considered in input of the Bayesian model. Furthermore, for the third scenario (Improvement of artificial recharge project), the monthly recharge rate from flood events in Birjand plain was simulated by using Bayesian model. Finally, for the last scenario of the installation of smart water meters, the monthly water saving rate was determined and introduced to Bayesian model similar to other scenarios. In all scenarios, parameter changes were applied in the recharge node. Eventually, the level of aquifer improvement in each of two hydrological periods was achieved.

3.4.3 C3: Cost of the Implementation of the Scenarios

Certainly, one of the most important measures in management scenarios assessment is the economic issue. The economic benefits of the management plan are low costs associated with its implementation. Hence, it is advisable that the proposed scenarios are reasonable in terms of operating costs. This criterion is a quantitative type and all values used in this criterion are based on financial year 2015.

3.4.4 C4: Feasibility of Implementation

Important criterion that is effective on the implementation of the proposed scenarios is the feasibility of implementation of the project with respect to the required time, facilities, human resources and skills in each scenario. This criterion is also qualitative and can be elicited trough questionnaire same as C1.

3.5 Criteria Weights

The criteria weights and their levels of importance were obtained by using the questionnaire and participation of experts in this research. The weights of the criteria related to two methods of direct weighing and pairwise comparison matrix (AHP technique) are presented in Table 4.
Table 4

Final weight of the criteria

Criterion

Direct Method

AHP method

C1: Socio-cultural acceptance and participation of stakeholders

0.24

0.28

C2: Efficiency of applying of scenarios in improvement of the aquifer’s water level

0.29

0.30

C3: Cost of implementation of the scenarios

0.32

0.33

C4: Feasibility of implementation

0.15

0.09

Based on this analysis, cost of implementation criterion (C3) was selected as the most important criterion. Furthermore, criteria of improvement of the aquifer’s water level (C2), socio-cultural acceptance and participation of stakeholder (C1) and feasibility of implementation (C4) had, respectively, next priorities by consideration and aggregation of decision makers’ opinions.

3.6 Final Decision Matrices

The decision matrix shows the preferences of the criteria regarding the management scenarios. In Tables 5 and 6, the overall decision matrices are shown for wet and dry weather scenarios, respectively:
Table 5

Decision matrix for the first ranked scenario in wet period

Scenario

C1

C2 (cm)

C3 (Million Rials)

C4

S1

5.7

14

32,513

4.9

S2

4.3

9

389

6.7

S3

6.6

25

5400

5.5

S4

5.5

12

16,775

5.7

Table 6

Decision matrix for the first ranked scenario in dry period

Scenario

C1

C2 (cm)

C3 (Milion Rials)

C4

S1

5.7

21

32,513

4.9

S2

4.3

12

389

6.7

S3

6.6

21

5400

5.5

S4

5.5

17

16,775

5.7

3.7 Implementation of MCDM Techniques and Ranking Of Scenarios

According to the results of the weighting of the criteria as well as the decision making matrix values of wet and dry conditions, the scenarios were ranked by application of SAW, TOPSIS and PROMETHEE decision making techniques. Final rankings along with obtained scores are illustrated in Tables 7 and 8. These score are based on weighted summation, closeness coefficient and net flow for SAW, TOPSIS and PROMETHEE-II techniques, respectively.
Table 7

Scenario ranking results using MCDM techniques for wet period

PROMETHEE-II-AHP

TOPSIS-AHP

SAW-AHP

PROMETHEE-II-Direct Weighting

TOPSIS-Direct Weighting

SAW-Direct Weighting

Rank

0.62

S3

0.86

S3

0.71

S2

0.56

S3

0.86

S3

0.74

S2

1

−0.17

S1

0.65

S2

0.67

S3

−0.16

S2

0.65

S2

0.67

S3

2

−0.21

S4

0.44

S4

0.47

S1

−0.19

S1

0.44

S4

0.48

S1

3

−0.24

S2

0.15

S1

0.46

S4

−0.20

S4

0.15

S1

0.47

S4

4

Table 8

Scenario ranking results using MCDM techniques for dry period

PROMETHEE-II-AHP

TOPSIS-AHP

SAW-AHP

PROMETHEE-II-Direct Weighting

TOPSIS-Direct Weighting

SAW-Direct Weighting

Rank

0.52

S3

0.85

S3

0.78

S2

0.46

S3

0.84

S3

0.80

S2

1

−0.07

S1

0.76

S2

0.67

S3

−0.10

S1

0.77

S2

0.67

S3

2

−0.21

S4

0.49

S4

0.61

S1

−0.16

S2

0.49

S4

0.60

S1

3

−0.24

S2

0.22

S1

0.56

S4

−0.20

S4

0.21

S1

0.57

S4

4

Although the ranking orders of scenarios in wet period are similar to dry period, but obtained scores in MCDM technique are totally different. According to the results presented in Tables 7 and 8, there are 12 different ranking sets that indicate a sensitivity analysis of applying different decision making and weighting techniques, but these results make it difficult to choice of the best management scenario. Therefore, in order to combine these ranking sets, a group decision method is needed. As outlined in the methodology section, Borda group decision making were applied and the final decision making results are shown in Table 9.
Table 9

Final ranking of management scenarios in Birjand aquifer based on Borda technique

Scenario

Score

Rank

S3

32

1

S2

23

2

S1

11

3

S4

6

4

Regarding Table 9 and based on the results of the final ranking of scenarios in both dry and wet periods, the scenario of Improvement of artificial recharge projects is selected as first ranked scenario, as it indicated a high potential for this scenario to improve the aquifer level in the Birjand plain.

Subsequently, the removal of unauthorized wells alternative is suggested as the second proposed scenario, a scenario which emphasizes the important role of unauthorized excess water depletion on the dropping of the groundwater level. Moreover, the scenario for changing and improving the current irrigation system was selected as the third ranked scenario and finally, the scenario of installing smart water meters was in the last rank. It should be noted that Borda method is a voting-based group decision making method based on aggregation of rankings obtained from different MCDM techniques or decision makers. In this basic approach, it is assumed that decision makers have the same power and importance in final ranking that is acceptable assumption in the case study mentioned in this paper, in which MCDM techniques have been considered as decision makers. But definitely taking into account their real power or importance can improve this method. Since the S3 scenario (Improvement of artificial recharge projects) was considered as the best solution, groundwater hydrographs were drawn for both of dry and wet periods in Figs. 8 and 9, respectively, assuming that artificial recharge projects will be implemented in the next two years.
Fig. 8

Impact of selected scenario on the groundwater level improvement in dry period (2014–2015)

Fig. 9

Impact of selected scenario on the groundwater level improvement in wet period (2014–2015)

These figures indicate that in both periods decline in groundwater level in the implementation of artificial recharge projects is less than the decline in the current trend without the implementation of these restoration projects. Based on the hydrographs outlined in Figs. 8 and 9, using S3 scenario leads to an increase in water levels about 25 cm and 21 cm for the next two wet and dry years, respectively. Unlike many other similar studies, the proposed approach in this research conducts groundwater management, using probabilistic prediction and multi criteria decision making, simultaneously.

4 Conclusion

In this research, a framework for groundwater risk management was proposed by integration of Dynamic Bayesian Network and MCDM techniques. The capabilities of this framework were evaluated in an under stressed aquifers in Iran. Time dependent Bayesian model which aims to reduce the uncertainty and predict the monthly groundwater level was capable to predict groundwater level and simulate the effects of various management scenarios on improving groundwater level in a short time period. After analysing the results of the selected structure of Bayesian Network, four appropriate criteria and their importance were determined to prioritize four restoration scenarios. Based on these criteria, the scenarios were evaluated using SAW, TOPSIS and PROMETHEE-II as three commonly used and applicable MCDM techniques. In this research, with respect to the experts’ opinions as well as BN model’s results, decision matrices were estimated and then by performing of three mentioned MCDM techniques and aggregation of their ranking outputs by Borda method as a group decision making model, improvement of artificial recharge projects was chosen as the best management scenario in the case study. Analysing the results presented in this study demonstrate that by applying risk management scenarios and taking into account the capabilities of MCDM approach in the aquifers suffering from water stress, not only we can obtain the appropriate alternative, but also the impact of these scenarios on groundwater levels can be squarely determined by DBN rather than existing groundwater models such as MODFLOW. The framework proposed in this study as a decision support approach, can be utilized by stakeholders to reduce water shortage crisis in other similar plains which are under stressful ground water conditions.

Footnotes

  1. 1.

    Preference Ranking Organization Method for Enrichment Evaluations

  2. 2.

    Simple Additive Weighting

  3. 3.

    Technique for Order of Preference by Similarity to Ideal Solution

Notes

Acknowledgements

A previous shorter version of the paper has been presented in the 10th World Congress of EWRA “Panta Rei” Athens, Greece, 5-9 July 2017.

Compliance with Ethical Standards

Conflict of Interest

None.

References

  1. Alameddine I, Cha YK, Reckhow KH (2010) An evaluation of automated structure learning with Bayesian Networks: an application to estuarine chlorophyll dynamics. Environ Model Softw 26(2):163–172CrossRefGoogle Scholar
  2. Anbari MJ, Tabesh M, Roozbahani A (2017) Risk assessment model to prioritize sewer pipes inspection in wastewater collection networks. J Environ Manag 190:91–101CrossRefGoogle Scholar
  3. Ashwell NEQ, Peterson JM, Hendricks NP (2018) Optimal groundwater management under climate change and technical progress. Resour Energy Econ 51:67–83CrossRefGoogle Scholar
  4. Azarnivand A, Banihabib ME (2017) A multi-level strategic group decision making for understanding and analysis of sustainable watershed planning in response to environmental perplexities. Group Decis Negot 26(3):629–648CrossRefGoogle Scholar
  5. Azarnivand A, Madani FSH, Banihabib ME (2015) Extended fuzzy analytic hierarchy process approach in water and environmental management (case study: Lake Urmia Basin, Iran). Environ Earth Sci 73(1):13–26CrossRefGoogle Scholar
  6. Babovic V, Drecourt JP, Keijzer M, Hansen PF (2002) Modeling of Water Supply Assets: A Data Mining Approach. Urban Water 4(4):404–414CrossRefGoogle Scholar
  7. Banihabib ME, Hashemi F, Shabestari MH (2017) A framework for sustainable strategic planning of water demand and supply in arid regions. Sustain Dev 25(3):254–266CrossRefGoogle Scholar
  8. Banihabib ME, Shabestari MH (2017) Fuzzy hybrid MCDM model for ranking the agricultural water demand management strategies in arid areas. Water Resour Manag 31(1):495–513CrossRefGoogle Scholar
  9. Batchelor C, Cain J (1999) Application of belief networks to water management studies. Agric Water Manag 40(1):51–57CrossRefGoogle Scholar
  10. Borda JC (1994) A Paper on Elections by Ballot. (English translation). In: Hewitt F, McLean I (eds) Condorcet: Foundations of Social Choice and Political Theory. Edward Elgar, Brookfield, pp 114–119Google Scholar
  11. Borsuk M, Stow C, Reckhow K (2004) A Bayesian network of eutrophication models for synthesis, prediction, and uncertainty analysis. Ecol Model 173(2–3):219–239CrossRefGoogle Scholar
  12. Brans J, Vincke P (1985) A preference ranking organization method (The PROMETHEE method for multiple criteria decision making). Manag Sci 31(6):647–656CrossRefGoogle Scholar
  13. Brans J, Vincke P, Mareschal B (1986) How to select and how to rank projects: the PROMETHEE method. Eur J Oper Res 24(2):228–238CrossRefGoogle Scholar
  14. Castelletti A, Soncini-Sessa R (2007) Bayesian networks and participatory modelling in water resource management. Environ Model Softw 22:1291–1233Google Scholar
  15. Cinar D, Kayakutlu G (2010) Scenario analysis using Bayesian networks: a case study in energy sector. Knowl-Based Syst 23(3):267–272CrossRefGoogle Scholar
  16. Dabral S, Bhatt B, Joshi JP, Sharma N (2014) Groundwater suitability recharge zones modelling - A GIS application. ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences XL-8:347–353CrossRefGoogle Scholar
  17. Dean T, Kanazawa K (1989) A model for reasoning about persistence and causation. Comput Intell 5(2):142–150CrossRefGoogle Scholar
  18. Farmani R, Henriksen HJ, Savic D (2009) An evolutionary Bayesian belief network methodology for optimum management of groundwater contamination. Environ Model Softw 24(3):303–310CrossRefGoogle Scholar
  19. Fawen L, Feng P, Zhang W, Zhang T (2013) An Integrated Groundwater Management Mode Based on Control Indexes of Groundwater Quantity and Level. Water Resour Manag 27(9):3273–3292CrossRefGoogle Scholar
  20. Fienen MN, Masterson JP, Plant NG, Gutierrez BT, Thieler ER (2013) Bridging groundwater models and decision support with a Bayesian network. Water Resour Res 49(10):6459–6473CrossRefGoogle Scholar
  21. Geng G, Wardlaw R (2013) Application of multi-criterion decision making analysis to integrated water resources management. Water Resour Manag 27(8):3191–3207CrossRefGoogle Scholar
  22. Hamilton GS, Fielding F, Chiffings AW, Hart BT, Johnstone RW, Mengersen K (2007) Investigating the use of a Bayesian Network to model the risk of Lyngbya majuscula bloom initiation in Deception Bay, Queensland, Australia. Hum Ecol Risk Assess 13(6):1271–1287CrossRefGoogle Scholar
  23. Heckerman D, Mamdani A, Wellman M (1995) Real world applications of Bayesian Networks. Communication of the ACM 38(3):24–26CrossRefGoogle Scholar
  24. Henriksen HJ, Rasmussen P, Brandt G, Bulow DV, Jensen FV (2007) Public participation modelling using Bayesian Networks in management of groundwater contamination. Environ Model Softw 22(8):1101–1113CrossRefGoogle Scholar
  25. Holzkämper A, Kumar V, Surridge BWJ, Paetzold A, Lerner DN (2012) Bringing diverse knowledge sources together – a meta-model for supporting integrated catchment management. J Environ Manag 96(1):116–127CrossRefGoogle Scholar
  26. Hugin Expert A/S (2012) Hugin Researcher User Guide, Version 7.6, AalborgGoogle Scholar
  27. Hwang CL, Yoon K (1981) Multiple Attribute Decision Making: Methods and Applications. Springer-Verlag, New YorkCrossRefGoogle Scholar
  28. Jensen F (1996) An Introduction to Bayesian Networks. Springer-Verlag D, HeidelbergGoogle Scholar
  29. Johnson S, Fielding F, Hamilton G, Mengersen K (2009) An integrated Bayesian Network approach to Lyngbya majuscula bloom initiation. Mar Environ Res 69(1):27–37CrossRefGoogle Scholar
  30. Kjaerulff U (1995) dHugin: a computational system for dynamic time-sliced Bayesian Networks. Int J Forecast 11(1):89–111CrossRefGoogle Scholar
  31. Koller D, Pfeffer A (1997) Object-oriented Bayesian Networks. In: Proceedings of the Thirteenth Annual Conference on Uncertainty in Artificial Intelligence UAI-97, Providence, Rhode IslandGoogle Scholar
  32. Kragt ME, Newham LTH, Jakeman AJ (2009) A Bayesian Network approach to integrating economic and biophysical modelling. 18th World IMACS/MODSIM Congress, CairnsGoogle Scholar
  33. Madadgar S, Moradkhani H (2014) Spatio-temporal drought forecasting within Bayesian Networks. J Hydrol 512:134–146CrossRefGoogle Scholar
  34. Merritt WS, Ticehurst JL, Pollinoa C, Fu B (2010) The Value of using Bayesian Networks in Environmental Decision Support Systems to support natural resource management. In: International Congress on Environmental Modelling and Software Modelling for Environment’s Sake.5th Biennial Meeting, OttawaGoogle Scholar
  35. Molina JL, Velázquez DP, Aróstegui JLG, Velázquez MP (2013) Dynamic Bayesian Networks as a Decision Support tool for assessing Climate Change impacts on highly stressed groundwater systems. J Hydrol 479:113–129CrossRefGoogle Scholar
  36. Murphy KP (2002) Dynamic Bayesian Networks: Representation, Inference and Learning. PHD. Thesis, University of California, BerkeleyGoogle Scholar
  37. Neapolitan RE (2003) Learning Bayesian Networks. Prentice Hall.Google Scholar
  38. Olalla FMDS, Dominguez A, Ortega F, Artigao A, Fabeiro C (2007) Bayesian Networks in planning a large aquifer in Eastern Mancha Spain. Environ Model Softw 22(8):1089–1100CrossRefGoogle Scholar
  39. Pearl J (1988) Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San MateoGoogle Scholar
  40. Roozbahani A, Ebrahimi E, Banihabib ME (2017) Ground water risk management using dynamic Bayesian Networks and PROMETHEE method. Proceedings of the 10th World Congress of EWRA ‘PantaRhei’, AthensGoogle Scholar
  41. Roozbahani A, Zahraie B, Tabesh M (2012) PROMETHEE with Precedence Order in the Criteria (PPOC) as a New Group Decision Making Aid: An Application in Urban Water Supply Management. Water Resour Manag 26(12):3581–3599CrossRefGoogle Scholar
  42. Rossettoa R, Filippis GD, Borsi I, Foglia L, Cannata M, Criollo R, Vázquez-Suñé E (2018) Integrating free and open source tools and distributed modelling codes in GIS environment for data-based groundwater management. Environ Model Softw 107:210–230CrossRefGoogle Scholar
  43. Saaty TL (1980) The Analytic Hierarchy Process. McGraw-Hill, New YorkGoogle Scholar
  44. Shin JY, Ajmal M, Yoo J, Kim TW (2016) A Bayesian Network-Based Probabilistic Framework for Drought Forecasting and Outlook. Adv Meteorol.  https://doi.org/10.1155/2016/9472605
  45. Srdjevic B (2007) Linking analytic hierarchy process and social choice methods to support group decision-making in water management. Decis Support Syst 42(4):2261–2273CrossRefGoogle Scholar
  46. Tabesh M, Roozbahani A, Roghani B, Rasi Faghihi N, Heydarzadeh R (2018) Risk Assessment of Factors Influencing Non-Revenue Water Using Bayesian Networks and Fuzzy Logic. Water Resour Manag 32(11):3647–3670CrossRefGoogle Scholar
  47. Thomas BF, Famiglietti JS (2015) Sustainable Groundwater Management in the Arid Southwestern US: Coachella Valley, California. Water Resour Manag 29(12):4411–4426CrossRefGoogle Scholar
  48. Zamani-Sabzi H, Phillip King J, Gard CC, Abudu S (2016) Statistical and analytical comparison of multi-criteria decision-making techniques under fuzzy environment. Operations Research Perspectives 3:92–117CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Irrigation and Drainage Engineering, Aburaihan CampusUniversity of TehranTehranIran

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