A Framework for Ground Water Management Based on Bayesian Network and MCDM Techniques
 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 semiarid 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 PROMETHEEII 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 PROMETHEEII TOPSIS Borda1 Introduction
The water tension impacts the aquifers and make critical situation in most of arid and semiarid 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 SonciniSessa 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 MultiCriteriaDecisionMaking (MCDM) method by combining of PROMETHEE^{1} and Multiattribute 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 AHPTOPSIS, 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.

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
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):
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
 Step 1:
Preparing input variables
 Step 2:
Calibration of Bayesian Network
 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
2.2 MCDM Techniques

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 PROMETHEEII 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
2.2.2 TOPSIS method
As N is a matrix whose index scores are nonscalable and comparable, and W is a matrix of diagonals that only the elements of its main diameter are nonzero.
It is obvious that the alternative S_{i} is closer to S^{+} and farther from S^{−}as the closeness coefficient approaches to 1. Accordingly, the ranking order of all alternatives can be obtained according to their closeness coefficients.
2.2.3 PROMETHEEII Method
 Step 1:
Determination of deviations based on pairwise comparison between each set of two alternatives a and b:
 Step 2:
Determination of preference functions p_{j}(a, b) (as shown in Fig. 3):
 Step 3:
Calculation of an overall preference index as follows:
 Step 4:
Calculation of outranking flows:
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
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
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 which s_{i} is the assigned score to the i^{th} rank, R_{i} is the number where the scenario obtains the i^{th} 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
3.2 Dynamic Bayesian Network Results
Water level prediction accuracy in 13 piezometers
Piezometer No.  R^{2}  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 
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 wellknown 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 semideep 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: SocioCultural 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
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 twoyears. 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
Final weight of the criteria
Criterion  Direct Method  AHP method 

C1: Sociocultural 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), sociocultural 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
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 
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
Scenario ranking results using MCDM techniques for wet period
PROMETHEEIIAHP  TOPSISAHP  SAWAHP  PROMETHEEIIDirect Weighting  TOPSISDirect Weighting  SAWDirect 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 
Scenario ranking results using MCDM techniques for dry period
PROMETHEEIIAHP  TOPSISAHP  SAWAHP  PROMETHEEIIDirect Weighting  TOPSISDirect Weighting  SAWDirect 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 
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.
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 PROMETHEEII 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
Notes
Acknowledgements
A previous shorter version of the paper has been presented in the 10th World Congress of EWRA “Panta Rei” Athens, Greece, 59 July 2017.
Compliance with Ethical Standards
Conflict of Interest
None.
References
 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
 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
 Ashwell NEQ, Peterson JM, Hendricks NP (2018) Optimal groundwater management under climate change and technical progress. Resour Energy Econ 51:67–83CrossRefGoogle Scholar
 Azarnivand A, Banihabib ME (2017) A multilevel 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
 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
 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
 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
 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
 Batchelor C, Cain J (1999) Application of belief networks to water management studies. Agric Water Manag 40(1):51–57CrossRefGoogle Scholar
 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
 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
 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
 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
 Castelletti A, SonciniSessa R (2007) Bayesian networks and participatory modelling in water resource management. Environ Model Softw 22:1291–1233Google Scholar
 Cinar D, Kayakutlu G (2010) Scenario analysis using Bayesian networks: a case study in energy sector. KnowlBased Syst 23(3):267–272CrossRefGoogle Scholar
 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 XL8:347–353CrossRefGoogle Scholar
 Dean T, Kanazawa K (1989) A model for reasoning about persistence and causation. Comput Intell 5(2):142–150CrossRefGoogle Scholar
 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
 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
 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
 Geng G, Wardlaw R (2013) Application of multicriterion decision making analysis to integrated water resources management. Water Resour Manag 27(8):3191–3207CrossRefGoogle Scholar
 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
 Heckerman D, Mamdani A, Wellman M (1995) Real world applications of Bayesian Networks. Communication of the ACM 38(3):24–26CrossRefGoogle Scholar
 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
 Holzkämper A, Kumar V, Surridge BWJ, Paetzold A, Lerner DN (2012) Bringing diverse knowledge sources together – a metamodel for supporting integrated catchment management. J Environ Manag 96(1):116–127CrossRefGoogle Scholar
 Hugin Expert A/S (2012) Hugin Researcher User Guide, Version 7.6, AalborgGoogle Scholar
 Hwang CL, Yoon K (1981) Multiple Attribute Decision Making: Methods and Applications. SpringerVerlag, New YorkCrossRefGoogle Scholar
 Jensen F (1996) An Introduction to Bayesian Networks. SpringerVerlag D, HeidelbergGoogle Scholar
 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
 Kjaerulff U (1995) dHugin: a computational system for dynamic timesliced Bayesian Networks. Int J Forecast 11(1):89–111CrossRefGoogle Scholar
 Koller D, Pfeffer A (1997) Objectoriented Bayesian Networks. In: Proceedings of the Thirteenth Annual Conference on Uncertainty in Artificial Intelligence UAI97, Providence, Rhode IslandGoogle Scholar
 Kragt ME, Newham LTH, Jakeman AJ (2009) A Bayesian Network approach to integrating economic and biophysical modelling. 18th World IMACS/MODSIM Congress, CairnsGoogle Scholar
 Madadgar S, Moradkhani H (2014) Spatiotemporal drought forecasting within Bayesian Networks. J Hydrol 512:134–146CrossRefGoogle Scholar
 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
 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
 Murphy KP (2002) Dynamic Bayesian Networks: Representation, Inference and Learning. PHD. Thesis, University of California, BerkeleyGoogle Scholar
 Neapolitan RE (2003) Learning Bayesian Networks. Prentice Hall.Google Scholar
 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
 Pearl J (1988) Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San MateoGoogle Scholar
 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
 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
 Rossettoa R, Filippis GD, Borsi I, Foglia L, Cannata M, Criollo R, VázquezSuñé E (2018) Integrating free and open source tools and distributed modelling codes in GIS environment for databased groundwater management. Environ Model Softw 107:210–230CrossRefGoogle Scholar
 Saaty TL (1980) The Analytic Hierarchy Process. McGrawHill, New YorkGoogle Scholar
 Shin JY, Ajmal M, Yoo J, Kim TW (2016) A Bayesian NetworkBased Probabilistic Framework for Drought Forecasting and Outlook. Adv Meteorol. https://doi.org/10.1155/2016/9472605
 Srdjevic B (2007) Linking analytic hierarchy process and social choice methods to support group decisionmaking in water management. Decis Support Syst 42(4):2261–2273CrossRefGoogle Scholar
 Tabesh M, Roozbahani A, Roghani B, Rasi Faghihi N, Heydarzadeh R (2018) Risk Assessment of Factors Influencing NonRevenue Water Using Bayesian Networks and Fuzzy Logic. Water Resour Manag 32(11):3647–3670CrossRefGoogle Scholar
 Thomas BF, Famiglietti JS (2015) Sustainable Groundwater Management in the Arid Southwestern US: Coachella Valley, California. Water Resour Manag 29(12):4411–4426CrossRefGoogle Scholar
 ZamaniSabzi H, Phillip King J, Gard CC, Abudu S (2016) Statistical and analytical comparison of multicriteria decisionmaking techniques under fuzzy environment. Operations Research Perspectives 3:92–117CrossRefGoogle Scholar