Optimal Design of Groundwater Quality Monitoring Using Entropy Theory

1. International conference on water Scarcity, Global Changes and Groundwater Management Responses Optimal Design of Groundwater Quality Monitoring Using Entropy Theory Ahmad Abrishamchi, Rashid Reza Owlia, Massoud Tajrishy and Ali Abrishamchi

2. INTRODUCTION • LITERATURE REVIEW • ENTROPY CONCEPT • METHODOLOGY • CASE STUDY • RESULTS AND DISCUSSION • CONCLUSION • REFERENCES Overview

3. Introduction • Purpose of GW quality monitoring To determine physical, chemical, and biological characteristics of groundwater resources • GW Quality Monitoring Issues: The main concern is to have a proper design for the groundwater quality monitoring networks • The sampling (monitoring) objective, monitoring variables, selection of sampling points, sampling frequency and duration of sampling

4. Introduction • Despite an enormous amount of efforts and investments made on monitoring of groundwater quality • a wide range of shortcomings has been identified in current monitoring networks, and as a result, • the outcome of the current data collection systems is very insufficient for providing needed information on groundwater quality

5. Introduction • Considering the aforementioned issues, the design procedures for groundwater quality networks need more critical investigations. • To do so, in the past few years, most of the developed countries have begun to redesign their monitoring programs to modify or revise their existing networks. • Assessment of groundwater quality monitoring networks requires methods to determine the potential efficiency and cost-effectiveness of the current monitoring programs

6. Introduction • Deficiency of Available Network Design Methods • lack of exact definition for the information contained in the data • lack of explanation on how the data was measured

7. Introduction • imprecisely definingthe data value or utility,which makes the network have weakness in the contained information and inefficiency in terms of the cost of getting the data • method’s restriction on transferring the information in space and time

8. Introduction • Still it remains a question on how to relate the assessment process criteria to the data value. • The entropy concept of information theory is a promising method to assess the networks. This theory has been used for hydrometric and water quality networks.

9. Introduction • Significant properties of entropy in monitoring systems assessment and redesign are the ability to: • provide exact definition of information in tangible terms, • quantitatively measure and express the information produced by a network,

10. Introduction • In this study, the measure of Transinformation in the discrete entropy theory and the Transinformation-Distance (T-D) curves are used to quantify the efficiency of a monitoring network. • This paper aims at decreasing the dispersion in results by using cluster analysis which utilizes fuzzy equivalence relations.

11. Introduction • The proposed methodology is applied to groundwater resources in the Tehran aquifer, in Tehran, Iran. • The results confirm the applicability and the efficiency of the model for optimal design of groundwater monitoring systems.

12. First in 1948 Shannon showed that entropy describes the amount of uncertainty in any probability distribution. • Yang and Burn (1994) showed that in comparison with other measures of association, entropy measures are more advantageous as they reflect a directional association among sampling sites on the basis of information transmission characteristics of each site. • Ozkul et al. (2000) presented a method using the entropy theory for assessing existing water quality monitoring networks. Literature Review

13. Literature Review Most of the referred studies were using analytical approaches which required incorporating probability distributions of the random variables; however, the alternative to the analytical approach is to adopt the discrete approach as addressed by Mogheir et al. (2004). • Mogheir et al. (2004) characterized the spatial variability of groundwater quality using discrete and analytical entropy-based approaches.

14. Entropy concept can be used as a measure of uncertainty and indirectly as a measure of information in probabilistic terms. • Information is attained only when there is uncertainty about an event. • Alternatives with a high probability of occurrence convey little information and vice versa. • The probability of occurrence of a certain alternative is the measure of uncertainty or the degree of expectedness of a sign, symbol or number. • When such uncertainty is removed, the result is information Therefore, the information gained is indirectly measured as the amount of uncertainty or of entropy Entropy Concept

15. Methodology To calculate the information measures, the joint or conditional probability is needed, and this can be obtained using a contingency table. To construct a contingency table, let the random variable x have a range of values consisting of v categories (class intervals), whereas the random variable y is assumed to have u categories (class intervals).

16. For a random variable x, the Marginal Entropy, H(x), can be defined as the potential information of the variable. • For two random variables, x and y, the Conditional Entropy, , is a measure of the information content of x that is not contained in the random variable y. • The Joint Entropy, is the total information content contained in both x and y. • The mutual entropy (information) between x and y, also called Transinformation, T(x,y), is interpreted as the reduction in uncertainty in x, due to the knowledge of the random variable y. It also can be defined as the information content of x that is contained in y. • The entropy theory has coefficients or information measures, such as information contents, marginal entropy, conditional entropy, joint entropy and Transinformation. Entropy Theory Coefficients

17. Schematisation of Entropy theory coefficients Full dependence between variables x and y Independence between variables x and y

18. Entropy Theory Coefficients • Transinformation-Distance curves (T-D curves) • To improve the accuracy of the T-D curves, fuzzy clustering is used to cluster the study area to some homogenous zones considering major characteristics of each station and finally different T-D curves were calculated for different zones. • Marginal Entropy, mean, variance and spatial location of potential stations were used to categorize stations in limited groups that had more resemblance. • Max-min method is used as a fuzzy equivalence relation to produce fuzzy similarity matrix.

19. Importance of Temporal Frequency • Small-scale sites and facing with several obstacles • The sampling frequency determination method is used for sampling frequency of each sampling location. (Future sampling frequency based on representative properties of historical concentration data) • Representative properties : • Properties in each well apart of others • Magnitude of concentration (Mean) • Direction of change (Iteratively Reweighted Least Square (IRLS) robust regression) • Dispersion and inhomogeneity of data around the mean (Standard deviation) Temporal Frequency

20. Temporal Frequency • The property in each well in relation with other wells : • correlation in one specific well with other wells (C.I indice) Using fuzzy clustering for categorizing similar station into four groups

21. Tehran-Karadj Aquifer, Tehran, Iran • coverage of area more than 1800 Km2 • About 865 million cubic meters of water per year is provided for domestic consumption of over 10 million people in this region • More than 30 percent of Tehran domestic water demand is supplied from Tehran-Karadj quifer • The share of groundwater in supplying water demand (domestic, agricultural, and industrial demand) is raised up to 60 percent during drought conditions • Considering 64 quality monitoring stations with semiannual temporal frequency from May 1998 to November 2007(16 Time intervals) Case Study

22. RESULT AND DISCUSSION Variation of the Transinformation versus Distance without fuzzy clustering Variation of Transinformation versus distance in different zones with fuzzy clustering

23. RESULT AND DISCUSSION Temporal Frequency of existing wells The location of the selected existing and potential monitoring wells

24. Spatial-Temporal methodology for improving existing groundwater quality monitoring network is presented. • An example application to a very important site with a network of 64 monitoring wells is provided to demonstrate the effectiveness of the proposed methodology. The fuzzy clustering divided the area into three homogeneous zones. • Among parameters that used for fuzzy clustering, “Marginal Entropy” had the most significant effect on decreasing the dispersion in T-D curves. • The sampling frequency determination method recommends sampling frequency for each sampling location based on the direction, magnitude, correlation with neighboring stations, and uncertainty of the concentration trend derived from representative historical concentration data. Conclusion

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