Optimal Design of Groundwater Quality Monitoring

Using Entropy Theory

International conference on water Scarcity, Global Changes and Groundwater Management

Responses

Ahmad Abrishamchi, Rashid Reza Owlia,

Massoud Tajrishy and Ali Abrishamchi

INTRODUCTION

LITERATURE REVIEW

ENTROPY CONCEPT

METHODOLOGY

CASE STUDY

RESULTS AND DISCUSSION

CONCLUSION

REFERENCES

Overview

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

Introduction

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

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

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

Introduction

Introduction

imprecisely defining the 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

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.

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,

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.

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.

Literature Review

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 ReviewMost 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.

Entropy Concept

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

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).

Entropy Theory Coefficients

The entropy theory has coefficients or information measures, such as information contents, marginal entropy, conditional entropy, joint entropy and Transinformation.

n

iii xPxPxH

1

)(ln)()(

)(ln),()(1 1

j

n

i

m

jiji yxPyxPyxH

n

i

m

jjiji yxPyxPyxH

1 1

),(ln),(),(

])()(

),(ln[),(),(

1 1

n

i

m

j ji

jiji yPxP

yxPyxPyxT

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.

Schematisation of Entropy theory

coefficients

Full dependence between variables

x and y

Independence between variables

x and y

Entropy Theory Coefficients •Transinformation-Distance curves (T-D curves)

min)(

min0 ).()( TeTTDT kD

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.

m

kjkik

m

kjkik

ij

xx

xx

r

1

1

),max(

),min(

Temporal Frequency

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 The property in each well in relation with other wells :

correlation in one specific well with other wells (C.I indice)

n1,2,...,ji, & ji 0.1

)X,n(XCorrelatio

0.1)(X .I

1

1

ji

i

n

j i

n

j i

D

DC

Using fuzzy clustering for categorizing similar station into four groups

Case Study

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)

RESULT AND DISCUSSION

Variation of the Transinformation versus Distance without fuzzy clustering

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 5000 10000 15000 20000 25000 30000 35000

Distance (m)

Tra

nsi

nfo

rmat

ion

(N

ats)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 5000 10000 15000 20000 25000 30000 35000

Distance (m)

Tra

nsi

nfo

rmat

ion

(N

ats)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 10000 20000 30000 40000

Distance (m)

Tra

nsi

nfo

rmat

ion

(N

ats)

Variation of Transinformation versus distance in different zones with fuzzy clustering

RESULT AND DISCUSSION

621.0)0006239.0(*8211.0 XEXP 3299.0))0009639.0(*8811.0( XEXP 3299.0))0002442.0(*9416.0( XEXP 617.0))001512.0(*893.0( XEXP

State Curve Fitted R2 Number of stations

Optimal Distance (m)

Without clustering 0.2512 64 4187

Cluster 1 0.9515 5 4648

Cluster 2 0.9844 5 6525

Cluster 3 0.5145 54 2970621.0)0006239.0(*8211.0 XEXP

wells in cluster 1wells in cluster 2wells in cluster 3 Potential wells

621.0)0006239.0(*8211.0 XEXP

3299.0))0009639.0(*8811.0( XEXP

3299.0))0002442.0(*9416.0( XEXP

617.0))001512.0(*893.0( XEXP

The location of the selected existing and potential

monitoring wells

Temporal Frequency of existing wells

Conclusion

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.

References

Husain, T. (1989). “Hydrologic uncertainty measure and network design” Water Resources Bulletin, 25(3),527-534.

Harmancioglu, N. B., Fistikoglu, O., Ozkul, S. D., Sing, V. P., and Alpaslan, N. (1999). “Water quality monitoring network design” Kluwer, Boston, USA.

Jager, H. I., Sale, M. J., and Schmayer, R. L. (1990). ‘‘Cokriging to assess regional stream quality in the Southern Blue Ridge Province.’’ Water Resour. Res., 26(7), 1401–1412.

Jessop A. (1995). “Informed Assessments, an Introduction to Information, Entropy and Statistics.” Ellis Horwood, New York, 366 pp.

Karamouz, M., Khajehzadeh Nokhandan, A., Kerachian, R. and Maksimovic, C. (2008). “Design of on-line river water quality monitoring systems using the entropy theory: A case study” Environmental Monitoring and Assessment, Springer, DOI: 10.1007/s10661-008-0418-z, 2008.

Khan, F. I., Husain, T. (2004). “An overview and analysis of site remediation technologies.” Journal of Environmental Management, 71, 95–122.

Ling, M., Rifai, H. S., Newell, C. J., Aziz, J. J., and Gonzales, J. R., (2003). “Groundwater monitoring plans at small scale sites-an innovative spatial and temporal methodology” Journal of Environ Monit., 5, 126-134.

Loaiciga, H. A., Charbeneau, R. J., Everett, L. G., Fogg, G. E., Hobbs, B. F., and Rouhani, S., (1992) “Review of Ground-Water Quality Monitoring Network Design”, journal of hydraulic

Engineering, Vol. 118, No.1, 11-37.Mogheir, Y., Lima, J. L. M. P. and Singh, V. P. (2004). “Characterizing the special variability of groundwater quality using the entropy theory.” Hydrological Processes, 18, 2165-2179.Motulsky H. J. and Christopoulos A. (2008). “Fitting Models to Biological Data using Linear and Nonlinear

Regression, A practical Guide to Curve Fitting.” GraphPad Softwater Inc., San Diego CA, www.graphpad.com

Ozkul, S., Harmancioglu, N. B. and Singh, V. P. (2000). “Entropy-based assessment of water quality monitoring networks.” Journal of Hydrologic Engineering, ASCE, 5(1), 90-100.

Sanders, T. G., Ward, R. C., Loftis, J. C., Steele, T. D., Adrian, D. D., and Yevjevich, V. (1983). “Design of networks for monitoring water quality” Water Resources Publications, Littleton, Colo.

Sarlak, N. and Sorman, A.U. (2006). “Evaluation and selection of stream flow network stations using entropy methods.” Turkish J. Eng. Env. Sci., 30, 91-100.

Schilperoort, T., and Groot, S. (1983). “Design and optimization of water quality monitoring networks” Proc., Int. Symp. on Methods and Instrumentation for the Investigation of Groundwater Systems (MIIGS).

Singh V. P. (1998). “Entropy-based Parameter Estimation in Hydrology” Kluwer Academic Publishers, Boston.

Strobel, R. O., Robillard, P. D. (2007). “Network design for water quality monitoring of surface freshwater: A review” Journal of Environmental Management, doi:10.1016/j.jenvman.

US EPA, “Use of Monitored Natural Attenuation at Superfund, RCRA Corrective Action, and Underground Storage Tank Site” Directive 9200.4-17P, Final Draft, US Environmental Protection Agency, Office of Solid Waste and Emergency Response, 1999, p. 23.

Ward, R. C., and Loftis, J. C. (1986). “Establishing statistical design criteria for water quality monitoring systems: Review and synthesis.” Water Resour. Bull., 22(5), 759–767.

Yang, Y. and Burn, D. ( 1994). “An entropy approach to data collection network design” Journal of Hydrology, 157, 307–324.

Ling, M., Rifai, H. S., Newell, C. J., Aziz, J. J., and Gonzales, J. R., (2003). “Groundwater monitoring plans at small scale sites-an innovative spatial and temporal methodology”, Journal of Environ Monit., 5, 126-134.

Zhou, Y. (1995). “Sampling frequency for monitoring the actual state of groundwater systems” Journal of Hydrology, SSDI 0022-1694(95)02892-7, 301-318.

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