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Optimal Design of Groundwater Quality Monitoring Using Entropy Theory


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Title: Optimal Design of Groundwater Quality Monitoring Using Entropy Theory

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

  • 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

  • Despite an enormous amount of efforts and
    investments made on monitoring of groundwater
  • 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

  • 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

  • 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
  • methods restriction on transferring the
    information in space and time

  • 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.

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

  • 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
  • This paper aims at decreasing the dispersion in
    results by using cluster analysis which utilizes
    fuzzy equivalence relations.

  • 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.

  • 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
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.

  • 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
  • The probability of occurrence of a certain
    alternative is the measure of uncertainty or the
    degree of expectedness of a sign, symbol or
  • When such uncertainty is removed, the result is
  • Therefore, the information gained is indirectly
    measured as the amount of uncertainty or of

Entropy Concept
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
  • 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
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)
  • 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.

  • Importance of Temporal Frequency
  • Small-scale sites and facing with several
  • The sampling frequency determination method is
    used for sampling frequency of each sampling
  • (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
Temporal Frequency
  • The property in each well in relation with other
  • correlation in one specific well with other
    wells (C.I indice)

Using fuzzy clustering for categorizing similar
station into four groups
  • 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
  • Considering 64 quality monitoring stations with
    semiannual temporal frequency from May 1998 to
    November 2007 (16 Time intervals)

Case Study
Variation of the Transinformation versus Distance
without fuzzy clustering
Variation of Transinformation versus distance in
different zones with fuzzy clustering
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 2970
Temporal Frequency of existing wells
The location of the selected existing and
potential monitoring wells
  • 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
  • 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
  • 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

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