Abstract
The present research focuses on addressing various ambiguities in the existing method of integrating information entropy and water quality, thereby presenting a novel approach for an entropy-weighted water quality index. A three-dimensional water quality dataset is considered in the proposed method, the third dimension being the sampling frequency factor. The probability of observed values adhering to desirable limits prescribed by a standard code is estimated, leading to the computation of information entropy and, eventually, entropy weights. These weights are then used for the computation of the Modified Entropy-weight Water Quality Index (MEWQI) values. To verify the proposed method’s applicability, the water quality dataset of Deepor Beel, India, was considered. IS 10500: 2012 was used for estimating MEWQI values. Results showed an excellent correlation with the observed dataset and their uncertainties of occurrence. The reliability and correctness of the proposed methodology were finally confirmed through both cluster analysis and sensitivity analysis. The cluster analysis showed remarkable associations with the computed MEWQI values, while the sensitivity analysis proved that no particular parameter was accountable for the contribution of MEWQI values; instead, all parameters exhibited equal contributions. The proposed methodology was thus found to be the most reasonable and reliable as it considered both factors, i.e., measured values concerning standard limits and the uncertainty, necessary for a consistent water quality monitoring program.
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Data availability
All data, models, or code generated or used during the study are available from the corresponding author by request.
Notes
It is important to note that since the proposed methodology is based on the probabilistic approach, thus, the more the sampling frequency, the better and a more practical picture of the uncertainty, and therefore a more reliable WQI, is obtained.
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The authors extend their sincere gratitude to Dr Kunwar Raghvendra Singh, Assistant Professor, GLA University Mathura for his valuable insights into the manuscript. The authors are also grateful to the Department of Civil Engineering, Indian Institute of Technology Guwahati for all the facilities needed to carry out this research.
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Siddhant Dash: Conceptualization, methodology, resources, investigation, data curation, writing—original draft.
Ajay S. Kalamdhad: conceptualization, resources, writing—review & editing.
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Appendix A: Details of the conflicting factors to the existing assignment of entropy weightages for determining WQI
Appendix A: Details of the conflicting factors to the existing assignment of entropy weightages for determining WQI
The assignment of entropy weights is based on the probabilistic approach. However, the method possesses some ambiguities in its approach, as described through the following paradigm.
Let us consider a small water quality dataset matrix X, given by Eq. 16.
where the rows and columns indicate the sampling locations and different water quality parameters respectively.
As per the protocol of the existing method, Eq. 17 represents the normalized dataset matrix.
This normalized matrix, then leads to the probability matrix P (Eq. 18).
From this probability matrix, the entropy weights are estimated. The following important observations are made from Eq. A1 - A3 (BDL is considered as 0).
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Firstly, it is observed that the value of Pab is directly dependent on the observed value of the water quality parameters, rather than considering the frequency factor. For example, for the first parameter, the highest probability is obtained for the fourth location, which is the same point where the particular parameter is observed to be the highest. Similar observations can be seen for second parameter (third location), fourth parameter (fourth location), and fifth parameter (second location). Hence, the probability function in this case is a function of the value, instead of the frequency.
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Secondly, it is seen that the probability values for each sampling location (for a particular parameter) are estimated as the ratio of the observed value in a particular location to the sum of all values at all locations, which is questionable. This is because the probability values do not take into consideration any frequency factor (of parameters adhering to exceeding a standard limit). Hence, it is unclear as to what the value of Pab indicates, as it does not explain whether any given sampling location has a contributing factor (parameter) to the pollution of the water body as a whole. In other words, Pab fails to comprehend whether any parameter for a given sampling location has its value exceeding or residing within the desirable standard limits.
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Thirdly, the probability values obtained is debatable, considering the fact that they carry huge degrees of certainty with them. Consider, for example, the probability value of parameter 2 at the third location (P = 0.9994), it suggests that the observed values of the specific parameter at that location will have a value close to 5 for 99.94% (almost 100%) of the times. Also, some values tend to 0, for example, first parameter at third location. This suggests that the values of the first parameter at the third location will have values other than 0.8 for 100% of the times, which is absurd. It is a well-known fact that the natural systems are highly dynamic with respect to time and space, and thus carry a huge quantum of uncertainty with them.
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Dash, S., Kalamdhad, A.S. Discussion on the existing methodology of entropy-weights in water quality indexing and proposal for a modification of the expected conflicts. Environ Sci Pollut Res 28, 53983–54001 (2021). https://doi.org/10.1007/s11356-021-14482-5
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DOI: https://doi.org/10.1007/s11356-021-14482-5