Skip to main content

Advertisement

SpringerLink
Log in

Discussion on the existing methodology of entropy-weights in water quality indexing and proposal for a modification of the expected conflicts

  • Research Article
  • Published:
Environmental Science and Pollution Research Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Data availability

All data, models, or code generated or used during the study are available from the corresponding author by request.

Notes

  1. 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.

References

  • Abtahi M, Golchinpour N, Yaghmaeian K, Rafiee M, Jahangiri-rad M, Keyani A, Saeedi R (2015) A modified drinking water quality index (DWQI) for assessing drinking source water quality in rural communities of Khuzestan Province, Iran. Ecol Indic 53:283–291

    Article  CAS  Google Scholar 

  • Adimalla N, Qian H, Li P (2019): Entropy water quality index and probabilistic health risk assessment from geochemistry of groundwaters in hard rock terrain of Nanganur County, South India. Chem. Erde

  • Ali MM, Ali ML, Islam MS, Rahman MZ (2016) Preliminary assessment of heavy metals in water and sediment of Karnaphuli River, Bangladesh. Environmental Nanotechnology, Monitoring & Management 5:27–35

    Article  Google Scholar 

  • Amiri V, Rezaei M, Sohrabi N (2014) Groundwater quality assessment using entropy weighted water quality index (EWQI) in Lenjanat, Iran. Environ Earth Sci 72:3479–3490

    Article  CAS  Google Scholar 

  • Amiri V, Sohrabi N, Dadgar MA (2015) Evaluation of groundwater chemistry and its suitability for drinking and agricultural uses in the Lenjanat plain, central Iran. Environ Earth Sci 74:6163–6176

    Article  CAS  Google Scholar 

  • APHA (2017) Standard methods for the Examination of Water and Wastewater. American Public Health Association, American Water Works Association, Water Environment Federation.

  • Banerjee S, Kumar A, Maiti SK, Chowdhury A (2016) Seasonal variation in heavy metal contaminations in water and sediments of Jamshedpur stretch of Subarnarekha river, India. Environ Earth Sci 75:265

    Article  CAS  Google Scholar 

  • Bao Q, Yuxin Z, Yuxiao W, Feng Y (2020) Can Entropy Weight Method Correctly Reflect the Distinction of Water Quality Indices? Water Resources Management

  • Beamonte E, Bermúdez JD, Casino A, Veres E (2005) A global stochastic index for water quality: the case of the river Turia in Spain. J Agric Biol Environ Stat 10:424–439

    Article  Google Scholar 

  • Chen J, Huang Q, Lin Y, Fang Y, Qian H, Liu R, Ma H (2019) Hydrogeochemical characteristics and quality assessment of groundwater in an irrigated region, Northwest China. Water (Switzerland) 11

  • Chung ES, Abdulai PJ, Park H, Kim Y, Ahn SR, Kim SJ (2017) Multi-criteria assessment of spatial robust water resource vulnerability using the TOPSIS method coupled with objective and subjective weights in the Han river basin. Sustainability 9

  • Cover TM (1999) Elements of information theory. John Wiley & Sons

  • Cui S, Yu T, Zhang F, Fu Q, Hough R, An L, Gao S, Zhang Z, Hu P, Zhu Q, Pei Z (2020) Understanding the risks from diffuse pollution on wetland eco-systems: The effectiveness of water quality classification schemes. Ecol Eng 155:105929

    Article  Google Scholar 

  • Dash S, Kalamdhad AS (2021) Hydrochemical dynamics of water quality for irrigation use and introducing a new water quality index incorporating multivariate statistics. Environ Earth Sci 80:73

    Article  CAS  Google Scholar 

  • Dash S, Borah SS, Kalamdhad A (2018) Monitoring and assessment of Deepor Beel water quality using multivariate statistical tools. Water Practice and Technology 13:893–908

    Article  Google Scholar 

  • Dash S, Borah SS, Kalamdhad A (2019) A modified indexing approach for assessment of heavy metal contamination in Deepor Beel, India. Ecol Indic 106:105444

    Article  CAS  Google Scholar 

  • Dash S, Borah SS, Kalamdhad AS (2020a) Application of Environmetrics tools for geochemistry, water quality assessment and apportionment of pollution sources in Deepor Beel, Assam, India. Water Practice and Technology

  • Dash S, Borah SS, Kalamdhad AS (2020b) Study of the limnology of wetlands through a one-dimensional model for assessing the eutrophication levels induced by various pollution sources. Ecol Model 416:108907

    Article  CAS  Google Scholar 

  • Dash S, Borah SS, Kalamdhad AS (2021) Heavy metal pollution and potential ecological risk assessment for surficial sediments of Deepor Beel, India. Ecol Indic 122:107265

    Article  CAS  Google Scholar 

  • Egbueri JC (2021) Prediction modeling of potentially toxic elements’ hydrogeopollution using an integrated Q-mode HCs and ANNs machine learning approach in SE Nigeria. Environmental Science and Pollution Research p 1–19

  • Egbueri JC, Ameh PD, Enyigwe MT, Unigwe CO (2020a) Entropy-Based Analysis of the Impact of Environmentally Sensitive Elements on Groundwater Quality of the Ameka Region of Southeast Nigeria: Medical Geology Implications. Anal Lett 1–31

  • Egbueri JC, Ameh PD, Unigwe CO (2020b) Integrating entropy-weighted water quality index and multiple pollution indices towards a better understanding of drinking water quality in Ojoto area, SE Nigeria. Scientific African 10:e00644

    Article  Google Scholar 

  • Egbueri JC, Ezugwu CK, Ameh PD, Unigwe CO, Ayejoto DA (2020c) Appraising drinking water quality in Ikem rural area (Nigeria) based on chemometrics and multiple indexical methods. Environmental Monitoring and Assessment 192

  • Fagbote EO, Olanipekun EO, Uyi HS (2014) Water quality index of the ground water of bitumen deposit impacted farm settlements using entropy weighted method. Int J Environ Sci Technol 11:127–138

    Article  CAS  Google Scholar 

  • Gao Y, Qian H, Ren W, Wang H, Liu F, Yang F (2020) Hydrogeochemical characterization and quality assessment of groundwater based on integrated-weight water quality index in a concentrated urban area. J Clean Prod 260:121006

    Article  CAS  Google Scholar 

  • Gazzaz NM, Yusoff MK, Aris AZ, Juahir H, Ramli MF (2012) Artificial neural network modeling of the water quality index for Kinta River (Malaysia) using water quality variables as predictors. Mar Pollut Bull 64:2409–2420

    Article  CAS  Google Scholar 

  • Gazzaz NM, Yusoff MK, Ramli MF, Juahir H, Aris AZ (2015) Artificial neural network modeling of the water quality index using land use areas as predictors. Water Environ Res 87:99–112

    Article  CAS  Google Scholar 

  • Ghorbani Mooselu M, Liltved H, Nikoo MR, Hindar A, Meland S (2020): Assessing optimal water quality monitoring network in road construction using integrated information-theoretic techniques. Journal of Hydrology 589

  • Gorgij AD, Kisi O, Moghaddam AA, Taghipour A (2017) Groundwater quality ranking for drinking purposes, using the entropy method and the spatial autocorrelation index. Environ Earth Sci 76

  • Hasan MSU, Rai AK (2020) Groundwater quality assessment in the Lower Ganga Basin using entropy information theory and GIS. J Clean Prod 274:123077

    Article  CAS  Google Scholar 

  • He S, Wu J (2019) Relationships of groundwater quality and associated health risks with land use/land cover patterns: A case study in a loess area, Northwest China. Hum Ecol Risk Assess 25:354–373

    Article  CAS  Google Scholar 

  • He S, Li P, Wu J, Elumalai V, Adimalla N (2019) Groundwater quality under land use/land cover changes: A temporal study from 2005 to 2015 in Xi’an, Northwest China. Hum Ecol Risk Assess.

  • IS:10500 (2012) Indian Standard Drinking Water–Specification (Second revision). Bureau of Indian Standards (BIS), New Delhi

    Google Scholar 

  • Islam ARMT, Ahmed N, Bodrud-Doza M, Chu R (2017) Characterizing groundwater quality ranks for drinking purposes in Sylhet district, Bangladesh, using entropy method, spatial autocorrelation index, and geostatistics. Environ Sci Pollut Res 24:26350–26374

    Article  CAS  Google Scholar 

  • Islam ARMT, Al Mamun A, Rahman MM, Zahid A (2020a) Simultaneous comparison of modified-integrated water quality and entropy weighted indices: Implication for safe drinking water in the coastal region of Bangladesh. Ecological Indicators 113

  • Islam ARMT, Islam HMT, Mia MU, Khan R, Habib MA, Bodrud-Doza M, Siddique MAB, Chu R (2020b) Co-distribution, possible origins, status and potential health risk of trace elements in surface water sources from six major river basins, Bangladesh. Chemosphere 249

  • Jena V, Dixit S, Gupta S (2013) Assessment of water quality index of industrial area surface water samples. Int J ChemTech Res 5:278–283

    CAS  Google Scholar 

  • Ji Y, Wu J, Wang Y, Elumalai V, Subramani T (2020) Seasonal Variation of Drinking Water Quality and Human Health Risk Assessment in Hancheng City of Guanzhong Plain, China. Exposure and Health

  • Juahir H, Zain SM, Toriman ME, Mokhtar M, Man HC (2004) Application of artificial neural network models for predicting water quality index. Malaysian Journal of Civil Engineering 16

  • Kamrani S, Rezaei M, Amiri V, Saberinasr A (2016) Investigating the efficiency of information entropy and fuzzy theories to classification of groundwater samples for drinking purposes: Lenjanat Plain, Central Iran. Environmental Earth Sciences 75

  • Khound NJ, Bhattacharyya KG (2017) Multivariate statistical evaluation of heavy metals in the surface water sources of Jia Bharali river basin, North Brahmaputra plain, India. Appl Water Sci 7:2577–2586

    Article  CAS  Google Scholar 

  • Kim DH, Nguyen TV, Heo M, Chon TS (2015) Subsequent application of self-organizing map and hidden Markov models infer community states of stream benthic macroinvertebrates. J Ecol Enviro 38:95–107

    Article  Google Scholar 

  • Lermontov A, Yokoyama L, Lermontov M, Machado MAS (2009) River quality analysis using fuzzy water quality index: Ribeira do Iguape river watershed, Brazil. Ecol Indic 9:1188–1197

    Article  CAS  Google Scholar 

  • Li P, Wu J, Qian H, Lyu X, Liu H (2014) Origin and assessment of groundwater pollution and associated health risk: A case study in an industrial park, northwest China. Environ Geochem Health 36:693–712

    Article  CAS  Google Scholar 

  • Li P, Wu J, Qian H (2016) Hydrochemical appraisal of groundwater quality for drinking and irrigation purposes and the major influencing factors: a case study in and around Hua County, China. Arab J Geosci 9:1–17

    Article  Google Scholar 

  • Li P, He X, Guo W (2019) Spatial groundwater quality and potential health risks due to nitrate ingestion through drinking water: A case study in Yan’an City on the Loess Plateau of northwest China. Hum Ecol Risk Assess 25:11–31

    Article  CAS  Google Scholar 

  • Li P, Rao C, Goh M, Yang Z (2021) Pricing strategies and profit coordination under a double echelon green supply chain. J Clean Prod 278:123694

    Article  Google Scholar 

  • Lodwick WA, Monson W, Svoboda L (1990) Attribute error and sensitivity analysis of map operations in geographical informations systems: suitability analysis. Int J Geogr Inf Syst 4:413–428

    Article  Google Scholar 

  • Lyu M, Pang Z, Huang T, Yin L (2019) Hydrogeochemical evolution and groundwater quality assessment in the Dake Lake Basin, Northwest China. J Radioanal Nucl Chem 320:865–883

    Article  CAS  Google Scholar 

  • Marghade D, Malpe DB, Duraisamy K, Patil PD, Li P (2020) Hydrogeochemical evaluation, suitability, and health risk assessment of groundwater in the watershed of Godavari basin, Maharashtra, Central India. Environmental Science and Pollution Research

  • Maskooni EK, Naseri-Rad M, Berndtsson R, Nakagawa K (2020) Use of heavy metal content and modified water quality index to assess groundwater quality in a semiarid area. Water (Switzerland) 12

  • Mirauda D, Ostoich M (2020) MIMR criterion application: Entropy approach to select the optimal quality parameter set responsible for river pollution. Sustainability 12

  • Misaghi F, Delgosha F, Razzaghmanesh M, Myers B (2017) Introducing a water quality index for assessing water for irrigation purposes: A case study of the Ghezel Ozan River. Sci Total Environ 589:107–116

    Article  CAS  Google Scholar 

  • MoEF (2008) Report on visit to Deepor Beel in Assam: a wetland included under national wetland conservation management programme of the Ministry of Environment and Forests. Govt. of India.

  • Mogheir Y, De Lima J, Singh V (2004) Characterizing the spatial variability of groundwater quality using the entropy theory: I. Synthetic data. Hydrol Process 18:2165–2179

    Article  Google Scholar 

  • Nasiri F, Maqsood I, Huang G, Fuller N (2007) Water quality index: A fuzzy river-pollution decision support expert system. J Water Resour Plan Manag 133:95–105

    Article  Google Scholar 

  • Pourshahabi S, Nikoo MR, Raei E, Adamowski JF (2018a) An Entropy-Based Approach to Fuzzy Multi-objective Optimization of Reservoir Water Quality Monitoring Networks Considering Uncertainties. Water Resour Manag 32:4425–4443

    Article  Google Scholar 

  • Pourshahabi S, Talebbeydokhti N, Rakhshandehroo G, Nikoo MR (2018b) Spatio-Temporal Multi-Criteria Optimization of Reservoir Water Quality Monitoring Network Using Value of Information and Transinformation Entropy. Water Resour Manag 32:3489–3504

    Article  Google Scholar 

  • Rakotondrabe F, Ngoupayou JRN, Mfonka Z, Rasolomanana EH, Abolo AJN, Ako AA (2018) Water quality assessment in the Bétaré-Oya gold mining area (East-Cameroon): multivariate statistical analysis approach. Sci Total Environ 610:831–844

    Article  CAS  Google Scholar 

  • Rao C, Lin H, Liu M (2019) Design of comprehensive evaluation index system for P2P credit risk of “three rural” borrowers. Soft Computing, 1-17

  • Rao C, He Y, Wang X (2020) Comprehensive evaluation of non-waste cities based on two-tuple mixed correlation degree. International Journal of Fuzzy Systems, 1-23

  • Reza R, Singh G (2010) Heavy metal contamination and its indexing approach for river water. Int J Environ Sci Technol 7:785–792

    Article  CAS  Google Scholar 

  • Rezaei A, Hassani H, Tziritis E, Fard Mousavi SB, Jabbari N (2020) Hydrochemical characterization and evaluation of groundwater quality in Dalgan basin. SE Iran Groundwater for Sustainable Development 10

  • Sahoo MM, Patra KC, Swain JB, Khatua KK (2017) Evaluation of water quality with application of Bayes' rule and entropy weight method. Eur J Environ Civ Eng 21:730–752

    Article  Google Scholar 

  • Sarkar BC, Mahanta BN, Saikia K, Paul PR, Singh G (2007) Geo-environmental quality assessment in Jharia coalfield, India, using multivariate statistics and geographic information system. Environ Geol 51:1177–1196

    Article  CAS  Google Scholar 

  • Shannon CE, Weaver W (1949)The Mathematical Theory of Communication, by CE Shannon (and Recent Contributions to the Mathematical Theory of Communication), W. Weaver. University of illinois Press

  • Shrestha S, Kazama F (2007) Assessment of surface water quality using multivariate statistical techniques: A case study of the Fuji river basin, Japan. Environ Model Softw 22:464–475

    Article  Google Scholar 

  • Singaraju S, Pasupuleti S, Hernandez EA, Uddameri V (2018) Prioritizing Groundwater Monitoring in Data Sparse Regions using Atanassov Intuitionistic Fuzzy Sets (A-IFS). Water Resour Manag 32:1483–1499

    Article  Google Scholar 

  • Singh S, Singh P, Gautam S (2016) Appraisal of urban lake water quality through numerical index, multivariate statistics and earth observation data sets. Int J Environ Sci Technol 13:445–456

    Article  Google Scholar 

  • Singh KR, Dutta R, Kalamdhad AS, Kumar B (2019) Information entropy as a tool in surface water quality assessment. Environ Earth Sci 78:15

    Article  CAS  Google Scholar 

  • Singh KR, Goswami AP, Kalamdhad AS, Kumar B (2020) Development of irrigation water quality index incorporating information entropy. Environ Dev Sustain 22:3119–3132

    Article  Google Scholar 

  • Su H, Kang W, Xu Y, Wang J (2017a) Assessment of Groundwater Quality and Health Risk in the Oil and Gas Field of Dingbian County, Northwest China. Exposure and Health 9:227–242

    Article  CAS  Google Scholar 

  • Su H, Kang W, Xu Y, Wang J (2017b) Assessing Groundwater Quality and Health Risks of Nitrogen Pollution in the Shenfu Mining Area of Shaanxi Province, Northwest China. Exposure and Health p 1–21

  • Subba Rao N (2020) Spatial distribution of quality of groundwater and probabilistic non-carcinogenic risk from a rural dry climatic region of South India. Environmental Geochemistry and Health

  • Subba Rao N, Sunitha B, Adimalla N, Chaudhary M (2020) Quality criteria for groundwater use from a rural part of Wanaparthy District, Telangana State, India, through ionic spatial distribution (ISD), entropy water quality index (EWQI) and principal component analysis (PCA). Environ Geochem Health 42:579–599

    Article  CAS  Google Scholar 

  • Sur S, Mandal J (2019): Deepor Beel: A Weeping and Blemishing Ramsar Site. Jalaplavit 9

  • Terrado M, Barceló D, Tauler R, Borrell E, de Campos S (2010) Surface-water-quality indices for the analysis of data generated by automated sampling networks. TrAC Trends Anal Chem 29:40–52

    Article  CAS  Google Scholar 

  • Ukah B, Ameh P, Egbueri J, Unigwe C, Ubido O (2020) Impact of effluent-derived heavy metals on the groundwater quality in Ajao industrial area, Nigeria: an assessment using entropy water quality index (EWQI). International Journal of Energy and Water Resources p 1–14

  • Van Eck NJ, Waltman L (2010) Software survey: VOSviewer, a computer program for bibliometric mapping. Scientometrics 84:523–538

    Article  Google Scholar 

  • Van Eck NJ, Waltman L (2014) Visualizing bibliometric networks, Measuring scholarly impact. Springer, pp 285–320

  • Wang D, Singh VP, Zhu Y, Wu J (2009) Stochastic observation error and uncertainty in water quality evaluation. Adv Water Resour 32:1526–1534

    Article  CAS  Google Scholar 

  • Wang J, Liu G, Liu H, Lam PK (2017) Multivariate statistical evaluation of dissolved trace elements and a water quality assessment in the middle reaches of Huaihe River, Anhui, China. Sci Total Environ 583:421–431

    Article  CAS  Google Scholar 

  • Wang D, Wu J, Wang Y, Ji Y (2020) Finding High-Quality Groundwater Resources to Reduce the Hydatidosis Incidence in the Shiqu County of Sichuan Province, China: Analysis, Assessment, and Management. Exposure and Health 12:307–322

    Article  CAS  Google Scholar 

  • Wilks DS (2011) Statistical methods in the atmospheric sciences, 100. Academic press, San Diego, United States

  • Wu J, Xue C, Tian R, Wang S (2017) Lake water quality assessment: a case study of Shahu Lake in the semiarid loess area of northwest China. Environ Earth Sci 76

  • Wu C, Wu X, Qian C, Zhu G (2018a) Hydrogeochemistry and groundwater quality assessment of high fluoride levels in the Yanchi endorheic region, northwest China. Appl Geochem 98:404–417

    Article  CAS  Google Scholar 

  • Wu C, Wu X, Zhu G, Qian C, Mu WP, Zhang YZ (2018b) Influence of a power plant in Ezhou City on the groundwater environment in the nearby area. Environ Earth Sci 77

  • Xiao Y, Yin S, Hao Q, Gu X, Pei Q, Zhang Y (2020) Hydrogeochemical appraisal of groundwater quality and health risk in a near-suburb area of North China. J Water Supply Res Technol AQUA 69:55–69

    Article  Google Scholar 

  • Yaseen ZM, Ramal MM, Diop L, Jaafar O, Demir V, Kisi O (2018) Hybrid adaptive neuro-fuzzy models for water quality index estimation. Water Resour Manag 32:2227–2245

    Article  Google Scholar 

  • Yi F, Chen L, Yan F (2019) The health risk weighting model in groundwater quality evaluation. Hum Ecol Risk Assess 25:2089–2097

    Article  CAS  Google Scholar 

  • Zhang J, Zhou J, Zhou Y, Zeng Y, Ji Y, Sun Y, Lei M (2021) Hydrogeochemical characteristics and groundwater quality assessment in the plain area of Yarkant River Basin in Xinjiang, PR China. Environ Sci Pollut Res:1–13

  • Zhou Y, Li P, Chen M, Dong Z, Lu C (2020) Groundwater quality for potable and irrigation uses and associated health risk in southern part of Gu’an County, North China Plain. Environmental Geochemistry and Health

Download references

Acknowledgements

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.

Author information

Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Technology Guwahati, Guwahati, Assam, 781039, India

    Siddhant Dash & Ajay S. Kalamdhad

Authors
  1. Siddhant Dash
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ajay S. Kalamdhad
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Siddhant Dash: Conceptualization, methodology, resources, investigation, data curation, writing—original draft.

Ajay S. Kalamdhad: conceptualization, resources, writing—review & editing.

Corresponding author

Correspondence to Siddhant Dash.

Ethics declarations

Ethics approval

The authors declare that the submitted manuscript is original. They also acknowledge that the current research has been conducted ethically and the final shape of the research has been agreed by all authors.

Consent to participate

The authors consent to participate in this research study.

Consent for publication

The authors consent to publish the current research in ESPR journal.

Conflict of interest

The authors declare no competing interests.

Additional information

Responsible Editor: Xianliang Yi

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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.

$$ X=\left[\begin{array}{lllll}1& BDL& 8& 5& 0.5\\ {}1.2& 0.005& 12& 7& 12\\ {}0.8& 10& 0.01& 4& 0.7\\ {}15& BDL& 14& 85& 0.6\\ {}3& 0.001& 28& 3& 0.7\end{array}\right] $$
(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.

$$ Y=\left[\begin{array}{lllll}0.0141& 0.0000& 0.2855& 0.0244& 0.0000\\ {}0.0282& 0.0005& 0.4284& 0.0488& 1.0000\\ {}0.0000& 1.0000& 0.0000& 0.0122& 0.0174\\ {}1.0000& 0.0000& 1.4998& 1.0000& 0.0087\\ {}0.1549& 0.0001& 1.0000& 0.0000& 0.0174\end{array}\right] $$
(17)

This normalized matrix, then leads to the probability matrix P (Eq. 18).

$$ P=\left[\begin{array}{lllll}0.0118& 0.0000& 0.1290& 0.0225& 0.0000\\ {}0.0235& 0.0005& 0.1935& 0.0449& 1.9583\\ {}0.0000& 0.9994& 0.0000& 0.0112& 0.0163\\ {}0.8353& 0.0000& 0.2258& 0.9213& 0.0083\\ {}0.1294& 0.0001& 0.4517& 0.0000& 0.0167\end{array}\right] $$
(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).

  • 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.

  • 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.

  • 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.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11356-021-14482-5

Keywords

Search

Navigation