Application of Principle of Maximum Entropy in Determining the Optimum Number of Surface Water Quality Monitoring Stations

Document Type : Research Paper


1 MSc student, Department of Watershed Management Engineering, Faculty of Agriculture and Natural Resources, Lorestan University, Khorramabad, Iran

2 Associate Prof. Department of Watershed Management Engineering, Faculty of Agriculture and Natural Resources, Lorestan University, Khorramabad, Iran


Optimization of monitoring network is a decision-making process through which, the best combination of existing stations is selected. Regarding the economic considerations and reducing monitoring costs, optimization approach in this study is to reduce the number of surface water quality monitoring stations in Dez basin in Lorestan province. In this regard, using an algorithm based on the principle of maximum entropy and water quality index of SO44, Cl, HCO3, K, Na, Ca, Mg, pH, TH, SAR, EC and TDS parameters, the optimization procedure was done for 18 existing monitoring stations during the statistical period of 1387-1396 (2008-2017). First, the average rank of each station in the mentioned 10 statistical years was obtained, then some models were proposed for the network entropy according to the number of stations and year. After fitting the best model, the results showed that based on SO4, Cl, HCO3, K, Na, Ca, Mg, pH, TH, TD, SAR and EC parameters, the number of sufficient stations as surface water quality monitoring network in the study area were 9, 9, 7, 11, 11, 11, 10, 7, 10, 10, 10, and 11, respectively. In order to validate the proposed network, by comparing the entropy of the proposed network with the entropy of random networks with the number of stations based on the 12 mentioned parameters in each year, the efficiency of the selected network was confirmed. Also, among the 12 evaluated quality indicators, chloride showed the highest entropy of weight. Therefore, chloride had the maximum entropy and was selected as the superior index.


Ahmadi, F., Radmanesh, F., Parham, Gh. and Mirabasi Najafabadi, R., (2017). Application of Archimedean joint functions in flood frequency analysis of Dez catchment, Iranian journal of soil and water, 48(3).
Akbarzadeh, M. and Ghahraman, B., (2013). A combined strategy of Entropy and spatio-temporal Kriging in determining optimal network for ground water quality monitoring of Mashhad basin. Journal of Water and Soil 27(3).613-629
Akbarzadeh, M., Ghahraman, B. and Davari, K., (2015). Optimization of Mashhad Aquifer Ground water Quality Monitoring Network using Spatio- Temporal Modeling, Iran water Resources Research, 12(1), 133-144
Alian Nejad, M., Bakhtiari, B. And Gaderi, K., (2016). Comparison of Monte Carlo methods and hybrid fso logic PSO method, 25(13), 105-112
Amiri, V., Rezaei, M., Sohrabi, N., (2014). Groundwater quality assessment using entropy Weighted water quality index (EWQI) in Lenjanat, Iran. Environ. Earth Sci. 72 (9), 3479–3490
Chadalavad, S., Datta, B. And Naidu, R., (2011). Uncertainty based optimal monitoring network design for a chlorinated hydrocarbon contaminated site. Journal of environment monitoring and assessment.173 (1-4), 929-940
Dimitris, M. and Metaxa, G., (2006). Geostatiscal analysis of spatial variability of rainfall and optimal design of a rainguage network, Water resources management, 10, 107-127
Fatahi, H., Abdi, H., Khosravi, F. and Karimi, SH., (2018). Comparison of point estimation methods and Monte carlo simulations in solving probabilistic optimal power dissipation in terms of renewable source uncertainties, 9(3), 72-85
Guey-Shin, S., Bai-You, C., Chi TC, Pei HY. Tsun KC., (2011). Applying factor analysis combined with kriging and information entropy theory for mapping and evaluating the stability of groundwater quality variation in Taiwan. International Journal of Environmental Resources and Public Health 8: 1084-1109
Kar, B., Ehodgson, M., (2008). A GIS-Based Model to Determine Site Suitability of Emergency Evacuation Shelters. Transactions in GIS 12(2):227-248.
Kim, Y., Chung, Eun-Sung, Jun, Sang-Mook, Kim, Sang UG., (2013). Prioritizing the best sites for treated wastewater instream use in an urban watershed using fuzzy TOPSIS. Resources, Conservation and Recycling, (73): 23-32.
Karamoz, M., Falahi, M. And Nazif, S., (2010). Spatial Precipitation Analysis: Comparison of Kriging Methods with Conventional Methods, Iranian water Resources Research Quarterly, 6(1).
Li, P., Qian, H., Wu, J., (2010). Groundwater quality assessment based on improved water quality index in Pengyang County, Ningxia, Northwest China. J. Chem. 7 (S1), S209–S216
Mogheir, De lima, JLMP and Singh VP., (2009). Entropy and Multi-Objective based approach for ground water quality monitoring network assessment and redesign, Journal of water Resources Management. 23(8):1603-1620
Pazirandeh, A., Shakorian, A., (2005). Optimization of neutron beam energy in neutron therapy with boron by Monte Carlo method, Iranian Journal of Physics Research, 6(2). 
Shannon, C. E., (1948). A Mathematical Theory of Communication. The Bell System Technical Journal. 27(4): 623-656
Singh, K.R., Ajays, R.D., Kumar, K.B., (2019). An investigation on water quality variability and identification of ideal monitoring locations by using entropy based disorder indices. The total of environment 647; 1444-1455
Singh, VP., (2013). Entropy Theory and its Application in Environmental and water Engineering, John Wiley and sons.
Wu JP, Li H, Qian M., (2011). Groundwater quality in Jingyuan County, a semi-humid area in Northwest China. E-Journal of Chemistry 8: 787-793.
Yeh, H.C., Chen, Y.C., Wei, C. And Chen, R.H., (2011). Entropy kriging approach to rain fall network design. Journal of paddy and water environment 9(3):343-355
Yufeng S, Fengxiang J., (2009). Landslide Stability Analysis Based on Generalized Information Entropy. International Conference on Environmental Science and Information Application Technology: 83–85.