Comprison of Fuzzy Possibilistic Regression and Fuzzy Least Square Regression Models to Estimate Groundwater Level of Neyshabour Aquifer

Document Type : Research Paper

Authors

1 M.Sc. Student of Water Resource Management, University of Birjand.

2 Associate Professor, Water Engineering Department, College of Agriculture, University of Birjand, Birjand, Iran

Abstract

Introduction
Groundwater has always been considered as one of the main sources of drinking, agriculture, and industrial water, especially in arid and semi-arid regions. Investigating groundwater level changes in any region has an important role in planning sustainable water resources management. Continuous decline of groundwater level has been observed worldwide in the past half-century. Groundwater is the most important and the only source of freshwater in Neyshabour plain. Unallowable discharges of the groundwater resources and the reduction of recharge factors have caused about 200 million cubic meters deficit in Neyshabour aquifer. Therefore, estimating groundwater is vitally important for the management of water resources.
 
Methodology
This study was conducted in Neyshabour aquifer in Khorasan Razavi province situated between 58o13' to 59o30' eastern longitude and 35o40' to 36o39' northern latitude. Neyshabour plain has an important role in agricultural productions of Khorasan Razavi. In this study, the fuzzy possibilistic regression and fuzzy least square regression approaches were evaluated in order to forecast the groundwater changes in Neyshabour aquifer. For this propose, the parameters affecting aquifer level, including monthly precipitation, discharge detected, and fuzzy regression approaches were employed to estimate groundwater level of aquifer, and then raster maps were determined by geostatistical methods. Data bank was determined by Arc GIS software from raster maps to train and test fuzzy regression models. 50 percent of data was selected as calibration data and 50 percent of data was selected as validation data in each model. In linear regression, for each series of input variables, only a specific output value is computed, while fuzzy regression models estimate the boundaries of possible values for the output variables. Therefore, unlike the classical regression, which was based on probability theory, the fuzzy regression is based on possibility and fuzzy sets theory. Fuzzy possibilistic regression, introduced by Tanaka et al. (1982), is an approach that provides the best regression equation by minimizing the amount of fuzzy. The general form of this fuzzy regression function is as follows:
[




Ỹ  =Ã0+Ã1X1+Ã2X2+ Ã3X3+…+ÃnXn                                                                                                                                     


(1)




 
where Ã0 and Ã1 are the fuzzy intercept and fuzzy slope coefficients, respectively, and X is the independent variable and the output Ỹ (or dependent variable) is a fuzzy number. 
Fuzzy least-squares regression (FLSR) method as proposed by Savic and Pedrycz (1991) was adopted for this analysis. For the purpose of current study, the efficiency of the fuzzy possibilistic and fuzzy least square regression models for groundwater prediction in Neyshabour aquifer were compared. Validation and Verification of models were determined based on mean error (ME), root mean square error (RMSE), and coefficient of determination (R2).

Keywords

Main Subjects

References

1-    Anonymous., 2009. Management Studies for Water Resources Reconciliation in Neyshabour Plain. Khorasan Razavi Regional Water Company, Technical Rep. (In Persian).
 
2-    Arabpour, A.S., 2014. Fuzzy Linear Regression and Effect of Percent Points. 4th Congress on Fuzzy and Intelligent Systems of Iran. Zahedan, University of Sistan and Baluchestan. (In Persian).
 
3-    Bardossy, A., Bogardi, I. and Duckstein, L., 1990. Fuzzy regression in hydrology. Water Resources Research, 26(7), pp.1497-1508.
 
4-    Chang, Y.H.O. and Ayyub, B.M., 2001. Fuzzy regression methods–a comparative assessment. Fuzzy Sets and Systems, 119(2), pp.187-203.
 
5-     Daliakopoulos, I.N., Coulibaly, P. and Tsanis, I.K., 2005. Groundwater level forecasting using artificial neural networks. Journal of Hydrology, 309(1-4), pp.229-240.
 
6-    Dastourani, M.T., Sharifi Darani, H., Talebi, A. and Moghaddamnia, A.S., 2011. Efficiency of Artificial Neural Networks and Adaptive Neuro-Fuzzy Inference System in Rainfall-Runoff Modeling in Zayandehrud Dam Watershed. Journal of Water and Sewage. 14(22), pp.114-125. (In Persian).
 
7-    Dillip, K.G., Sudhansu, S.P. and Prakash, C.S.  2010. Prediction of water table depth in western region, Orissa interpolation of groundwater head series. Journal of Hydrology. 192, pp.65–80.
 
8-    Farahi, G., Kodashenas, S. and Alizadeh, A., 2011. Estimation of sediment of watersheds in northern Khorasan province using fuzzy regression model. Iran-Watershed Management Science & Engineering 5(15), pp.11-24. (In Persian).
 
9-    Fathi, F. and Zibaei, m., 2010. Water management in the common water conditions. Journal of Agricultural Economics. 4(4), pp.47-63. (In Persian).
 
10- Hellegers, P., 2002. Treating water in irrigated agriculture as an economic good. Presented on the Conference of Irrigation Water Policies, June, Agadir, Morocco.
 
11-  Heshmaty, B. and Kandel, A., 1985. Fuzzy linear regression and its applications to forecasting in uncertain environment. Fuzzy Sets and Systems, 15(2), pp.159-191.
 
12- Hosseini, A., Farajzadeh, M. and velayati, S., 2005. Analysis of Water Crisis in Neyshabur with Environmental Planning Approach, Research Committee of Regional Water Company of Khorasan, Technical Rep (In Persian).
 
13- Izadi, A., Davari, K., Alizadeh, A. and Ghahreman, B., 2008. Application of Panel Data Model in Predicting Groundwater Level. Iranian Journal ofIrrigation&Drainage, 2(2): 133-144 (In Persian).
 
14-  Jusseret, S., Tam, V.T. and Dassargues, A., 2009. Groundwater flow modelling in the central zone of Hanoi, Vietnam. Hydrogeology Journal, 17(4), pp.915-934.
 
15- Khashei-Siuki. A.,  Ghahraman, B. and Kouchakzadeh, M., 2013. Comparison of ANN, ANFIS and Regression Models to Estimate Groundwater level of Neyshaboor Aquifer. Iranian Journal of lrrigation and Drainage. 7(1), pp.10-22. (In Persian).
 
16- Koorehpazan Dezfouli, A., 2014. The Principles of Fuzzy sets Theory and Its Applications in Modeling Water Engineering Issues. Jahad University Press. Amirkabir University of Technology. Fourth Edition. pp. 261. (In Persian).
 
17- Kurduvani, p., 1995. Geohydrology. Tehran University Press, Tehran University Press. (In Persian).
 
18-  Kurtulus, B. and Razack, M., 2010. Modeling daily discharge responses of a large karstic aquifer using soft computing methods: Artificial neural network and neuro-fuzzy. Journal of Hydrology, 381(1-2), pp.101-111.
 
19- Lai, Y.J. and Chang, S.I., 1994. A fuzzy approach for multiresponse optimization: An off-line quality engineering problem. Fuzzy Sets and Systems, 63(2), pp.117-129.
 
20-  Larroque, F., Treichel, W. and Dupuy, A., 2008. Use of unit response functions for management of regional multilayered aquifers: application to the North Aquitaine Tertiary system (France). Hydrogeology Journal, 16(2), pp.215-233.
 
21- Lashkaripour, G.H., Ghafouri, M., Kazemi Golian, R. and Damshenas, M., 2007. Land Summit due to groundwater subsidence in Neishabour plain. Iranian Geology and Engineering Conference. pp.1082-1090. (In Persian).
 
22-  Lohani, A.K. and Krishan, G., 2015. Application of artificial neural network for groundwater level simulation in Amritsar and Gurdaspur districts of Punjab, India. Journal of Earth Science & Climatic Change, 6(4), p.1.
 
23- Parviz, L., Kholghi, M. and Fakhorifard, A., 2010. Forecasting annual streamflow using autoregressive integrated moving average model and fuzzy regression. Journal of Soil and Water Science. 19(1), pp.66-82. (In Persian).
 
24-  Reghunath, R., Murthy, T.S. and Raghavan, B.R., 2005. Time series analysis to monitor and assess water resources: A moving average approach. Environmental Monitoring and Assessment, 109(1-3), pp.65-72.
 
25- Sadatinezhad, S.J., Hasanshahi, R., Shayanfar, M. and Abdollahi, K.H., (2011) Evaluation of Fuzzy Regression Efficiency for Reconstructing Missing Annual Precipitation Data in Karoon Basin. Environmental Sciences. 8(3), pp.109-116. (In Persian).
 
26-  Savic, D.A. and Pedrycz, W., 1991. Evaluation of fuzzy linear regression models. Fuzzy Sets and Systems, 39(1), pp.51-63.
 
27- Shizeradi, S. and Saboisaboni, M., 2014. Investigating the stability and equilibrium of groundwater table in order to achieve sustainable management (Case study: Neyshabour basin). Journal of Agricultural Economics Researches. 6(4), pp.107-128 (In Persian).
 
28- Soltani, F., 2006. Comparison of Application of Neuro-Fuzzy Adaptive Network (ANFIS) to Artificial Neural Network (ANN) in forecasting the flow of Zayanderad River. 7th International River Engineering Workshop. Shahid Chamran University of Ahvaz.
 
29-  Sun, Y., Wendi, D., Kim, D.E. and Liong, S.Y., 2015. Application of artificial neural networks in groundwater table forecasting-a case study in Singapore swamp forest. Hydrology & Earth System Sciences Discussions, 12(9).
 
30- Tanaka, H. and Uejima, S., 1982. Linear regression analysis with fuzzy model. IEEE Transactions on Systems, Man, And Cybernet. 12, pp.903-907.
 
31- Velayati, S., 2000. The most important factors affecting the quality changes of the Neyshabour plain. Quarterly Journal Of Geographic Research. 15, pp.102-134. (In Persian).
 
32-  Wang, H.F. and Tsaur, R.C., 2000. Insight of a fuzzy regression model. Fuzzy Sets and Systems, 112(3), pp.355-369.
 
33- Yan, Q. and Ma, C., 2016. Application of integrated ARIMA and RBF network for groundwater level forecasting. Environmental Earth Sciences, 75(5), p.396.
 
34-  Yen, K.K., Ghoshray, S. and Roig, G., 1999. A linear regression model using triangular fuzzy number coefficients. Fuzzy Sets and Systems, 106(2), pp.167-177.
 
35- Zhang, N., Xiao, C., Liu, B. and Liang, X., 2017. Groundwater depth predictions by GSM, RBF, and ANFIS models: a comparative assessment. Arabian Journal of Geosciences, 10(8), p.189.
 
36- Zhou, Y. and Li, W., 2011. A review of regional groundwater flow modeling. GeoscienceFrontiers, 2(2), pp.205-214.
Irrigation Sciences and Engineering
Volume 43, Issue 1
March 2020
Pages 131-143

Files

History

  • Receive Date: 14 February 2018
  • Revise Date: 24 April 2018
  • Accept Date: 28 April 2018
  • Publish Date: 20 March 2020

Share

How to cite

Statistics