A combined Time Series – Wavelet Model For Prediction of Ground Water Level (Case Study: Firuzabad Plain)

Document Type : Research Paper


1 MSc of Water resource Engineering Department of Shahid Chamran University of Ahvaz, Iran.

2 Associate Professor, Water Engineering Department, Shahid Chamran University of Ahvaz, Iran

3 Associate Professor, Water Engineering Department, Shahid Chamran University of Ahvaz, Iran.

4 Assistant Professor, Faculty of Mathematics and Computer Sciences, Shahid Chamran University of Ahvaz, Iran.

5 PhD Candidate, Faculty of Water Sciences, Shahid Chamran University of Ahvaz, Iran.


Recently, the phenomenon of climate change, drought, the exploitation of the ground water has caused a sharp decline in groundwater levels, which has also led to groundwater related subsidence and desertification. Therefore, reliable prediction of groundwater level for managing these resources is of prime importance. Nowadays wavelet transforms through signal decomposition to time and frequency has created an exceptional method for signal processing, with the help of the transformation of the wavelet that has the ability to split the time series into a multi-dimensional substrate with different scales.
One of the useful characteristics of wavelet transforms is the filtering algorithm, which divids the data into two groups of approximation and details by passing them through the wavelet filter. In this study, monthly groundwater surface, rainfall, and temperature data were used. Using the program code written in MATLAB software, it is necessary to analyze the time series data of all three parameters of temperature, precipitation, and water level. The values ​​of the parameters were selected as inputs and placed in the wavelet function. For analyzing all the parameters, according to various mother-wavelet experiments, and considering the above mentioned point, five mother-wavelets (Haar, Coif, Symlet, Db, Db4) were selected. For this purpose, the program was first implemented for each of the following wavelets with 4 different decomposition levels. After several software runs under specific conditions and scenarios and then comparing them with each other, results were obtained.


1-    Adamowski, J. and Sun, K., 2010. Development of a coupled wavelet transform and neural network method for flow forecasting of non-perennial rivers in semi-arid watersheds. Journal of Hydrology, 390, pp. 85-91.
2-    Box, G.E.P., and Jenkins, G.M., 1994. time series analysis. forecasting and control third edition, Holden-day.
3-    Choobin, B., Malekian, A., Sajedi, H. and Rahmati, A., 2014. Predicting the phreatic zone level using time series and Fuzzy Inference - Adaptive Neural System. Journal of Soil and Water Research, 45(1), pp. 19-28. (In Persian).
4-    Fathi, P., Mohammadi, Y. and Homaee, M., 2010. Smart modeling of time series of monthly inflow to the Vahdat dam, Sanandaj. Journal of Soil and Water (Agricultural sciences and industry), 23(1), pp. 220-209. (In Persian).
5-    Grossmann, A. and Morlet, J., 1984. Decomposition of hardy function into square integrable wavelets of constant shape. SIMA J Math Anal, 5, pp. 723-736.
6-    Jayawardena, A.w. and Tsang, F.L.L., 2004. Rainfall predication by wavelet decomposition. In 2nd Asia Pacific Association of Hydrology and Water Resources Conference, Singapore, volume II, pp. 11-19.
7-    Kisi, O., 2008. Stream flow forecasting using neuro-wavelet technique. Hydrological Processes, 22, pp. 4142–4152.
8-    Komasi, M., 2008. Modeling of rainfall - runoff using the hybrid wavelet - neural network model, Master's thesis; University of Tabriz. (In Persian).
9-    Miner, N. E., 1998. An introduction to wavelet theory and analysis. Intelligent Systems and Robotics Division Sandia International Laboratories. P. O. Box 5800 Albuquerque, pp. 87185-1008.
10- Mireh, S. and Amin Ghafari, M., 2009.  Presenting new methods to predict time series by using wavelets. Journal of Iran Statistical Research, 6(1), pp. 73-91. (In Persian).
11- Nakken, M., 1999. Wavelet analysis of rainfall–runoff variability isolating climatic from anthropogenic patterns. Environmental Modelling & Software, 14(4), pp. 283-295.
12- Nikmanesh, M.R. and Taleb Bidakhti, N., 2013. Comparison the ability of wavelet theory and time series in modeling of monthly rainfall in SaadatShahr and Arsanjan regions in Fars province. Natural Geography Quarterly, Issue 16. (In Persian).
13- Nourani, V., Alami, M.T. and Aminfar, M.H., 2009. A combined neural-wavelet model for prediction of Ligvanchai watershed precipitation. Engineering Applications of Artificial Intelligence, 22(3), pp. 466-472.
14- Polikar, R., 1996. Fundamental concepts and an overview of the wavelet theory. Second Edition, Rowan University, College of Engineering Web Servers, Glassboro. NJ. 08028.
15- Rajai, T. and Ebrahimi, H., 2013. "Modeling the monthly fluctuations in groundwater by wavelet transform and dynamic neural network"; Journal of water and irrigation, Volume 4, No. 1, 2015, pp. 73-87(In Persian).
16- Riad, S., Mania, J., Bouchaou, L. and Najjar, Y.  2004. "Rainfall-runoff model usingan artificial neural network approach." Mathematical and Computer Modelling 40(7–8): 839-846.
17- Rostami, M., Fakherifard, A., Ghorbani, M.A., Darbandi, S. and DinPajooh, Y., 2012. "Study the application of wavelet analysis to predict river flow rate", Journal of Irrigation Engineering and Science, Volume 35, Issue 2, 2013, pp. 73-81(In Persian).
18- Solgi, A., Nourani, V.  and Pourhaghi, A., 2014. Forecasting Daily Precipitation Using Hybrid Model of Wavelet-Artificial Neural Network and Comparison with Adaptive Neuro Fuzzy Inference System (Case Study: Verayneh Station, Nahavand). Advances in Civil Engineering.
19- Toofani, P., Mosaedi, A. and Fakherifard, A., 2011. Forecasting the rainfall using wavelet theory. Journal of Soil and Water (Agricultural sciences and industry), 25(5), pp. 1226-1217.(In Persian).
20- Wang, W and Ding, S., 2003. Wavelet network model and its application to the predication of hydrology. Nature and Science, 1, pp. 67-71
21- Young, R.K., 1993. Wavelet Theory and Its Applications. Kluwer Academic Publishers, Boston.
Volume 41, Issue 4
January 2019
Pages 1-16
  • Receive Date: 20 October 2015
  • Revise Date: 30 November 2016
  • Accept Date: 03 December 2016
  • Publish Date: 22 December 2018