Abstract
Prediction of pH is an important issue in managing water quality in surface waters (e.g., rivers, lakes) as well as drinking water. The capacity of artificial neural network (ANN), wavelet-artificial neural network (WANN), traditional multiple linear regression (MLR), and wavelet-multiple linear regression (WMLR) models to predict daily pH levels (1, 2, and 3 days ahead) at the Chattahoochee River gauging station (near Atlanta, GA, USA) was assessed. In the proposed WANN model, the original time series of pH and discharge (Q) were decomposed (after being split into training and testing series) into several sub-series by the the à trous (AT) wavelet transform algorithm. The wavelet coefficients were summed to obtain useful input time series for the ANN model to then develop the WANN model for pH prediction. The redundant à trous algorithm was used for data decomposition. Model implementation indicated the values of 1-day-ahead pH predicted by the WANN model closely matched the observed values (with a coefficient of determination, R2 = 0.956; Root Mean Square Error, RMSE = 0.019; and Mean Absolute Error, MAE = 0.015). It is therefore possible that the WANN model’s accuracy can be attributed to its better predictive ability (due to the use of the AT) to remove the noise caused by pH shifts (e.g., acid precipitation). Peak pH values predicted by the WANN model were also closer to observed values compared to the other machine learning models.
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Abdollahi, S., Raeisi, J., Khalilianpour, M., Ahmadi, F., & Kisi, O. (2017). Daily mean streamflow prediction in perennial and non-perennial rivers using four data driven techniques. Water Resour Manage. https://doi.org/10.1007/s11269-017-1782-7.
Adamowski, J., & Chan, H. F. (2011). A wavelet neural network conjunction model for groundwater level forecasting. Journal of Hydrology, 407(1–4), 28–40. https://doi.org/10.1016/j.jhydrol.2011.06.013.
Adamowski, J., & Karapataki, C. (2010). Comparison of multivariate regression and artificial neural networks for peak urban water-demand forecasting: evaluation of different ANN learning algorithms. J. Hydrol. Eng., 15, 729–743.
Alhadeff, S.J., Landers, M.N., McCallum, B.E. (2010). USGS Water-Data Report GA-99-1: Surface-Water Data, Georgia, Water Year 1999. Active and Discontinued Stations. Chattahoochee River near Fairburn. Available at http://pubs.usgs.gov/wdr/wdr-ga-99-1/summary/sp02337170.pdf (seen 5 April 2016).
Altun, H., Bilgil, A., & Fidan, B. C. (2007). Treatment of multi-dimensional data to enhance neural network estimators in regression problems. Expert Systems with Applications, 32(2), 599–605. https://doi.org/10.1016/j.eswa.2006.01.054.
Barzegar, R., Fijani, E., Asghari-Moghaddam, A., & Tziritis, E. (2017). Forecasting of groundwater level fluctuations using ensemble hybrid multi-wavelet neural network-based models. Science of the Total Environment, 599–600, 20–31.
Çamdevýrena, H., Demýra, N., Kanika, A., & Keskýn, S. (2005). Use of principal component scores in multiple linear regression models for prediction of Chlorophyll-a in reservoirs. Journal of Ecological Modelling, 181(4), 581–589. https://doi.org/10.1016/j.ecolmodel.2004.06.043.
Chau, K. W., Wu, C. L., & Li, Y. S. (2005). Comparison of several flood forecasting models in Yangtze River. Journal of Hydrologic Engineering, 10(6), 485–491. https://doi.org/10.1061/(ASCE)1084-0699(2005)10:6(485).
Civelekoglu, G., Yigit, N. O., Diamadopoulos, E., & Kitis, M. (2007). Prediction of bromate formation using multi-linear regression and artificial neural networks. Journal of Science and Engineering, 29(5), 353–362. https://doi.org/10.1080/01919510701549327.
Daliakopoulos, I. N., Coulibalya, P., & Tsani, I. K. (2005). Groundwater level forecasting using artificial neural network. Journal of Hydrology, 309(1–4), 229–240.
Daubechies, I. (1990). The wavelet transform, time–frequency localization and signal analysis. IEEE Transactions on Information Theory, 36(5), 961–1005.
Doglioni, A., & Simeone, V. (2014). Geomorphometric analysis based on discrete wavelet transform. Environmental Earth Sciences, 71(7), 3095–3108.
Ebrahimi, H., & Rajaee, T. (2017). Simulation of groundwater level variations using wavelet combined with neural network, linear regression and support vector machine. Global and Planetary Change, 148, 181–191. https://doi.org/10.1080/02626667.2010.508871.
Faruk, D. Ö. (2009). A hybrid neural network and ARIMA model for water quality time series prediction. Journal of Engineering Applications of Artificial Intelligence, 23(4), 586–594. https://doi.org/10.1016/j.engappai.2009.09.015.
Hagan, M. T., & Menhaj, M. B. (1994). Training feed forward networks with the Marquardt algorithm. IEEE Transactions on Neural Networks, 5(6), 989–993. https://doi.org/10.1109/72.329697.
Karakaya, N., Evrendilek, F., Gungor, K., & Onal, D. (2013). Predicting diel, diurnal and nocturnal dynamics of dissolved oxygen and chlorophyll-a using regression models and neural networks. Clean – Soil, Air, Water, 41(9), 872–877. https://doi.org/10.1002/clen.201200683.
Karran, D., Morin, E., & Adamowski, J. (2014). Multi-step streamflow forecasting using data-driven non-linear methods in contrasting climate regimes. Journal of Hydroinformatics, 16(3), 671–689.
Karunanithi, N., Grenney, W. J., Whitley, D., & Bovee, K. (1994). Neural networks for river flow prediction. J Comp Civ Eng ASCE, 8(2), 201–220.
Khani, S., & Rajaee, T. (2016). Modeling of dissolved oxygen concentration and its hysteresis behavior in rivers using wavelet transform-based hybrid models. Clean-Soil, Air, Water. https://doi.org/10.1002/clen.201500395.
Kişi, Ö. (2009). Neural networks and wavelet conjunction model for intermittent streamflow forecasting. Journal of Hydrological Engineering, 14(8), 773–782. https://doi.org/10.1061/(ASCE)HE.1943-5584.0000053.
Kisi, O., & Parmar, K. S. (2016). Application of least square support vector machine and multivariate adaptive regression spline models in long term prediction of river water pollution. Journal of Hydrology, 534, 104–112.
Kişi, Ö. (2010). Daily suspended sediment estimation using neuro-wavelet models. International Journal of Earth Sciences, 99(6), 1471–1482. https://doi.org/10.1007/s00531-009-0460-2.
Labat, D., Ababou, R., & Mangin, A. (2000). Rainfall–runoff relation for karstic spring. Part II: continuous wavelet and discrete orthogonal multi resolution analyses. Journal of Hydrology, 238(3–4), 149–178. https://doi.org/10.1016/S0022-1694(00)00322-X.
Liu, Q.-J., Shi, Z.-H., Fang, N.-F., Zhu, H.-D., & Ai, L. (2013). Modeling the daily suspended sediment concentration in a hyper concentrated river on the Loess Plateau, China, using the Wavelet–ANN approach. Geomorphology, 186, 181–190. https://doi.org/10.1016/j.geomorph.2013.01.012.
Mallat S. (1999). A wavelet tour of signal processing, 2nd ed. Academic Press, San Diego, CA. Available at http://www.sciencedirect.com/science/book/9780124666061 (seen 6 April 2016).
Masters T. (1993). Practical neural network recipes in C++. Academic Press: San Diego, CA. Available at http://www.sciencedirect.com/science/book/9780080514338 (seen 6 April 2006).
Mashford, J., Rahilly, M., Lane, B., Marney, D., & Burn, S. (2014). Edge detection in pipe mages using classification of Haar wavelet transforms. Applied Artificial Intelligence, 28(7), 675–689. https://doi.org/10.1080/08839514.2014.927689.
Moatar, F., Fessant, F., & Poirel, A. (1999). pH modelling by neural networks. Application of control and validation data series in the Middle Loire River. Journal of Ecological Modelling, 120(2–3), 141–156. https://doi.org/10.1016/S0304-3800(99)00098-8.
Muralidharan, V., & Sugumaran, V. (2013). Selection of discrete wavelets for fault diagnosis of monoblock centrifugal pump using the j48 algorithm. Journal of Applied Artificial Intelligence., 27(1), 1–19. https://doi.org/10.1080/08839514.2012.721694.
Nourani, V., & Kalantari, O. (2010). Integrated artificial neural network for spatiotemporal modeling of rainfall–runoff–sediment processes. Environmental Engineering Science, 27(5), 411–422. https://doi.org/10.1089/ees.2009.0353.
Nourani, V., Hosseini, A., Adamowski, J., & Kisi, O. (2014). Applications of hybrid wavelet–Artificial Intelligence models in hydrology: a review. Journal of Hydrology, 514, 358–377. https://doi.org/10.1016/j.jhydrol.2014.03.057.
Olyaie, E., Zare-Abyaneh, H., & Danandeh-Mehr, A. (2017). A comparative analysis among computational intelligence techniques for dissolved oxygen prediction in Delaware River. Geoscience Frontiers, 8, 517–527.
Partal, T., & Cigizoglu, H. K. (2008). Estimation and forecasting of the daily suspended sediment data using wavelet-neural networks. Journal of Hydrology, 358(3–4), 317–331. https://doi.org/10.1016/j.jhydrol.2008.06.013.
Petchinathan, G., Valarmathi, K., Devaraj, D., & Radhakrishnan, T. K. (2013). Local linear model tree and Neuro-Fuzzy system for modelling and control of an experimental pH neutralization process. Brazilian Journal of Chemical Engineering, 31(2), 483–495. https://doi.org/10.1590/0104-6632.20140312s00002287.
Rajaee, T., & Boroumand, A. (2015). Forecasting of chlorophyll-a concentrations in South San Francisco Bay using five different models. Applied Ocean Research., 53, 208–217.
Rajaee, T., & Shahabi, A. (2016). Evaluation of wavelet-GEP and wavelet-ANN hybrid models for prediction of total nitrogen concentration in coastal marine waters. Arabian Journal of Geosciences doi, 9, 176. https://doi.org/10.1007/s12517-015-2220-x.
Rakhshandehroo, G. H., Akbari, H., Afshari-Igder, M., & Ostadzadeh, E. (2018). Long-term groundwater-level forecasting in shallow and deep wells using wavelet neural networks trained by an improved harmony search algorithm. J Hydrol. Eng., 23(2), 04017058.
Ravansalar, M., & Rajaee, T. (2015). Evaluation of wavelet performance via an ANN-based electrical conductivity prediction model. Journal of Environmental Monitoring and Assessment., 187(6), 366. https://doi.org/10.1007/s10661-015-4590-7.
Ravansalar, M., Rajaee, T., & Ergil, M. (2015). Prediction of dissolved oxygen in River Calder by noise elimination time series using wavelet transform. Journal of Experimental and Theoretical Artificial Intelligence., 28(4), 689–706.
Ravansalar, M., Rajaee, T., & Zounemat-Kermani, M. (2016). A wavelet-linear genetic programming model for sodium (Na+) concentration forecasting in rivers. Journal of Hydrology., 537, 398–407.
Ravansalar, M., Rajaee, T., & Kisi, O. (2017). Wavelet-linear genetic programming: a new approach for modeling monthly streamflow. Journal of Hydrology., 549, 461–475.
Samadianfard, S., Sattari, M. T., Kisi, O., & Kazemi, H. (2014). Determining flow friction factor in irrigation pipes using data mining and artificial intelligence approaches. Applied Artificial Intelligence, 28(8), 793–813. https://doi.org/10.1080/08839514.2014.952923.
Saoud, L., Rahmoune, F., Tourtchine, V., & Baddari, K. (2011). Modeling pH neutralization process using fuzzy dynamic neural units approaches. International Journal of Computer Applications, 28(4), 22–29. https://doi.org/10.5120/3375-4666.
Singh, K., Basant, A., Malik, A., & Jain, G. (2009). Artificial neural network modeling of the river water quality—a case study. Ecological Modelling, 220(6), 888–895. https://doi.org/10.1016/j.ecolmodel.2009.01.004.
Sreekanth, P. D., Sreedevi, P. D., Ahmed, S., & Geethanjali, N. (2011). Comparison of FFNN and ANFIS models for estimating groundwater level. Environmental Earth Sciences, 62(6), 1301–1310. https://doi.org/10.1007/s12665-010-0617-0.
Snedecor G.W, Cochran W.G. (1981) Statistical methods (seventh ed.), Iowa State University Press, Iowa.
Tan, Y., & Cauwenberghe, A. (1999). Neural-network-based d-step-ahead predictors for nonlinear systems with time delay. Engineering Applications of Artificial Intelligence, 12(1), 21–25. https://doi.org/10.1016/S0952-1976(98)00043-8.
United States Geologic Survey (USGS). (2016). USGS surface-water daily data for the Nation. Available at http://waterdata.usgs.gov/nwis/dv? (seen 5 April 2016).
Verma, A. K., & Singh, T. N. (2013). Prediction of water quality from simple field parameters. Environmental Earth Sciences, 69(3), 821–829. https://doi.org/10.1007/s12665-012-1967-6.
Wang, Z., Wu, Q., & Zhang, Y. (2011). Confined groundwater pollution mechanism and vulnerability assessment in oilfields, North China. Environmental Earth Sciences, 64(6), 1547–1553. https://doi.org/10.1007/s12665-010-0697-x.
Zossid, A. M., Elias, A. G., & de Campra, P. F. (2006). Discrete wavelet analysis to assess long-term trends in geomagnetic activity. Physics and Chemistry of the Earth, Parts A/B/C., 31, 77–80.
Zounemat-Kermani, M., Kisi, O., & Rajaee, T. (2013). Performance of radial basis and LM-feed forward artificial neural networks for predicting daily watershed runoff. Applied Soft Computing, 13(12), 4633–4644.
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This research was partially funded by an NSERC Discovery and Accelerate Grant held by Jan Adamowski.
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Rajaee, T., Ravansalar, M., Adamowski, J.F. et al. A New Approach to Predict Daily pH in Rivers Based on the “à trous” Redundant Wavelet Transform Algorithm. Water Air Soil Pollut 229, 85 (2018). https://doi.org/10.1007/s11270-018-3715-3
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DOI: https://doi.org/10.1007/s11270-018-3715-3