Time Series Modeling of River Flow Using Wavelet Neural Networks

References

[1] H. Raman and N. Sunil Kumar, “Multivariate Modeling of Water Resources Time Series Using Artificial Neural Networks,” Journal of Hydrological Sciences, Vol. 40, No. 4, 1995, pp. 145-163.
doi:10.1080/02626669509491401

[2] H. R. Maier and G. C. Dandy, “Determining Inputs for Neural Network Models of Multivariate Time Series,” Microcomputers in Civil Engineering, Vol. 12, 1997, pp. 353-368.

[3] M. C. Deo and K. Thirumalaiah, “Real Time Forecasting Using Neural Networks: Artificial Neural Networks in Hydrology,” In: R. S. Govindaraju and A. Ramachandra Rao, Kluwer Academic Publishers, Dordrecht, 2000, pp. 53-71.

[4] B. Fernandez and J. D. Salas, “Periodic Gamma Autoregressive Processes for Operational Hydrology,” Water Resources Research, Vol. 22, No. 10, 1986, pp. 1385- 1396. doi:10.1029/WR022i010p01385

[5] S. L. S. Jacoby, “A Mathematical Model for Non-Linear Hydrologic Systems,” Journal of Geophysics Research, Vol. 71, No. 20, 1966, pp. 4811-4824.

[6] J. Amorocho and A. Brandstetter, “A Critique of Current Methods of Hydrologic Systems Investigations,” Eos Transactions of AGU, Vol. 45, 1971, pp. 307-321.

[7] S. Ikeda, M. Ochiai and Y. Sawaragi, “Sequential GMDH Algorithm and Its Applications to River Flow Prediction,” IEEE Transactions of System Management and Cy- bernetics, Vol. 6, No. 7, 1976, pp. 473-479.
doi:10.1109/TSMC.1976.4309532

[8] ASCE Task Committee, “Artificial Neural Networks in hydrology-I: Preliminary Concepts,” Journal of Hydrolo- gic Engineering, Vol. 5, No. 2, 2000(a), pp. 115-123.

[9] ASCE Task Committee, “Artificial Neural Networks in Hydrology-II: Hydrologic Applications,” Journal of Hydrologic Engineering, Vol. 5, No. 2, 2000(b), pp. 124- 137.

[10] D. W. Dawson and R. Wilby, “Hydrological Modeling Using Artificial Neural Networks,” Progress in Physical Geograpgy, Vol. 25, No. 1, 2001, pp. 80-108.

[11] S. Birikundavy, R. Labib, H. T. Trung and J. Rousselle, “Performance of Neural Networks in Daily Stream Flow Forecasting,” Journal of Hydrologic Engineering, Vol. 7, No. 5, 2002, pp. 392-398.
doi:10.1061/(ASCE)1084-0699(2002)7:5(392)

[12] P. Hettiarachchi, M. J. Hall and A. W. Minns, “The Extrapolation of Artificial Neural Networks for the Modeling of Rainfall-Runoff Relationships,” Journal of Hydroinformatics, Vol. 7, No. 4, 2005, pp. 291-296.

[13] E. J. Coppola, M. Poulton, E. Charles, J. Dustman and F. Szidarovszky, “Application of Artificial Neural Networks to Complex Groundwater Problems,” Journal of Natural Resources Research, Vol. 12, No. 4, 2003(a), pp. 303- 320.

[14] E. J. Coppola, F. Szidarovszky, M. Poulton and E. Charles, “Artificial Neural Network Approach for Predicting Transient Water Levels in a Multilayered Groundwater System under Variable State, Pumping and Climate Conditions,” Journal of Hydrologic Engineering, Vol. 8, No. 6, 2003(b), pp. 348-359.

[15] P. C. Nayak, Y. R. Satyaji Rao and K. P. Sudheer, “Gro- undwater Level Forecasting in a Shallow Aquifer Using Artificial Neural Network Approach,” Water Resources Management, Vol. 20, No. 1, 2006, pp. 77-90.
doi:10.1007/s11269-006-4007-z

[16] B. Krishna, Y. R. Satyaji Rao and T. Vijaya, “Modeling Groundwater Levels in an Urban Coastal Aquifer Using Artificial Neural Networks,” Hydrological Processes, Vol. 22, No. 12, 2008, pp. 1180-1188.
doi:10.1002/hyp.6686

[17] D. Wang and J. Ding, “Wavelet Network Model and Its Application to the Prediction of Hydrology,” Nature and Science, Vol. 1, No. 1, 2003, pp. 67-71.

[18] S. R. Massel, “Wavelet Analysis for Processing of Ocean Surface Wave Records,” Ocean Engineering, Vol. 28, 2001, pp. 957-987. doi:10.1016/S0029-8018(00)00044-5

[19] M. C. Huang, “Wave Parameters and Functions in Wa- velet Analysis,” Ocean Engineering, Vol. 31, No. 1, 2004, pp. 111-125. doi:10.1016/S0029-8018(03)00047-7

[20] L. C. Smith, D. Turcotte and B. L. Isacks, “Stream Flow Characterization and Feature Detection Using a Discrete Wavelet Transform,” Hydrological Processes, Vol. 12, No. 2, 1998, pp. 233-249.
doi:10.1002/(SICI)1099-1085(199802)12:2<233::AID-HYP573>3.0.CO;2-3

[21] D. Labat, R. Ababou and A. Mangin, “Rainfall-Runoff Relations for Karstic Springs: Part II. Continuous Wavelet and Discrete Orthogonal Multiresolution Analyses,” Journal of Hydrology, Vol. 238, No. 3-4, 2000, pp. 149- 178. doi:10.1016/S0022-1694(00)00322-X

[22] P. Saco and P. Kumar, “Coherent Modes in Multiscale Variability of Stream Flow over the United States,” Water Resources Research, Vol. 36, No. 4, 2000, pp. 1049- 1067.doi:10.1029/1999WR900345

[23] P. Kumar and E. Foufoula-Georgiou, “A Multicomponent Decomposition of Spatial Rainfall Fields: Segregation of Large- and Small-Scale Features Using Wavelet Transforms,” Water Resources Research, Vol. 29, No. 8, 1993, pp. 2515-2532. doi:10.1029/93WR00548

[24] P. Kumar, “Role of Coherent Structure in the Stochastic Dynamic Variability of Precipitation,” Journal of Geophysical Research, Vol. 101, 1996, pp. 393-404.
doi:10.1029/96JD01839

[25] K. Fraedrich, J. Jiang, F.-W. Gerstengarbe and P. C. Werner, “Multiscale Detection of Abrupt Climate Cha- nges: Application to the River Nile Flood,” International Journal of Climatology, Vol. 17, No. 12, 1997, pp. 1301- 1315.doi:10.1002/(SICI)1097-0088(199710)17:12<1301::AID-JOC196>3.0.CO;2-W

[26] R. H. Compagnucci, S. A. Blanco, M. A. Filiola and P. M. Jacovkis, “Variability in Subtropical Andean Argentinian Atuel River: A Wavelet Approach,” Environmetrics, Vol. 11, No. 3, 2000, pp. 251-269.
doi:10.1002/(SICI)1099-095X(200005/06)11:3<251::AID-ENV405>3.0.CO;2-0

[27] S. Tantanee, S. Patamatammakul, T. Oki, V. Sriboonlue and T. Prempree, “Coupled Wavelet-Autoregressive Mo- del for Annual Rainfall Prediction,” Journal of Environmental Hydrology, Vol. 13, No. 18, 2005, pp. 1-8.

[28] P. Coulibaly, “Wavelet Analysis of Variability in Annual Canadian Stream Flows,” Water Resources Research, Vol. 40, 2004.

[29] F. Xiao, X. Gao, C. Cao and J. Zhang, “Short-Term Prediction on Parameter-Varying Systems by Multiwavelets Neural Network,” Lecture Notes in Computer Science, S- pringer-Verlag, Vol. 3630, No. 3611, 2005, pp. 139- 146.

[30] D. J. Wu, J. Wang and Y. Teng, “Prediction of Underground Water Levels Using Wavelet Decompositions and Transforms,” Journal of Hydro-Engineering, Vol. 5, 2004, pp. 34-39.

[31] A. Aussem and F. Murtagh, “Combining Neural Network Forecasts on Wavelet Transformed Series,” Connection Science, Vol. 9, No. 1, 1997, pp. 113-121.
doi:10.1080/095400997116766

[32] T. Partal and O. Kisi, “Wavelet and Neuro-Fuzzy Conjunction Model for Precipitation Forecasting,” Journal of Hydrology, Vol. 342, No. 1-2, 2007, pp. 199-212.
doi:10.1016/j.jhydrol.2007.05.026

[33] A. Grossmann and J. Morlet, “Decomposition of Hardy Functions into Square Integrable Wavelets of Constant shape,” SIAM Journal on Mathematical Analysis, Vol. 15, No. 4, 1984, pp. 723-736. doi:10.1137/0515056

[34] A. Antonios and E. V. Constantine, “Wavelet Exploratory Analysis of the FTSE ALL SHARE Index,” Preprint submitted to Economics Letters University of Durham, Durham, 2003.

[35] D. Benaouda, F. Murtagh, J. L. Starck and O. Renaud, “Wavelet-Based Nonlinear Multiscale Decomposition M- odel for Electricity Load Forecasting,” Neurocomputing, Vol. 70, No. 1-3, 2006, pp. 139-154.
doi:10.1016/j.neucom.2006.04.005

[36] W. McCulloch and W. Pitts, “A Logical Calculus of the Ideas Immanent in Nervous Activity,” Bulletin of Mathematical Biophysics, Vol. 5, 1943, pp. 115-133.
doi:10.1007/BF02478259

[37] D. E. Rumelhart, G. E. Hinton and R. J. Williams, “Lear- ning Representations by Back-Propagating Errors,” Nature, Vol. 323, No. 9, 1986, pp. 533-536.
doi:10.1038/323533a0

[38] M. T. Hagan and M. B. Menhaj, “Training Feed forward Networks with Marquardt Algorithm,” IEEE Transactions on Neural Networks, Vol. 5, No. 6, 1994, pp. 989- 993. doi:10.1109/72.329697

[39] P. Coulibaly, F. Anctil, P. Rasmussen and B. Bobee, “A Recurrent Neural Networks Approach Using Indices of Low-Frequency Climatic Variability to Forecast Regional Annual Runoff,” Hydrological Processes, Vol. 14, No. 15, 2000, pp. 2755-2777.
doi:10.1002/1099-1085(20001030)14:15<2755::AID-HYP90>3.0.CO;2-9