Abstract
Rainfall is a principal element of the hydrological cycle and its variability is important from both the scientific as well as practical point of view. Wavelet regression (WR) technique is proposed and developed to analyze and predict the rainfall forecast in this study. The WR model is improved combining two methods, discrete wavelet transform and linear regression model. This study uses rainfall data from 21 stations in Assam, India over 102 years from 1901 to 2002. The calibration and validation performance of the models is evaluated with appropriate statistical methods. The root mean square errors (RMSE), N-S index, and correlation coefficient (R) statistics were used for evaluating the accuracy of the WR models. The accuracy of the WR models was then compared with those of the artificial neural networks (ANN) models. The results of monthly rainfall series modeling indicate that the performances of wavelet regression models are found to be more accurate than the ANN models.
Similar content being viewed by others
References
Ajmera TK, Goyal MK (2012) Development of stage discharge rating curve using model tree and neural networks: an application to peachtree creek in Atlanta. Expert Systems With Applications, Elsevier Ltd. 39(5):5702–5710
Antonios A, Constantine EV (2003) Wavelet exploratory analysis of the FTSE ALL SHARE index. In proceedings of the 2nd WSEAS international conference on non-linear analysis. Non-linear systems and Chaos, Athens.
ASCE Task Committee on Application of Artificial Neural Networks in Hydrology (2000a) Artificial neural networks in hydrology-I: Preliminary concepts. J Hydrol Engrg 5(2):115–123
ASCE Task Committee on Application of Artificial Neural Networks in Hydrology (2000b) Artificial neural networks in hydrology-II: Hydrologic applications. J Hydrol Engrg 5(2):124–137
Baratta D, Cicioni G, Masulli F, Studer L (2003) Application of an ensemble technique based on singular spectrum analysis to daily rainfall forecasting. Neural Networks 16:375–387
Burney SMA, Jilani TA, Ardil C (2005) Levenberg-Marquardt Algorithm for Karachi Stock Exchange Share Rates Forecasting. World Acad Sci Eng Technol 3:171–176
Chien-Ming C (2011) Wavelet-based multi-scale entropy analysis of complex rainfall time series. Entropy 13:241–253. doi:10.3390/e13010241
Chien-ming C (2013) Enhanced accuracy of rainfall–runoff modeling with wavelet transform. J Hydroinf 15(2):392–404
Chou CM, Wang RY (2002) On-line estimation of unit hydrographs using the wavelet-based LMS algorithm. Sci J Hydrol 47(5):721–738
Coulibaly P, Burn HD (2004) Wavelet analysis of variability in annual Canadian streamflows. Water Resour Res 40, W03105
Fernando DAK, Shamseldin AY (2009) Investigation of the internal functioning of the radial basis function neural network river flow forecasting models. J Hydrol Eng 14(3):286–292. doi:10.1061/(ASCE)1084-0699(2009)14:3(286)
FSI, 2009. State of Forest Report, 2009. Forest Survey of India (FSI), Ministry of Environment and Forests, Government of India
Grossman A, Morlet J (1984) Decomposition of hardy functions into square integrable wavelets of constant shape. SIAM J Math Anal 15:723–736
Hagan MT, Menhaj MB (1994) Training feed forward networks with the Marquardt algorithm. IEEE Trans Neural Netw 6:861–867
Hsu K-L, Gupta HV, Sorooshian S (1995) Artificial neural network modeling of the rainfall-runoff process. Water Resour Res 31(10):2517–2530
Jain A, Srinivasulu S (2004) Development of effective and efficient rainfall-runoff models using integration of deterministic, real-coded genetic algorithms, and artificial neural network techniques. Water Resour Res 40(4):W04302 doi:10.1029/2003WR002355
Jain SK, Kumar V (2012) Trend analysis of rainfall and temperature data for India. Curr Sci 102(1):37–49
Jain SK, Das A, Srivastava DK (1999) Application of ANN for reservoir inflow prediction and operation. J Water Resour Plan Manag ASCE 125(5):263–271
Kisi O (2009) Wavelet regression model as an alternative to neural networks for monthly streamflow forecasting. Hydrol Process 23:3583–3597
Kisi O (2011) Wavelet regression model as an alternative to neural networks for river stage forecasting. Water Resour Manag 25(2):579–600
Labat D, Ababou R, Mangin A (2000) Rainfall–runoff relations for karstic springs. Part II. Continuous wavelet and discrete orthogonal multiresolution analyses. J Hydrol 238(3–4):149–178
Labat D, Ronchail J, Guyot JL (2005) Recent advances in wavelet analyses. Part 2—Amazon, Parana, Orinoco and Congo discharges time scale variability. J Hydrol 314(1–4):289–311
Lindsay RW, Percival DB, Rothrock DA (1996) The discrete wavelet transform and the scale analysis of the surface properties of sea ice. IEEE Trans Geosci Remote Sens 34:771–787
Mahanta et al. (2003) Assam Human Development Report 2003, available at http://hdr.undp.org/en/reports/nationalreports/asiathepacific/india/name,3268,en.html. Accessed 20 July 2013
Maier HR, Dandy GC (2000) Neural networks for the prediction and forecasting of water resources variables: a review of modelling issues and applications. Environ Model Softw 15:101–124
Mallat SG (1989) A theory for multi resolution signal decomposition: the wavelet representation. IEEE T Pattern Anal Mach Intell 11(7):674–693
Minns AW, Hall MJ (1996) Artificial neural networks as rainfall runoff models. Hydrol Sci J 41(3):399–418
Partal T, Kucuk M (2006) Long-term trend analysis using discrete wavelet components of annual precipitations measurements in Marmara region. Phys Chem Earth 31:1189–1200, Turkey
Quiroz R, Yarlequé C, Posadas A, Mares V, Immerzee Walter W (2011) Improving daily rainfall estimation from NDVI using a wavelet transform. Environ Model Softw 26:201–209
Raman H, Chandramauli V (1996) Deriving a general operating policy for reservoirs using neural network. J Water Resour Plan Manag ASCE 122(5):342–347
Rosso OA, Figliola A, Blanco S, Jacovkis PM (2004) Signal separation with almost periodic components: a wavelets based method. Rev Mex Fis 50(1):179–186
Rumelhart DE, Hinton E, Williams J (1986) Learning internal representation by error propagation, Parallel Distributed Processing, Vol. 1. MIT Press, Cambridge, pp 318–362
Sang Y (2013) Improved wavelet modeling framework for hydrologic time series forecasting. Water Resour Manag 27(8):2807–2821
Santos Celso AG, Freire Paula KMM (2012) Analysis of Precipitation Time Series of Urban Centers of Northeastern Brazil using Wavelet Transform. World Acad Sci Eng Technol 67:845–850
Senthil Kumar AR, Ojha CSP, Goyal MK, Singh RD, Swamee PK, (2012) Modelling of suspended sediment concentration at Kasol in India using ANN, fuzzy logic and decision tree algorithms. ASCE's J Hydrol Eng 17(3):394–404
Senthil Kumar AR, Sudheer KP, Jain SK, Agarwal PK (2005) Rainfall-runoff modelling using artificial neural networks: comparison of network types. Hydrol Process 19:1277–1291
Srinivasulu S, Jain A (2009) River flow prediction using an integrated approach. J Hydrol Engrg, ASCE 14(1):75–83
Sudheer KP, Gosain AK, Ramasastri KS (2002) A data-driven algorithm for constructing artificial neural network rainfall-runoff models. Hydrol Process 16:1325–1330
Tantanee S, Patamatammakul S, Oki T, Sriboonlue V, Prempree T, (2005) Coupled wavelet-autoregressive model for annual rainfall prediction. J Environ Hydrol 13
Thirumalaiah K, Deo MC (1998) River stage forecasting using artificial neural networks. J Hydrol Engrg 3(1):26–32
Torrence C, Compo GP (1998) A practical guide to wavelet analysis. Bull Am Meteorol Soc 79(1):61–78. doi:10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2
Vos NJ, Rientjes THM (2008) Multiobjective training of artificial neural networks for rainfall-runoff modelling. Water Resour Res 44(W08434):1–15
Wang W, Ding J (2003) Wavelet network model and its application to the prediction of the hydrology. Nature and Science 1(1):67–71
Xingang D, Ping W, Jifan C (2003) Multiscale characteristics of the rainy season rainfall and interdecadal decaying of summer monsoon in North China. Chin Sci Bull 48:2730–2734
Zhou HC, Peng Y, Liang G-H (2008) The research of monthly discharge predictor–corrector model based on wavelet decomposition. Water Resour Manag 22(2):217–227
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Goyal, M.K. Monthly rainfall prediction using wavelet regression and neural network: an analysis of 1901–2002 data, Assam, India. Theor Appl Climatol 118, 25–34 (2014). https://doi.org/10.1007/s00704-013-1029-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00704-013-1029-3