Monthly Rainfall Prediction Using Wavelet Neural Network Analysis

R. Venkata Ramana 0 B. Krishna 0 S. R. Kumar 0 N. G. Pandey 0 N. G. Pandey e-mail: 0 0 B. Krishna Deltaic Regional Center, National Institute of Hydrology , Kakinada 533 003, Andhra Pradesh, India Rainfall is one of the most significant parameters in a hydrological model. Several models have been developed to analyze and predict the rainfall forecast. In recent years, wavelet techniques have been widely applied to various water resources research because of their timefrequency representation. In this paper an attempt has been made to find an alternative method for rainfall prediction by combining the wavelet technique with Artificial Neural Network (ANN). The wavelet and ANN models have been applied to monthly rainfall data of Darjeeling rain gauge station. The calibration and validation performance of the models is evaluated with appropriate statistical methods. The results of monthly rainfall series modeling indicate that the performances of wavelet neural network models are more effective than the ANN models. Rainfall is a complex atmospheric process, which is space and time dependent and it is not easy to predict. Due to the apparent random characteristics of rainfall series, they are often described by a stochastic process (Chinchorkar et al. 2012). For water resources planning purposes, a long-term rainfall series is required in hydrological and simulation models (Tantanee et al. 2005). There have been many attempts to find the most appropriate method for rainfall prediction for example, coupling physical, marine, and meteorological or satellite data with a forecasting model, or even - applying several techniques such as the artificial neural network or fuzzy logic as a forecasting approach (Hsu et al. 1995; Dawson and Wilby 2001; Hettiarachchi et al. 2005). In recent years, several numerical weather forecasts have been proposed for weather prediction but most of these models are limited to short period forecasts. This paper introduces a new approach for prediction of rainfall series. Several time series models have been proposed for modeling monthly rainfall series (Bhakar et al. 2006) and annual rainfall series such as the autoregressive model (AR) (Yevjevich 1972), the fractional Guassian noise model (Matalas and Wallis 1971), autoregressive moving-average models (ARMA) (Carlson et al. 1970) and the disaggregation multivariate model (Valencia and Schaake 1973). Moustris et al. (2011) examine the possibility of long term precipitation forecast (four consecutive months) by the application of ANNs, using long monthly precipitation time series of four meteorological stations in Greece. In the past decade, wavelet theory has been introduced to signal processing analysis. In recent years, the wavelet transform has been successfully applied to wave data analysis and other ocean engineering applications (Massel 2001; Teisseire et al. 2002; Huang 2004). The time-frequency character of long-term climatic data is investigated using the continuous wavelet transform technique (Lau and Weng 1995; Torrence and Compo 1997; Mallat 1998) and wavelet analysis of wind wave measurements obtained from a coastal observation tower (Huang 2004). Chou (2011) used wavelet denoising method in linear perturbation models (LPMs) and simple linear models (SLMs) for rainfall and runoff time series data. Wang and Li (2011) used a new wavelet transform method for developing the synthetic generation of daily stream flow sequences. Wu et al. (2004) used a combination of neural networks and wavelet methods to predict underground water levels. Dynamical Recurrent Neural Network (DRNN) on each resolution scale of the sunspot time series resulting from the wavelet decomposed series with the Temporal Recurrent Back propagation (TRBP) algorithm (Aussem and Murtagh 1997). There are some appreciable studies of wavelet transform based neural network models (Wang and Ding 2003; Anctil and Tape 2004; Cannas et al. 2006; Kisi 2008; Wang et al. 2009). The wavelet transform is also integrated with multiple linear regression (Kucuk and Agiraliolu 2006; Kisi 2009, 2010) and support vector machine approach (Kisi and Cimen 2011). Adamowski and Sun (2010) compared the relative performance of the coupled wavelet-neural network models (WAANN) and regular artificial neural networks (ANN) for flow forecasting at lead times of 1 and 3 days for two different non-perennial rivers in semiarid watersheds of Cyprus. Kisi (2011) investigated the performance of the wavelet regression (WR) technique in daily river stage forecasting and determined the WR model was improved combining two methods, discrete wavelet transform and a linear regression model. Sang (2013), developed a method for discrete wavelet decomposition and an improved wavelet modeling framework, WMF for short was proposed for hydrologic time series forecasting. By coupling the wavelet method with the traditional AR model, the Wavelet-Autoregressive model (WARM) is developed for annual rainfall prediction (Tantanee et al. 2005). Partal and Kisi (2007) used a conjunction model (wavelet-neuro-fuzzy) to forecast the Turkey daily precipitation. The observed daily precipitations are decomposed to some sub series by using Discrete Wavelet Transform (DWT) and then appropriate sub series are used as inputs to neuro-fuzzy models for forecasting of daily precipitations. Each of these studies showed that different black box models trained or calibrated with decomposed data resulted in higher accuracy than the single models that were calibrated with an undecomposed and noisy time series. In this paper, a Wavelet Neural Network (WNN) model, which is the combination of wavelet analysis and ANN, has been proposed for rainfall forecast Darjeeling station, India. 2 Wavelet Analysis The wavelet analysis is an advanced tool in signal processing that has attracted much attention since its theoretical development (Grossmann and Morlet 1984). Its use has increased rapidly in communications, image processing and optical engineering applications as an alternative to the Fourier transform in preserving local, non-periodic and multiscaled phenomena. The difference between wavelets and Fourier transforms is that wavelets can provide the exact locality of any changes in the dynamical patterns of the sequence, whereas the Fourier transforms concentrate mainly on their frequency. Moreover, Fourier transform assume infinite length signals, whereas wavelet transforms can be applied to any kind and any size of time series, even when these sequences are not homogeneously sampled in time (Antonios and Constantine 2003). In general, wavelet transforms can be used to explore, denoise and smoothen time series which aid in forecasting and other empirical analysis. Wavelet analysis is the breaking up of a signal into shifted and scaled versions of the original (or mother) wavelet. In wavelet analysis, the use of a fully scalable modulated window solves the signal-cutting problem. The window (...truncated)