International Journal of Mechanical and Production Engineering Research and Development (IJMPERD) ISSN (P): 2249–6890; ISSN (E): 2249–8001 Vol. 10, Issue 3, Jun 2020, 7281-7290 © TJPR Pvt. Ltd. CONVENTIONAL MODELING FOR FORECASTING ANNUAL RAINFALL IN CHENNAI CITY M. NIRMALA Department of Mathematics, Sathyabama Institute of Science and Technology, Tamilnadu, India ABSTRACT This research work deals with the forecasting of annual rainfall of Chennai city, India using conventional and computational models. Chennai is one of the most populous metropolitan city in India the knowledge of extreme precipitation in advance helps the disaster management for the control of floods and droughts. For this purpose, the annual rainfall of Chennai is modeled by filtering the white noise and then the smoothened data series were fed into the conventional Auto Regressive Integrated Moving Average (ARIMA) model for forecasting. The experimental result shows that the conventional ARIMA model gives better accuracy. The error measure indicates the proposed model’s performance accuracy. KEYWORDS: Rainfall, Forecasting, ARIMA & Error measure Original Article Received: May 25, 2020; Accepted: Jun 27, 2020; Published: Aug 07, 2020; Paper Id.: IJMPERDJUN2020688 1. INTRODUCTİON Rainfall prediction is one of the most important and challenging task carried over by meteorologists all over the world. Rainfall prediction is also useful for disaster management in tackling the extreme precipitations. There are many forecasters doing lot of research to obtain more accuracy in the model they construct. There are many factors which affects rainfall prediction such as temperature, humidity, wind speed, pressure, dew point etc. and hence prediction becomes more complicated for them since the real life data are nonlinear in nature. Nowadays Artificial Neural Network algorithms are applied to time series analysis. 2. RELATED WORK Artificial Neural Network plays a major role in learning and capturing the characteristics of any nonlinear natural phenomena. MoniraSumi et al [9] made an attempt for deriving forecasting models for average daily and monthly rainfall of the Fukuoka city in Japan using the artificial neural network, multivariate adaptive regression splines, the k-nearest neighbor and radial basis support vector regression together with preprocessing techniques like moving average method and principal component analysis. The K-nearest neighbor, artificial neural network, and extreme learning machine were applied for the seasonal forecasting of summer monsoon (June-September) and post- monsoon (October-December) rainfall for the Kerala state of India by Yejnaseni Dash et al and proved that extreme machine learning performed better when compared to the other two models [12]. FhiraNhita et al constructed a forecasting system with evolving neural network algorithm to forecast the monthly rainfall of Bandung Regency in Indonesia [4] and were successful by arriving a forecast accuracy of 70%. Duong Tran Anh et al [3] combined two pre processing methods seasonal decomposition and Discrete Wavelet Transform to decompose the monthly rainfall series in Vietnam and constructed the prediction models based on Artificial Neural Network and Seasonal Artificial www.tjprc.org SCOPUS Indexed Journal [email protected] 7282 M. Nirmala Neural Network. Kavitha Rani et al developed Artificial Neural Network based rainfall prediction model with teaching learning optimization algorithm to improve the accuracy of the model [7]. A feed forward neural network with back propagation and Levenberg-Marquardt algorithms based prediction models were constructed by Neelam Mishra et al for forecasting one-month and two-month ahead rainfall of Northern India [10]. In this study, a forecasting model for annual rainfall in Chennai is constructed using the conventional ARIMA model. 3. STUDY AREA AND MATERİALS Chennai is the capital city of Tamil Nadu state in India. Its geographic location is 13°04'N latitude and 80°17'E longitude [5]. According to the 2011 Indian census, it is the sixth-most populous city and fourth-most populous urban agglomeration in India.Chennai has a tropical wet and dry climate.. The hottest part of the year is late May to early June with maximum temperatures around 35 °C – 40 °C (95–104 °F). The coolest part of the year is January, with minimum temperatures around 19 °C –25 °C (66–77 °F). The lowest recorded temperature was 13.9 °C (57.0 °F) on 11th December 1895 and 29th January 1905. The highest recorded temperature was 45 °C (113 °F) on 31 May 2003. The average annual rainfall is about 140 cm (55 in). The city gets most of its seasonal rainfall from the north–east monsoon winds, from mid–October to mid–December. Cyclones in the Bay of Bengal sometimes hit the city. The highest annual rainfall recorded is 257 cm (101 in) in 2005. Prevailing winds in Chennai are usually southwesterly between April and October and north-easterly during the rest of the year. Figure 1: Geographical Location, Boundaries and Water bodies of Chennai Chennai has relied on the annual rains to replenish water reservoirs, as no major rivers flow through the area. Chennai has a water table at 2 metres for 60 percent of the year. Two major rivers flow through Chennai, the CooumRiver through thecentre and the Adyar River to the south. A third river, the Kortalaiyar, travels through the northern fringes of the city before draining into the Bay of Bengal, at Ennore. All the three rivers are heavily polluted by the industrial wastages and hence the water is not suitable for the use of public. As Chennai is one among the metropolitan city in India, it depends entirely on rainfall to fulfill the daily needs of water for its people. Due to extreme precipitation during December 2015, the people in Chennai suffered for many days without food and drinking water. Many lost their lives, their belongings during the flood. Hence the knowledge of flood or drought is necessary for disaster management to take necessary precautionary actions to manage both. This research article develops a prediction model based on ARIMA for predicting the annual rainfall in Chennai. For this purpose, a dataset containing the monthly rainfall of chennai, from 1901 to 2017 were obtained from India Meteorological Department, Pune, India and India Water Portal. Impact Factor (JCC): 8.8746 SCOPUS Indexed Journal NAAS Rating: 3.11 Conventional Modeling for Forecasting Annual Rainfall in Chennai City 7283 4. METHODOLOGY 4.1 AutoCorrelation and Partial AutoCorrelation Functions Let z1, z2, z3,…,zn denote observations made at equidistant time intervals. A stochastic process is a statistical phenomenon that evolves in time according to probabilistic laws. The process is stationary if the properties of the time series are unaffected by a change of time origin. The covariance between zt and its value zt+k separated by k intervals of time which under the stationarity assumption must be the same for all t is called the autocovariance at lag k and is defined as k covzt , ztk Ezt ztk (1) The autocorrelation function (ACF) and the partial autocorrelation function (PACF) explain the internal structure of the analysed series. The ACF, k at lag k of the time series zt is the linear correlation coefficient between zt and zt+k is E[(zt )(ztk )] (2) k 2 2 E[(zt ) (ztk ) ] The PACF is the linear correlation between zt and zt+k by controlling the possible effects of linear relationships among values at intermediate lags. 4.2 Auto Regressive Integrated Moving Average (ARIMA) Model The ARIMA models are a combination of autoregressive models and moving average models. The autoregressive models AR(p) base their predictions of the values of a variable xt, on a number p of past values of the same variable number of autoregressive delays xt−1,xt−2,. ,xt−p. They include a random disturbance et. The moving average models MA(q) generate predictions of a variable xt based on a number q of past disturbances of the same variable prediction errors of past values et−1,et−2,...,et−q. The combination of the auto regressive and moving average models AR(p) and MA(q) generates more flexible models called ARMA(p,q) models. A simple regression model can be represented as Yt = b0 + b1 Yt –1 + b2 Yt –2 + …+ bpYt –p + et (3) where Yt is the forecast variable, Yt –1,…, Yt –p are explanatory variables and et is the error term. The name autoregression is used to denote the above equation due to time-lagged values of the explanatory variable. The moving average model uses the past errors as explanatory variables. A simple moving average model is represented as follows: Yt = b0 + b1 et –1 + b2 et –2 + …+ bq et –q + et (6) The autoregressive model and the moving average model are efficiently coupled to form a general and useful class of time series model called ARMA. This class of models can be extended as ARIMA model for non-stationary time series by differencing the data series. The real time data are non stationary data which are unpredictable and cannot be modeled or forecasted. The non stationary data needs to be transformed into stationary data to obtain consistent and reliable results. The Box-Jenkins methodology requires the time series to be analyzed is stationary. The ARIMA model of order (p,d,q) or an ARIMA process is defined as d (B) zt (B)et (4) where Zt denoted the observed value at time t, B represents the backward shift operator the autoregressive www.tjprc.org SCOPUS Indexed Journal [email protected] 7284 M. Nirmala operator (B) is of order p, d is the order of difference taken and the moving average operator (B) is of order q. (B)and (B) have the following representations: 2 p (B) 11B 2 B ...p B (5) 2 q (6) (B) 11B 2B ... qB For the stationary process, the ARIMA model is (B)zt (B)et (7) The various steps involved in building an ARIMA model are iterative identification, estimation, diagnosis and forecasting.