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Stochastic Generation and Forecasting Of Weekly Rainfall for Rahuri Region

P. G. Popale* and S.D. Gorantiwar

One of the major problems in water resources management is the advanced knowledge of future sequences of rainfall or rainfall forecast. With the effect of rainfall on water resources as a foregone conclusion, more accurate prediction of rainfall would enable more efficient of water resources. Regions depending on agro-based economy could benefit tremendously from accurate rainfall predictions. This study, is therefore, particularly focused on rainfall forecasting and generation since a forecasting could provide better information for optimal management of a resource over a substantial period of time. There are several techniques of rainfall forecasting that include autoregressive (AR) and moving average (MA) models of different orders, ARMA, ARIMA, Thomas Feiring etc. These are also called as stochastic or time series models. Autoregressive integrated moving average (ARIMA) models have been found to be more useful for forecasting and generation of hydrological events. Therefore, in this study ARIMA models of different orders have been used for generation and forecasting rainfall in advance. The present study attempts to develop the ARIMA model for forecasting and generation of weekly rainfall. Data were collected from National Data Centre of India Meteorological Department, Pune. Rainfall data series of 31 years (1982 – 2012) of Rahuri region of Ahmednagar district were used for developing ARIMA models. The series of 30 years i.e. from 1982 to 2011 was used for the development of the models and series of 2012 was used for testing the validity of the models. ARIMA models of different orders were selected based on observing autocorrelation functions (ACF) and partial autocorrelation functions (PACF) of the historical rainfall series. The parameters of selected model were obtained with the help of maximum likelihood method. The diagnostic checking of the selected models was then performed with the help of three test (standard error of parameters, ACF and PACF of residuals and Akaike Information Criteria) to know the adequacy of the selected models. The ARIMA models that passed the adequacy test were selected for forecasting. The weekly rainfall values 2012 year were forecasted with the help of these selected models and compared with the actual weekly rainfall values of the year 2012 by root mean square error (RMSE). The ARIMA (1,1,1) (1,0,1) 52 gave the lowest value of RMSE and hence is considered as the best model for generation and forecasting of weekly rainfall values.