Time-series analysis of monthly rainfall data for the Mahanadi River Basin, India

Abstract

Time series analysis has two goals, modeling random mechanisms and predicting future series using historical data. In the present work, a uni-variate time series autoregressive integrated moving average (ARIMA) model has been developed for (a) simulating and forecasting mean rainfall, obtained using Theissen weights; over the Mahanadi River Basin in India, and (b) simulating and forecasting mean rainfall at 38 rain-gauge stations in district towns across the basin. For the analysis, monthly rainfall data of each district town for the years 1901-2002 (102 years) were used. Theissen weights were obtained over the basin and mean monthly rainfall was estimated. The trend and seasonality observed in ACF and PACF plots of rainfall data were removed using power transformation (α=0.5) and first order seasonal differencing prior to the development of the ARIMA model. Interestingly, the ARIMA model (1,0,0)(0,1,1) 12 developed here was found to be most suitable for simulating and forecasting mean rainfall over the Mahanadi River Basin and for all 38 district town rain-gauge stations, separately. The Akaike Information Criterion (AIC), goodness of fit (Chi-square), R 2 (coefficient of determination), MSE (mean square error) and MAE (mea absolute error) were used to test the validity and applicability of the developed ARIMA model at different stages. This model is considered appropriate to forecast the monthly rainfall for the upcoming 12 years in each district town to assist decision makers and policy makers establish priorities for water demand, storage, distribution, and disaster management.