​Rainfall Probability Distribution and Forecasting Monthly Rainfall of Navsari using ARIMA Model

Abstract

Background: Reliable rainfall forecast could be helpful to farmers as major decisions regarding selection of crops and sowing time are based on the rainfall. The univariate time series ARIMA model requires only past data for model formulation and to simulate stochastic processes. The current study was aimed to obtain the probability distribution of monthly rainfall using the method of moments and to forecast rainfall using the ARIMA model. Methods: The method of moments was used to determine the parameters of distributions and the chi-square test was used as a goodness of fit test to obtain the best fit distribution for monthly rainfall of Navsari, Gujarat utilizing 36 years of rainfall data. Auto regressive moving average (ARIMA) model, popular owing to its simplicity and ability to simulate various stochastic processes was used in the study. Result: It was revealed that the Weibull distribution was the best fit distribution for June and September, whereas Gumbel was the best fit distribution for July. For simulating monthly rainfall, the seasonal ARIMA model (0,0,1) (0,1,1)12 was found to be the appropriate model based on its performance. The model had the least root mean square value and also the residuals were found to have no correlation.