Stochastic ARIMA model for annual rainfall and maximum temperature forecasting over Tordzie watershed in Ghana

Abstract

AbstractThe forecast of rainfall and temperature is a difficult task due to their variability in time and space and also the inability to access all the parameters influencing rainfall of a region or locality. Their forecast is of relevance to agriculture and watershed management, which significantly contribute to the economy. Rainfall prediction requires mathematical modelling and simulation because of its extremely irregular and complex nature. Autoregressive integrated moving average (ARIMA) model was used to analyse annual rainfall and maximum temperature over Tordzie watershed and the forecast. Autocorrelation function (ACF) and partial autocorrelation function (PACF) were used to identify the models by aid of visual inspection. Stationarity tests were conducted using the augmented Dickey–Fuller (ADF), Mann–Kendall (MK) and Kwiatkowski–Phillips–Schmidt–Shin (KPSS) tests respectively. The chosen models were evaluated and validated using the Akaike information criterion corrected (AICC) and also Schwartz Bayesian criteria (SBC). The diagnostic analysis of the models comprised of the independence, normality, homoscedascity, P–P and Q–Q plots of the residuals respectively. The best ARIMA model for rainfall for Kpetoe and Tordzinu were (3, 0, 3) and (3, 1, 3) with AICC values of 190.07 and 178.23. That of maximum temperature for Kpetoe and Tordzinu were (3, 1, 3) and (3, 1, 3) and the corresponding AICC values of 23.81 and 36.10. The models efficiency was checked using sum of square error (SSE), mean square error (MSE), mean absolute percent error (MAPE) and root mean square error (RMSE) respectively. The results of the various analysis indicated that the models were adequate and can aid future water planning projections.