Time Series Models Adoptable for Forecasting Nile Floods and Ethiopian Rainfalls

Abstract

Long-term rainfall forecasting is used in making economic and agricultural decisions in many countries. It may also be a tool in minimizing the devastation resulting from recurrent droughts. To be able to forecast the total annual rainfall or the levels of seasonal floods, a class of models has first been chosen. The model parameters have then been estimated with an appropriate parameter estimation algorithm. Finally, diagnostic tests have been performed to verify the adequacy of the model. These are the general principles of system identification, which is the most crucial part of the forecasting procedure. In this paper several sets of data have been studied using different statistical procedures. The examined data include a historical 835-year record representing the levels of the seasonal Nile floods in Cairo, Egypt, during the period A.D. 622?1457. These readings were originally carried out by the Arabsto a great degree of accuracy in order to be used in estimating yearly taxes or Zacat (islamic duties). The observations also comprise recent total annual rainfall data over Addis Ababa (Ethiopia) (1907?1984), the total annual discharges of Ethiopian rivers (including the river Sobat discharges at Hillet Doleib, Blue Nile discharge at Roseris, river Dinder, river Rahar, and river Atbara), equatorial lake plateau supply as contributed at Aswan during the period 1912?1982, and the total annual discharges at Aswan during the period 1871?1982. Periodograms have been used to uncover possible peridodicities. Trends of rainfall and discharges of some rivers of east and central Africa have been also estimated. Using the first half of the available record, two autoregressive integrated moving average (ARIMA) time series models have been identified, one for the levels of the seasonal Nile floods in Cairo, the second to model the annual rainfall over Ethiopia. The time series models have been applied in 1-year-ahead forecasting to the other hall of the available record and give fairly promising results, thus indicating the adequacy of the fitted models.