摘要
For many years planning and management of water resources involved modeling and simulation of temporally sequenced and stochastic hydrologic events. Rainfall process is one of such hydrologic events which calls for time series analysis to better understand interesting features contained in it. Many statistics-based methods are available to simulate and predict such a kind of time series. Autoregressive (AR), moving average (MA), autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) models are among those methods. In this study a search was conducted to identify and examine a capable stochastic model for annual rainfall series (over the period 1954-2015) of Debre Markos town, Ethiopia. For the historical series, normality and stationarity tests were conducted to check if the time series was from a normally distributed and stationary process. Shapiro-Wilk (SW), Anderson-Darling (AD) and Kolmogorov-Smirnov (KS) tests were among the normality tests conducted whereas, Augmented Dickey-Fuller (ADF), Phillips-Perron (PP) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests were among the stationarity tests. Based on the test results, logarithmic transformation and first order differencing were performed to bring the original series to a normal and stationary series. Results of model fitting showed that three models namely, AR (2), MA (1) and ARMA (2,1) were capable in describing the annual rainfall series. A diagnostic check was performed on model residuals and ARMA (2,1) was found to be the best model among the candidates. Furthermore, three information criteria: Akaike Information Criterion (AIC), the corrected Akaike Information Criterion (AICc) and Bayesian Information Criterion (BIC) were used to select the best model. In this regard, too, the least information discrepancy between the underlying process and the fitted model was obtained from ARMA (2,1) model. Hence, this model was considered as a better representative of the annual rainfall values and was used to predict five years ahead values. The mean absolute percentage error (MAPE) of the prediction was found to be less than 10%. Thus, ARMA (2,1) model could be used for forecasting and simulation of annual rainfall for planning, management and design of water resources systems in Debre Markos town.
For many years planning and management of water resources involved modeling and simulation of temporally sequenced and stochastic hydrologic events. Rainfall process is one of such hydrologic events which calls for time series analysis to better understand interesting features contained in it. Many statistics-based methods are available to simulate and predict such a kind of time series. Autoregressive (AR), moving average (MA), autoregressive moving average (ARMA) and autoregressive integrated moving average (ARIMA) models are among those methods. In this study a search was conducted to identify and examine a capable stochastic model for annual rainfall series (over the period 1954-2015) of Debre Markos town, Ethiopia. For the historical series, normality and stationarity tests were conducted to check if the time series was from a normally distributed and stationary process. Shapiro-Wilk (SW), Anderson-Darling (AD) and Kolmogorov-Smirnov (KS) tests were among the normality tests conducted whereas, Augmented Dickey-Fuller (ADF), Phillips-Perron (PP) and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests were among the stationarity tests. Based on the test results, logarithmic transformation and first order differencing were performed to bring the original series to a normal and stationary series. Results of model fitting showed that three models namely, AR (2), MA (1) and ARMA (2,1) were capable in describing the annual rainfall series. A diagnostic check was performed on model residuals and ARMA (2,1) was found to be the best model among the candidates. Furthermore, three information criteria: Akaike Information Criterion (AIC), the corrected Akaike Information Criterion (AICc) and Bayesian Information Criterion (BIC) were used to select the best model. In this regard, too, the least information discrepancy between the underlying process and the fitted model was obtained from ARMA (2,1) model. Hence, this model was considered as a better representative of the annual rainfall values and was used to predict five years ahead values. The mean absolute percentage error (MAPE) of the prediction was found to be less than 10%. Thus, ARMA (2,1) model could be used for forecasting and simulation of annual rainfall for planning, management and design of water resources systems in Debre Markos town.
