Time series analysis for the dam water levels and rainfall for Albasini Dam in Limpopo Province, South Africa

Abstract

Changes in precipitation characteristics and trends can cause extreme events such as drought and floods to occur more frequently in river basins around the world. Also, the impact of these changes on dam infrastructure is very high. Therefore, continuous research and quantitative assessment of the data surrounding dams is highly recommended. This study focused on the time series analysis of Albasini Dam in Limpopo Province using the Autoregressive Integrated Moving Average (ARIMA) model. This was done to assess the hydrological hazard and dam safety risks by using historic and future seasonal trends of the rainfall and dam levels. ARIMA is one of the most widely used models for time series forecasting. It is particularly effective for univariate time series data that exhibit patterns of autocorrelation, trends, and non-stationarity. The monthly historic data for dam water levels and rainfall from 1997 to 2024 for the study area were obtained from the Department of Water and Sanitation. In applying the ARIMA model to the datasets, the time series plot for the dam water level and rainfall from 1997 to 2024 was done. Afterwards, the time series went through the differencing and both rainfall and dam water level indicated a correct pattern and constant mean. The Ljung Box test was also conducted to test the presence of the unit root. Standard deviation for the rainfall was 116.20 mm and dam water level was 2.70 m, indicating the sample mean being low and accurate. Lag 1 and 2 from the Auto Correlation Function and Partial Auto Correlation Function correlation analysis resulted in less than 5% significant from 24 lag transformation. The Mean Absolute Percentage Error of 0.72, RMSE of 0.15, MAE of 0.11 indicated a good model fit for rainfall and dam water level. The rainfall indicates a higher value of the residual ACF and PACF by showing no significant spikes. The optimum models were used to forecast rainfall and water dam levels for 5, 10, and 15 years at the case study. One major observation was that the predicted April 2040 data show a worrisome dam water level of 19.60 m, which is the highest recording when compared to April 2000, which was 19.53 m. The prediction provides the output value that needs preparation in terms of dam safety for overflooding of downstream villages and aquatic life. The ARIMA models demonstrate robust performance for prolonged seasonal time series and time series chart that shows the historic trend of the dam level and the rainfall activity showing similar trend for the forecasted years (2029).