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Titre : Time series modelling of water evaporation from selected dams in the Limpopo Province of South Africa

Auteur : Phasha, Mmanyaku Goitsemang

Université de soutenance : University of Limpopo

Grade : Master of Science (MS) Statistics 2022

Résumé
Water is a precious natural resource and one of the most vital substance for sustainability of life . The increase in water evaporation is a major prob lem where factors such as high temperature and minimum rainfall are the contributing factors. The aim of the study was to perform time series mod elling of water evaporation from the selected dams in the Limpopo province South Africa. A daily evaporation time series data was used in the study with variables such as temperature and rainfall. Daily water evaporation rate time series data was differenced to make the data series stationary and Dickey-Fuller test was used to test the stationarity of the data series. The Autoregressive Conditional Heteroskasticity (ARCH) and Generalized Au toregressive Conditional Heteroskasticity (GARCH) model was performed on the water evaporation time series data from the selected dams. Vec tor Autoregression (VAR) was used to determine the relationship between the variables evaporation, rainfall and temperature. Identification of time series models was done using the autoregressive integrated moving average (ARIMA). The best ARIMA models were selected based on the autocor relation function (ACF) and partial autocorrelation function (PACF), and the smallest value of Bayseian Information (BIC). The best models selected for each dam are : Mokolo dam, ARIMA (1, 1, 2) model ; Ga-Rantho dam, ARIMA (1, 1, 2) model ; Leeukraal DeHoop dam, ARIMA (1, 1, 1) model and Luphephe dam, ARIMA (2, 1, 3) model. The correlation coefficient, coefficient of determinant (R2 ) and root mean square (RMSE) were used to determine the performance of the model. The water evaporation time series data from the selected dams was forecasted using the best selected ARIMA models from the selected dams and then predicted for the next 3 years, where the results showed a positive constant water evaporation rate.

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