MSc (Physics) / Department of Physics

MSc (Physics) / Department of Physics

MSc (Statistics) / Department of Statistics / This study discusses an application of partially linear additive quantile regression models in predicting medium-term global solar irradiance using data from Tellerie radiometric station in South Africa for the period August 2009 to April 2010. Variables are selected using a least absolute shrinkage and selection operator (Lasso) via hierarchical interactions and the parameters of the developed models are estimated using the Barrodale and Roberts's algorithm. The best models are selected based on the Akaike information criterion (AIC), Bayesian information criterion (BIC), adjusted R squared (AdjR2) and generalised cross validation (GCV). The accuracy of the forecasts is evaluated using mean absolute error (MAE) and root mean square errors (RMSE). To improve the accuracy of forecasts, a convex forecast combination algorithm where the average loss su ered by the models is based on the pinball loss function is used. A second forecast combination method which is quantile regression averaging (QRA) is also used. The best set of forecasts is selected based on the prediction interval coverage probability (PICP), prediction interval normalised average width (PINAW) and prediction interval normalised average deviation (PINAD). The results show that QRA is the best model since it produces robust prediction intervals than other models. The percentage improvement is calculated and the results demonstrate that QRA model over GAM with interactions yields a small improvement whereas QRA over a convex forecast combination model yields a higher percentage improvement. A major contribution of this dissertation is the inclusion of a non-linear trend variable and the extension of forecast combination models to include the QRA. / NRF

PhD (Physics) / Department of Physics / The knowledge of solar radiation in this dispensation is crucial. The lack of grid lines in the remote rural areas of South Africa necessitates the use of solar energy as an alternative energy resource. Solar radiation data is one of the primary factors considered for the installation of renewable energy devices and they are very useful for solar technology designers and engineers. In some developing countries, estimation of solar radiation becomes a challenge due to the lack of weather data. This scenario is also applicable to South Africa (SA) wherein there are limited weather stations and hence there is a dire need of estimating the global solar radiation data for all climatic regions. Using a five year global solar radiation (𝐻) and bright sunshine (𝑆) data from the Agricultural Research Council (ARC) and South African Weather Service (SAWS) in SA, linear Angstrom – Prescott solar empirical model was used to determine regression coefficients. MATLAB interface was used whereby the linear regression plots were drawn. Annual empirical coefficients of 22 stations were determined and later the provincial values. The range of the regression coefficients, a and b were 0.216 – 0.301 and 0.381 – 0.512 respectively. The 2006 estimated global solar radiation per station in a province calculated from the modified models were compared with the observed and statistically tested. The root mean square errors were less than 0.600 MJm−2day−1 while the correlation relation ranged from 0.782 – 0.986 MJm−2day−1. The results showed the regression coefficients performed well in terms of prediction accuracy. / NRF