Predicting clear-sky global horizontal irradiance at eight locations in South Africa using four models


  • Evans Zhandire



Clear-sky irradiation, Linke turbidity index, ESRA and Ineichen-Perez models


Solar radiation under clear-sky conditions provides information about the maximum possible magnitude of the solar resource available at a location of interest. This information is useful for determining the limits of solar energy use in applications such as thermal and electrical energy generation. Measurements of solar irradiance to provide this information are limited by the associated cost. It is therefore of great interest and importance to develop models that generate these data in lieu of measurements. This study focused on four such models: Ineichen-Perez (I-P), European Solar Radiation Atlas model (ESRA), multilayer perceptron neural network (MLPNN) and radial basis function neural network (RBFNN) models. These models were calibrated and tested using solar irradiance data measured at eight different locations in South Africa. The I-P model showed the best performance, recording relative root mean square errors of less than 2% across all hours, months and locations. The performances of the MLPNN and RBFNN were poor when averaged over all stations, but tended to show performance similar to that of the I-P model for some of the stations. The ESRA model showed performance that was in between that of the Artificial Neural Networks and that of the I-P model.


Download data is not yet available.


Metrics Loading ...


Twidell, J. and Weir, T. 2006. Renewable energy resources, second edition, Taylor and Francis.

Duffie, J. and Beckman, W. 2013. Solar Engineer-ing of Thermal Processes, fourth edition, John Wiley and sons.

Dai, Q. and Fang, X. 2014. A simple model to pre-dict solar radiation under clear sky conditions. Ad-vances in Space Research, 53: 1239-1245.

Badescu, V., Gueymard, C. A., Cheval, S., Oprea, C., Baciu, M., Dumitrescu, A., Iacobescu, F., Milos, I. and Rada, C. 2013. Accuracy analysis for fifty-four clear-sky solar radiation models using routine hourly global irradiance measurements in Roma-nia. Renewable Energy, 55: 85-103. 10.1016/j.renene.2012.11.037.

Reno, M. J., Hansen, C. W. and Stein, J. S. 2012. Global horizontal irradiance clear sky models: Im-plementation and analysis. SANDIA report SAND2012-2389:

Gueymard, C. A. 2012. Clear-sky irradiance predic-tions for solar resource mapping and large-scale applications: Improved validation methodology and detailed performance analysis of 18 broad-band radiative models. Solar Energy, 86: 2145–2169.

Badescu, V., Gueymard, C. A., Cheval, S., Oprea, C., Baciu, M., Dumitrescu, A., Iacobescu, F., Milos, I. and Rada, C. 2012. Computing global and dif-fuse solar hourly irradiation on clear sky. Review and testing of 54 models. Renewable and Sustain-able Energy Reviews, 16: 1636-1656.

Annear, R. L. and Wells, S. A. 2007. A comparison of five models for estimating clear‐sky solar radia-tion. Water resources research, 43: 1-15. doi:10.1029/2006WR005055.

Ineichen, P. 2006. Comparison of eight clear sky broadband models against 16 independent data banks. Solar Energy, 80: 468-478.

Ineichen, P. and Perez, R. 2002. A new airmass independent formulation for the Linke turbidity co-efficient. Solar Energy, 73: 151-157.

Rigollier, C., Bauer, O. and Wald, L. 2000. On the clear sky model of the ESRA — European Solar Radiation Atlas — with respect to the heliosat method. Solar Energy, 68: 33-48.

Linke, F. 1922. Transmissions-koeffizient und Trübungsfaktor. Beitr. Phys. Fr. Atmos, 10: 91-103.

Kasten, F. 1996. The linke turbidity factor based on improved values of the integral Rayleigh optical thickness. Solar Energy, 56: 239-244.

Ångström, A. 1929. On the atmospheric transmis-sion of sun radiation and on dust in the air. Geo-grafiska Annaler, 11: 156-166. 10.2307/519399.

Louche, A., Maurel, M., Simonnot, G., Peri, G. and Iqbal, M. 1987. Determination of Ångström's tur-bidity coefficient from direct total solar irradiance measurements. Solar Energy, 38: 89-96.

Gueymard, C. A. Aerosol turbidity derivation from broadband irradiance measurements: methodolog-ical advances and uncertainty analysis. Solar 2013 Conference. Baltimore, MD, 2013.

Haykin, S. 2009. Neural networks and learning machines, Third edition, Pearson Upper Saddle River, NJ, USA.

Paoli, C., Voyant, C., Muselli, M. and Nivet, M.-L. 2010. Forecasting of preprocessed daily solar radi-ation time series using neural networks. Solar En-ergy, 84: 2146-2160. j.solener.2010.08.011.

Voyant, C., Notton, G., Kalogirou, S., Nivet, M.-L., Paoli, C., Motte, F. and Fouilloy, A. 2017. Machine learning methods for solar radiation forecasting: A review. Renewable Energy, 105: 569-582.

Lauret, P., Voyant, C., Soubdhan, T., David, M. and Poggi, P. 2015. A benchmarking of machine learn-ing techniques for solar radiation forecasting in an insular context. Solar Energy, 112: 446-457.

Kashyap, Y., Bansal, A. and Sao, A. K. 2015. Solar radiation forecasting with multiple parameters neu-ral networks. Renewable and Sustainable Energy Reviews, 49: 825-835. j.rser.2015.04.077.

Božnar, M. Z., Grašič, B., Oliveira, A. P. d., Soares, J. and Mlakar, P. 2017. Spatially transferable re-gional model for half-hourly values of diffuse solar radiation for general sky conditions based on per-ceptron artificial neural networks. Renewable Ener-gy, 103: 794-810. j.renene.2016.11.013.

Hussain, S. and AlAlili, A. 2016. Online Sequential Learning of Neural Networks in Solar Radiation Modeling Using Hybrid Bayesian Hierarchical Ap-proach. Journal of Solar Energy Engineering, 13

: 061012-061012-10. 1.4034907.

Chen, J.-L., Li, G.-S., Xiao, B.-B., Wen, Z.-F., Lv, M.-Q., Chen, C.-D., Jiang, Y., Wang, X.-X. and Wu, S.-J. 2015. Assessing the transferability of support vector machine model for estimation of global solar radiation from air temperature. Energy Conversion and Management, 89: 318-329.

Lauret, P., Boland, J. and Ridley, B. 2013. Bayesi-an statistical analysis applied to solar radiation modelling. Renewable Energy, 49: 124-127.

Koca, A., Oztop, H. F., Varol, Y. and Koca, G. O. 2011. Estimation of solar radiation using artificial neural networks with different input parameters for Mediterranean region of Anatolia in Turkey. Expert Systems with Applications, 38: 8756-8762.

Brooks, M. J., du Clou, S., van Niekerk, W. L., Gauché, P., Leonard, C., Mouzouris, M. J., Meyer, R., van der Westhuizen, N., van Dyk, E. E. and Vor-ster, F. J. 2015. SAURAN: A new resource for solar radiometric data in Southern Africa. Journal of En-ergy in Southern Africa, 26: 2-10.

Engerer, N. A. and Mills, F. P. 2015. Validating nine clear sky

radiation models in Australia. Solar Energy, 120: 9-24.

Kasten, F. and Young, A. T. 1989. Revised optical air mass tables and approximation formula. Ap-plied optics, 28: 4735-4738. AO.28.004735.

Bishop, C. M. 1995. Neural Networks for Pattern Recognition, Clarendon Press.

Nabney, I. T. 2002. NETLAB: Algorithms for pat-tern recognition., Great Britain, Springer.

Sethabane, T. and Winkler, H. Atmospheric turbidi-ty over Soweto. SAIP 2011, 2011. South Afica In-stitute of Physics, 525-530.

Walther, B. A. and Moore, J. L. 2005. The concepts of bias, precision and accuracy, and their use in testing the performance of species richness estima-tors, with a literature review of estimator perfor-mance. Ecography, 28: 815-829.




How to Cite

Zhandire, E. (2017). Predicting clear-sky global horizontal irradiance at eight locations in South Africa using four models. Journal of Energy in Southern Africa, 28(4).