A review of regression models employed for predicting diffuse solar radiation in North-Western Africa

Julie C. Ogbulezie, Ogri James Ushie, Samuel Chukwujindu Nwokolo


The knowledge of diffuse solar radiation (Hd) is of almost importance for determining the gross primary productivity, net ecosystem, exchange of carbon dioxide, light use efficiency and changing colour of the sky. However, routine measurement of Hd is not available in most locations in North-Western Africa. During the past 36 years in order to predict Hd in the horizontal surface on hourly, daily and monthly mean basis, several regression models have been developed for numerous locations in North-Western Africa. As a result, several input parameters have been utilized and different functional forms applied. The regression models so far utilized were classified into six main categories and presented based on the input parameters applied. The models were further reclassified into numerous main groups and finally represented according to their developing year. In general, 188 regression models, 33 functional forms and 20 groups were reported in literature for predicting Hd in North-Western Africa. The regression and soft computing models developed within North-Western Africa and across the globe were examined in order to determine the best technique of prediction. The result revealed that soft computing models are more suitable for predicting Hd in North-Western Africa and across the globe. 

Citation: Ogbulezie, J., Ushie, O., and Nwokolo, S. (2017). A review of regression models employed for predicting diffuse solar radiation in North-Western Africa. Trends in Renewable Energy, 3(2), 160-206. DOI: 10.17737/tre.2017.3.2.0042


Diffuse solar radiation; Regression models; Classification; Functional forms; North-Western Africa

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International Energy Agency (IEA) Report (Report IEA PVPS TI-26:2015): Snapshot of Global PV markets (1992-2014), ISBN: 978-3-906042-32-9.

McCree K J. Test of current definitions of photosynthetically active radiation against leaf photosynthesis data. Agric. For. Meteorol., 1972, 10: 443–453.

Wang Q, Kakubari Y, Kubota M. Variation of PAR to global solar radiation ratios along altitude gradient in Naeba Mountain. Theo. and Appl. Clima., 2007, 87: 239-253.

El-Sebaii A A, Al-Agel F. Estimation of horizontal diffuse solar radiation from common meteorological parameters: a case study for Jeddah, Saudi Arabia, International Journal of Ambient Energy, 2012, 34: 1-8.

Mohammed A A A. The Analysis of the characteristics of the solar radiation climate of the daily global radiation and diffuse radiation in Amman, Jordan, International Journal of Renewable Energy, 2010, 5, 23-38.

Bhattacharya A B, Kar S K, Bhattacharya R. Diffuse solar radiation and associated meteorological parameters in India, Ann. Geophysi., 1996, 14: 1051-1059.

Nwokolo S C. A comprehensive review of empirical models for estimating global solar radiation in Africa. Renewable and Sustainable Energy Reviews, 2017, 78: 955-995.

Nwokolo S C, Ogbulezie J C, Toge C K, John-Jaja S A. Modeling the influence of relative humidity on photosynthetically active radiation from global horizontal irradiation in six tropical ecological zones in Nigeria. New York Science Journal, 2016a, 9: 40-55.

Nwokolo S C, Ogbulezie J C. A quantitative view and classification of empirical models for predicting global solar radiation in West Africa. Beni-Suef Univ J. Basis Appl. Sci., 2017a, DOI: 10.1016/j.bjbus.2017.05.001.

Nwokolo S C, Ogbuezie J C. Modelling the influence of cloudiness on diffuse horizontal irradiation under various sky conditions over six tropical ecological zones in Nigeria. International Journal Physical Sciences, 2017b, 5(2): 91-100.

Liu B V H, Jordan R C. The interrelationship and characteristics distribution of direct, diffuse and total solar radiation, Solar Radiation, 1960, 22: 87-90.

Feng Y, Cui N, Zhang Q, Zhao L, Gong D. Comparison of artificial intelligence and empirical models for estimation of daily diffuse solar radiation in North China plain. International Energy of Hydrogen Energy, 2017, DOI: 10.1016/jijhydene.2017.04.084.

Elminir H K, Azzam Y A, Younes E L. Prediction of hourly and daily diffuse fraction using neural network, compared to linear regression models. Energy, 2007, 32: 1513-1523.

Soares J, Oliveira A P, Boznar M Z, Mlakar P, Escobedo J F, Machado A J. Modeling hourly diffuse solar-radiation in the City of Sao Paulo using a neural-network technique. Applied Energy, 2004, 79: 201-214.

Lou S, Li D H W, Lam J C, Chun W W H. Prediction of diffuse irradiance using machine learning and multivariable regression. Applied Energy, 2016, 181: 367-374.

Mohammadi K, Shamshirband S, Petkovic D, Khoronsanizadeh H. Determining the most important variables of diffuse solar radiation prediction using adaptive neuro-fuzzy methodology: Case study: City of Kerman, Iran. Renewable and Sustainable Energy Reviews. 2016, 53: 1570-1579.

Shamshirband S, Mohammadi K, Yee P L, Petkovic D, Mostafaeipour A. A. comparative evaluation for identifying the suitability of extreme learning machine to predict horizontal global solar radiation. Renewable and Sustainable Energy Reviews, 2016, 52: 1031-1042.

Boland J, Scott L. Predicting the diffuse fraction of global solar radiation using regression and fuzzy logic. In: Proceedings of the ANZSES Conference, Geelong, Nov, 1999.

Jiang Y. Predicting of monthly mean daily diffuse solar radiation using artificial neural networks and comparison with other empirical models. Energy Policy, 2008, 36: 3833-3837.

Alam S, Kaushik S C, Garg S N. Assessment of diffuse energy under general sky condition using artificial neural network. Applied Energy, 2009, 86: 554-564.

Lazarevska E, Trpovski J. A neuro-fuzzy model of the solar diffuse radiation with relevance vector machine. In: Proceedings of 11th international Conference on electrical power quality and utilization (EPQU); 2011, p. 1-6. 10.1109/EPQU.2011.6128803.

Yaniktepe B, Genc Y A. Estimating new model for predicting the global solar radiation on horizontal surface. International Journal of Hydrogen, 2015, 40: 15278-15283.

Zhang J, Zhao L, Deng S, Xn W, Zhang Y. A critical review of the models used to estimate solar radiation. Renewable and Sustainable Energy Reviews, 2017, 70: 314-329.

Sperati S, Alessandrini S, Pinson P, Kariniotakis G. The “Weather Intelligence for Renewable Energies†Benchmarking Exercise on Short-Term Forecasting of Wind and Solar Power Generation. Energies, 2015, 8:9594–9619. DOI: 10.3390/en8099594.

Pelland S, Galanis G, Kallos G. Solar and photovoltaic forecasting through post-processing of the Global Environmental Multiscale numerical weather prediction model, Prog. Photovolt. Res. Appl. 2013, 21: 284–296. DOI: 10.1002/pip.1180.

COST|About COST, (n.d.). http://www.cost.eu/about_cost (accessed on June 31, 2017).

Lauret P, Voyant C, Soubdhan T, David M, Poggi P. A benchmarking of machine learning techniques for solar radiation forecasting in an insular context. Solar Energy, 2015, 112: 446–457. DOI: 10.1016/j.solener.2014.12.014.

Besharat F, Dehghan A, Faghih A R. Empirical models for estimating global solar radiation: A review and case study, Renewable and Sustainable Energy Review, 2013, 21: 798-821.

Ertekin C, Yaldiz O. Estimating of monthly average daily global radiation on horizontal surface for Antalya, Turkey. Renewable Energy, 1999; 17: 95-102.

Nwokolo S C, Ogbulezie J C, Toge C K, John-Jaja S A. Photosynthetically active radiation estimation and modeling over different climatic zones in Nigeria. Journal of Agriculture and Ecology Research International 2016b, Article ID: 2016/JAERI/30000, http://sciencedomain.org/journal/37/articles-press (accessed on November 22, 2017).

Etuk S E, Nwokolo S C, Okechukwu E A, John-Jaja S A. Analysis of photosynthetically active radiation over six tropical ecological zones in Nigeria, Journal of Geography, Environment and Earth Science International, 2016a, 7: 1-15.

Etuk S E, Nwokolo S C, Okechukwu E A. Modelling and estimating photosynthetically active radiation from measured global solar radiation at Calabar, Nigeria, Physical Science International Journal, 2016b, 12: 1-12.

Ezekwe C I, Ezeilo C C O. Measured Solar Radiation in a Nigeria Environment compared with predicted data. Solar Energy, 1981, 26: 181-186.

Said R, Ibrahim S M A. Diffuse solar radiation in Cairo, Egypt. Energy Conversion and Management, 1985, 25: 69-72.

Maduekwe A A l, Chendo M A C. Atmospheric turbidity and the diffuse irradiance in Lagos, Nigeria. International Atomic Energy Agency and United National Education Scientific and Cultural Organization; International Centre for Theoretical Physics, 1994, 1-9.

Babatunde F B, Aro TO. Relationship between clearness Index and Cloudiness at a tropical station (Ilorin, Nigeria). Renewable Energy, 1995, 6 (7): 801-805.

Maduekwe A A L, Chendo M A C. Predicting the component of the total hemispherical solar radiation from sunshine duration measurement in Lagos, Nigeria. Renewable Energy, 1995, 6(7): 807-812.

Trabea A A. A multiple linear correlation for diffuse radiation from global solar radiation and sunshine data over Egypt. Renewable Energy, 1999, 17: 411-420.

Maduekwe A A L, Garba B. Characteristics of the monthly average hourly diffuse irradiance at Lagos and Zaira, Nigeria Renewable Energy, 1999, 17: 213-225.

Shaltout M A M, Hassan A H, Fathy A M. Total suspended particles and solar radiation over Cairo and Aswan. Renewable Energy, 2011, 23: 605-619.

El-Sebaii A A, Trabea A A. Estimation of horizontal diffuse solar radiation in Egypt. Energy Conversion and Management, 2003, 44: 2471-2482.

Burari F W. Correlation of global and diffuse solar radiation compoonents with meteorological parameters for Bauchi. Jolova, 2004, 5 (1): 49-55.

Ugwuoke P E, Okeke C E. Statistical assessment of average global and diffuse solar radiation on horizontal surfaces in typical climate. International Journal of Renewable Energy Research, 2012, 2: 269-273.

Khalil S A, Shaffie A M. A comparative study of total, direct and diffuse solar irradiance by using different models on horizontal and inclined surfaces for Cairo, Egypt. Renewable and Sustainable Energy Reviews, 2013, 27: 853-863.

Okundamiya M S, Emagbetere J O, Ogujor E A. Assessment of six daily diffuse solar radiation models for Nigeria. The 4th Interntional Workshop on Computer Science and Engineering-Summer, WCSE 2014; Dubai; UAE; Page 13-21, August 22-23, 2014.

Okundamiya M S, Nzeake A N. Estimation of diffuse solar radiation for selected cities in Nigeria. International Scholarly Research Network, 2011, 12; 1-6.

Sanusi Y K, Abisoye S G. Estimation of diffuse solar radiation in Lagos, Nigeria. 2nd International Conference on Chemical, Environmental and Biological Sciences (ICCEBS, 2013) March 17-18 Dubai (UAE), 2013, pp 6-9.

Olopade M A, Sanusi V K. Solar Radiation Characteristics, and the performance of photovoltaic (PV) Module in a tropical stratum. Journal of Science Research, 2009, 11: 100-109.

Bamiro O A. Empirical radiation for the determination of solar radiation Ibadan, Nigeria. Solar Energy, 1983, 31(1): 85-94.

Erusiafe F, Chendo M A C. Estimating Diffuse Solar radiation from global solar radiation, International Solar Energy Society, Aix-les-Rains, France, 2014, 16-19 September.

Sambo A S, Doyle M D C. The correlation off global and diffuse solar radiation components with meteorological data for Zaira. Jolova 1998, 5 (1): 40-448.

Falayi E O, Rabiu A B, Teliat R O. Correlations to estimate monthly mean of daily diffuse solar radiation in some selected cities in Nigeria. Advances in Applied Science Research, 2011, 2(4): 480-490.

Khorasanizadeh H, Mohammadi G. Diffuse solar radiation on a horizontal surface: Reviewing and categorizing the empirical models. Renewable and Sustaining Energy Reviews, 2016, 53: 338-362.

Badescu V. Correlations to estimate monthly mean daily solar global irradiation: application to Romania. Energy, 1993, 24: 883–893.

Page J K. The estimation of monthly mean values of daily total short-wave radiation on vertical and inclined surfaces from sunshine records for latitude 40oN and 40oS. Proceedings UN Conference on New Sources of Energy, Rome, Italy, United Nations, 1961, 4: 378-390.

Iqbal M. Correlation of average diffuse and beam radiation with hours of bright sunshine. Solar Energy, 1979, 23(2): 169–73.

Boukelia T E, Mecibah M S, Meriche I E. General models for estimation of the monthly mean daily diffuse solar radiation (Case Study: Algeria). Energy Conversion and Management, 2014, 81: 211-219.

Lewis G. Diffuse irradiance over Zimbabwe. Solar Energy, 1983, 331, 125-128.

Jain P C. A model for diffuse and global irradiation on horizontal surfaces. Solar Energy, 1990, 45: 301-308.

Bashahu M. Statistical comparison of models for estimating the monthly average daily diffuse radiation at a subtropical African site. Solar Energy, 2003, 75: 43-51.

Hove T, Gottsche I. Mapping global and beam solar radiation over Zimbabwe. Renewable Energy, 1999, 18: 535-556.

Lealea T, Tchinda R. Estimation of monthly mean daily diffuse solar radiation in the north and far north of Cameroon. European Science Journal, 2013a, 9 (18): 34-43.

Lealea T, Tchinda R. Estimation of diffuse solar radiation in Area between 5oN and 10oN of Cameroon. Natural Resources, 2013b, 4: 279-285.

Mohammed O W, Yanling G. Estimation of diffuse solar radiation in the region of Northern Sudan. International Energy Journal, 2016, 16: 163-172.

Butt S R, Mansor M, Abuam T. Estimation of global and diffuse solar radiation at Tripoli. Renewable Energy, 1998, 14: 121-127.

Karakoti I, Das P K, Singh S K. Predicting monthly mean daily diffuse radiation for India. Applied Energy, 2012, 91(1): 412–25.

Muneer T, Munawwar S. Improved accuracy models for hourly diffuse solar radiation. J. Sol. Energy Eng., 2006, 128: 104–117.

Mubiru J, Banda E J K B. Performance of empirical correlations for predicting monthly mean daily diffuse radiation values at Kampala, Uganda. Theoretical and Applied Climatology, 2007, 88: 127-131.

Maduekwe A A L, Chendo M A C. Atmospheric Turbidity and the diffuse in glance in Lagos, Nigeria Solar Energy, 1997, 61(4): 241-249.

Mohammadi K, Shamshirband S. Long C W, Arif M, Petkovic D, Ch S. A New hybrid support vector machines-wavelet transform approach for estimation of horizontal global solar radiation. Energy conversion and management, 2015a, 92: 162-171.

Mohammadi K, Shamshirband S, Anisi M H, Alam K A, Petkovic D. Support Vector regression based prediction of global solar radiation on a horizontal surface. Energy conversion and management 2015b, 91: 133-147.

Chen J L, Li G S, Wu S J. Assessing the potential of support vector machines for estimating daily solar radiation using sunshine duration. Energy conversion and management, 2013,73:311-318.

Ramedani Z, Omid M, Keyhani A, Khoshnevisan B, Saboohi H. A. Comparative Study between fuzzy inear regression and support vector regression for global solar radiation prediction in Iran Solar Energy, 2014, 109: 135-143.

Ramedani Z, Omid M, Keyhani A, Shamshirhand S, Khoshnevisan B. Potential of radial basis function based support with regression for global solar radiation prediction. Renewable and Sustainable Energy Review, 2015, 39: 1003-1011.

Landerous G, Lopez J J, O, Kisi O, Shiri J. Comparison of gene expression programming with neuro-suzzy and neural network computing techniques in estimating daily incoming solar radiation in the Basque Country (Northern Spain). Energy Conversion and Management, 2012, 102: 1-13.

Petkovic D, Cojbasic Z, Lukie S. Adaptive neuro-suzzy selection of heat rate variability parameters affected by autonomic nervous system. Expert Syst. App., 2013, 40: 4490-4493.

Petkovic D, Gocic M, Trajkovic S, Shamshirbrand S, Motamedi S, Aaishim R., et al. Determination of the most influential weather parameter on reference evaporatranspiration by adoptive; neuro-fuzzy methodology. Comput Electron Agric, 2015, 114: 277-284.

Bosch J L, Lopz G, Battles F J. Daily Solar irradiation estimation over a mountainous area using artificial neutral networks, Renewable Energy, 2008, 33: 1622-1628.

Oliveira A.P. Escobedo J F, Machado A J, Soares J. Correlation models of diffuse solar-radiation applied to the City of Sao Paulo, Brazil. Applied Energy, 2002, 71: 59-73.

Lawrence J. Data preparation for a neural network. Artif Intell Expert, 1991: 34-41.

Shamshirband S, Mohammadi K, Khoronsanizadeh H, Yee P L, Lee M, Petkovic D, Zalnezhad E. Estimating the diffuse solar radiation using a coupled support vector machine-wavelet transform model. Renewable and Sustainable Energy Reviews, 2015, 56: 428-435.

DOI: http://dx.doi.org/10.17737/tre.2017.3.2.0042


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