Effects of Angstrom-Prescott and Hargreaves-Samani Coefficients on Climate Forcing and Solar PV Technology Selection in West Africa

Mfongang Erim Agbor, Sunday O. Udo, Igwe O. Ewona, Samuel Chukwujindu Nwokolo, Julie C. Ogbulezie, Solomon Okechukwu Amadi, Utibe Akpan Billy


We evaluated and compared the performance of simulated Angström-Prescott (AP) and Hargreaves-Samani (HS) models on monthly and annual timescales using generalized datasets covering the entire West African region. The fitted AP model yielded more efficient parameters of a = 0.366 and b = 0.459, whereas the HS model produced a 0.216 coefficient based on an annual timescale, which is more suitable in the region compared to coefficients recommended by the Food and Agriculture Organization (FAO) (a = 0.25 and b = 0.5) and HS (0.17), respectively. Employing the FAO and HS recommended coefficients will introduce a relative percentage error (RPE) of 18.388% and 27.19% compared to the RPEs of 0.0014% and 0.1036% obtained in this study, respectively. When considering time and resource availability in the absence of ground-measured datasets, the coefficients obtained in this study can be used for predicting global solar radiation within the region. According to the AP and HS coefficients, the polycrystalline module (p-Si) is more reliable than the monocrystalline module (m-Si) because the p-Si module has a higher tendency to withstand the high temperatures projected to affect the region due to its higher intrinsic properties based on the AP and HS coefficients assessment in the region.

Citation: Agbor, M. E., Udo, S. O., Ewona, I. O., Nwokolo, S. C., Ogbulezie, J. C., Amadi, S. O., and Billy, U. A. (2023). Effects of Angstrom-Prescott and Hargreaves-Samani Coefficients on Climate Forcing and Solar PV Technology Selection in West Africa. Trends in Renewable Energy, 9, 78-106. DOI: 10.17737/tre.2023.9.1.00150


Ångström-Prescott coefficient; Hargreaves-Samani coefficient; Global solar radiation; Solar PV technologies; Climate forcing

Full Text:



Beiter, P. C., Vincent, N. M., and Ma, O. (2018). 2016 Renewable Energy Grid Integration Data Book (No. NREL/BK-6A20-71151). National Renewable Energy Lab.(NREL), Golden, CO (United States).

Benatallah, M., Bailek, N., Bouchouicha, K., Sharifi, A., Abdel-Hadi, Y., Nwokolo, S., S. Band, S., Jamil, B., Mosavi, A., and El-kenawy, E.-S. (2022). Exploring the ability of hybrid extreme machine-based methods to predict solar radiation-a case study of Sahara middle South, Algeria. NRIAG Journal of Astronomy and Geophysics.

Kimball, H. H. (1919). Variations in the total and luminous solar radiation with geographical position in the United States. Monthly Weather Review, 47(11), 769-793. DOI: https://doi.org/10.1175/1520-0493(1919)47<769:vittal>2.0.co;2

Angstrom, A. (1924). Solar and terrestrial radiation. Report to the international commission for solar research on actinometric investigations of solar and atmospheric radiation. 50(210), 121-126. DOI: https://doi.org/10.1002/qj.49705021008

Prescott, J. (1940). Evaporation from Water Surface in Relation to Solar Radiation. Trans R Soc South Aust, 64,114–118.

Nwokolo, S. C., Amadi, S. O., Obiwulu, A. U., Ogbulezie, J. C., and Eyibio, E. E. (2022). Prediction of global solar radiation potential for sustainable and cleaner energy generation using improved Angstrom-Prescott and Gumbel probabilistic models. Cleaner Engineering and Technology, 6, 100416. DOI: https://doi.org/10.1016/j.clet.2022.100416

Paulescu, M., Stefu, N., Calinoiu, D., Paulescu, E., Pop, N., Boata, R., and Mares, O. (2016). Ångström–Prescott equation: Physical basis, empirical models and sensitivity analysis. Renewable and Sustainable Energy Reviews, 62, 495-506.

Nwokolo, S. C., Obiwulu, A. U., Ogbulezie, J. C., and Amadi, S. O. (2022). Hybridization of statistical machine learning and numerical models for improving beam, diffuse and global solar radiation prediction. Cleaner Engineering and Technology, 9, 100529. DOI: https://doi.org/10.1016/j.clet.2022.100529

Obiwulu, A. U., Erusiafe, N., Olopade, M. A., and Nwokolo, S. C. (2022). Modeling and estimation of the optimal tilt angle, maximum incident solar radiation, and global radiation index of the photovoltaic system. Heliyon, 8(6). DOI: 10.1016/j.heliyon.2022.e09598

Obiwulu, A. U., Chendo, M. A. C., Erusiafe, N., and Nwokolo, S. C. (2020). Implicit meteorological parameter-based empirical models for estimating back temperature solar modules under varying tilt-angles in Lagos, Nigeria. Renewable Energy, 145, 442-457. DOI: https://doi.org/10.1016/j.renene.2019.05.136

Obiwulu, A. U., Erusiafe, N., Olopade, M. A., and Nwokolo, S. C. (2020). Modeling and optimization of back temperature models of mono-crystalline silicon modules with special focus on the effect of meteorological and geographical parameters on PV performance. Renewable Energy, 154, 404-431. DOI: https://doi.org/10.1016/j.renene.2020.02.103

Amadi, S. O., Dike, T., and Nwokolo, S. C. (2020). Global Solar Radiation Characteristics at Calabar and Port Harcourt Cities in Nigeria. Trends in Renewable Energy, 6(2), 111-130. DOI: https://doi.org/10.17737/tre.2020.6.2.00114

Nwokolo, S. C., Ogbulezie, J. C., and Obiwulu, A. U. (2022). Impacts of climate change and meteo-solar parameters on photosynthetically active radiation prediction using hybrid machine learning with Physics-based models. Advances in Space Research, 70(11), 3614-3637. DOI: https://doi.org/10.1016/j.asr.2022.08.010

Ramanathan, V., and Feng, Y. (2009). Air pollution, greenhouse gases and climate change: Global and regional perspectives. Atmospheric Environment, 43(1), 37-50. DOI: https://doi.org/10.1016/j.atmosenv.2008.09.063

Nwokolo, S.C., and Ogbulezie, J.C. (2017). A single hybrid parameter-based model for calibrating hargreaves-samani coefficient in Nigeria. Int J Phys Res 5(2), 49. DOI: https://doi.org/10.14419/ijpr.v5i2.8042

Nwokolo, S.C., and Ogbulezie, J.C. (2018). A quantitative review and classification of empirical models for predicting global solar radiation in West Africa. Beni-Suef Univ J Basic Appl Sci, 7,367–396. DOI: https://doi.org/10.1016/j.bjbas.2017.05.001

Nwokolo, S.C. (2017). A comprehensive review of empirical models for estimating global solar radiation in Africa. Renew Sustain Energy Rev, 78, 955–995. DOI: https://doi.org/10.1016/j.rser.2017.04.101

Makade, R. G., Chakrabarti, S., and Jamil, B. (2021). Development of global solar radiation models: A comprehensive review and statistical analysis for Indian regions. Journal of Cleaner Production, 293, 126208. DOI: https://doi.org/10.1016/j.jclepro.2021.126208

Gouda, S. G., Hussein, Z., Luo, S., and Yuan, Q. (2020). Review of empirical solar radiation models for estimating global solar radiation of various climate zones of China. 44(2), 168-188. DOI: https://doi.org/10.1177/0309133319867213

Almorox, J., Voyant, C., Bailek, N., Kuriqi, A., and Arnaldo, J. A. (2021). Total solar irradiance's effect on the performance of empirical models for estimating global solar radiation: An empirical-based review. Energy, 236, 121486. DOI: https://doi.org/10.1016/j.energy.2021.121486

Hargreaves, G. H., and Samani, Z. A. (1982). Estimating potential evapotranspiration. Journal of the irrigation and Drainage Division, 108(3), 225-230. DOI: https://doi.org/10.1061/taceat.0008673

Allen, R. G., Pereira, L. S., Raes, D., and Smith, M. (1998). Crop evapotranspiration-Guidelines for computing crop water requirements-FAO Irrigation and drainage paper 56. Fao, Rome, 300(9), D05109.

Hargreaves, G. L., Hargreaves, G. H., and Riley, J. P. (1985). Irrigation Water Requirements for Senegal River Basin. 111(3), 265-275. DOI: doi:10.1061/(ASCE)0733-9437(1985)111:3(265)

Nwokolo, S.C. and Otse, C.Q. (2019). Impact of Sunshine Duration and Clearness Index on Diffuse Solar Radiation Estimation in Mountainous Climate. Trends in Renewable Energy, 5, 307-332. DOI: 10.17737/tre.2019.5.3.00107

Zhu, W., Wu, B., Yan, N., Ma, Z., Wang, L., Liu, W., Xing, Q., and Xu, J. (2019). Estimating sunshine duration using hourly total cloud amount data from a geostationary meteorological satellite. Atmosphere, 11(1), 26. DOI: https://doi.org/10.3390/ATMOS11010026

Khorasanizadeh, H., and Mohammadi, K. (2016). Diffuse solar radiation on a horizontal surface: Reviewing and categorizing the empirical models. Renewable and Sustainable Energy Reviews, 53, 338-362. DOI: https://doi.org/10.1016/j.rser.2015.08.037

Besharat, F., Dehghan, A. A., and Faghih, A. R. (2013). Empirical models for estimating global solar radiation: A review and case study. Renewable and Sustainable Energy Reviews, 21, 798-821. DOI: https://doi.org/10.1016/j.rser.2012.12.043

Liu, Y., Zhou, Y., Chen, Y., Wang, D., Wang, Y., and Zhu, Y. (2020). Comparison of support vector machine and copula-based nonlinear quantile regression for estimating the daily diffuse solar radiation: A case study in China. Renewable Energy, 146, 1101-1112. DOI: https://doi.org/10.1016/j.renene.2019.07.053

Govindasamy, T. R., and Chetty, N. (2021). Machine learning models to quantify the influence of PM10 aerosol concentration on global solar radiation prediction in South Africa. Cleaner Engineering and Technology, 2, 100042. DOI: https://doi.org/10.1016/j.clet.2021.100042

Li, M.-F., Fan, L., Liu, H.-B., Guo, P.-T., and Wu, W. (2013). A general model for estimation of daily global solar radiation using air temperatures and site geographic parameters in Southwest China. Journal of Atmospheric and Solar-Terrestrial Physics, 92, 145-150. DOI: https://doi.org/10.1016/j.jastp.2012.11.001

Liu, Y., Zhou, Y., Wang, D., Wang, Y., Li, Y., and Zhu, Y. (2018). Reply to “Comments on [“Classification of solar radiation zones and general models for estimating the daily global solar radiation on horizontal surfaces in China”[Energy Convers. Manage. 154 (2017) 168–179] by Liu et al.]”. Energy Conversion and Management, 168, 653-654.

Liu, Y., Tan, Q., and Pan, T. (2019). Determining the parameters of the Ångström‐Prescott model for estimating solar radiation in different regions of China: Calibration and modeling. Earth and Space Science, 6(10), 1976-1986. DOI: https://doi.org/10.1029/2019EA000635

Paulescu, M., Badescu, V., Budea, S., and Dumitrescu, A. (2022). Empirical sunshine-based models vs online estimators for solar resources. Renewable and Sustainable Energy Reviews, 168, 112868. DOI: https://doi.org/10.1016/j.rser.2022.112868

Almorox, J., Hontoria, C., and Benito, M. (2011). Models for obtaining daily global solar radiation with measured air temperature data in Madrid (Spain). Applied Energy, 88(5), 1703-1709. DOI: https://doi.org/10.1016/j.apenergy.2010.11.003

Chen, R., Ersi, K., Yang, J., Lu, S., and Zhao, W. (2004). Validation of five global radiation models with measured daily data in China. Energy Conversion and Management, 45(11), 1759-1769. DOI: https://doi.org/10.1016/j.enconman.2003.09.019

de Barros Silva, A. W., Freitas, B. B., de Alencar Filho, C. L., de Freitas, C. D., de Sousa Junior, E. A., de Castro, E. S., de Araújo, E.M., Correia, F.I.F., da Silva, F.R.P., de Souza, J.J.S., and Martins, L.L.A.P. (2022). Methodology Based on Artificial Neural Networks for Hourly Forecasting of PV Plants Generation. IEEE Latin America Transactions, 20(4), 659-668. DOI: https://doi.org/10.1109/TLA.2022.9675472

Nwokolo, S.C., Obiwulu, A.U., and Ogbulezie, J.C. (2023). Machine learning and analytical model hybridization to assess the impact of climate. Phys Chem Earth, (In press)

Hassan, M. A., Bailek, N., Bouchouicha, K., and Nwokolo, S. C. (2021). Ultra-short-term exogenous forecasting of photovoltaic power production using genetically optimized non-linear auto-regressive recurrent neural networks. Renewable Energy, 171, 191-209. DOI: https://doi.org/10.1016/j.renene.2021.02.103

Hassan, M. A., Bailek, N., Bouchouicha, K., Ibrahim, A., Jamil, B., Kuriqi, A., Nwokolo, S. C., and El-kenawy, E.-S. M. (2022). Evaluation of energy extraction of PV systems affected by environmental factors under real outdoor conditions. Theoretical and Applied Climatology, 150(1), 715-729. DOI: 10.1007/s00704-022-04166-6

Ohunakin, O. S., Adaramola, M. S., Oyewola, O. M., and Fagbenle, R. O. (2013). Correlations for estimating solar radiation using sunshine hours and temperature measurement in Osogbo, Osun State, Nigeria. Frontiers in Energy, 7(2), 214-222. DOI: 10.1007/s11708-013-0241-2

Dutta, R., Chanda, K., and Maity, R. (2022). Future of solar energy potential in a changing climate across the world: A CMIP6 multi-model ensemble analysis. Renewable Energy, 188, 819-829. DOI: https://doi.org/10.1016/j.renene.2022.02.023

Crook, J. A., Jones, L. A., Forster, P. M., and Crook, R. (2011). Climate change impacts on future photovoltaic and concentrated solar power energy output. Energy & Environmental Science, 4(9), 3101-3109. DOI: https://doi.org/10.1039/c1ee01495a

Adaramola, M. S. (2012). Estimating global solar radiation using common meteorological data in Akure, Nigeria. Renewable Energy, 47, 38-44. DOI: https://doi.org/10.1016/j.renene.2012.04.005

Gaetani, M., Huld, T., Vignati, E., Monforti-Ferrario, F., Dosio, A., and Raes, F. (2014). The near future availability of photovoltaic energy in Europe and Africa in climate-aerosol modeling experiments. Renewable and Sustainable Energy Reviews, 38, 706-716. DOI: https://doi.org/10.1016/j.rser.2014.07.041

Huber, I., Bugliaro, L., Ponater, M., Garny, H., Emde, C., and Mayer, B. (2016). Do climate models project changes in solar resources? Solar Energy, 129, 65-84. DOI: https://doi.org/10.1016/j.solener.2015.12.016

Zou, L., Wang, L., Li, J., Lu, Y., Gong, W., and Niu, Y. (2019). Global surface solar radiation and photovoltaic power from Coupled Model Intercomparison Project Phase 5 climate models. Journal of Cleaner Production, 224, 304-324. DOI: https://doi.org/10.1016/j.jclepro.2019.03.268

Bazyomo, S. D. Y. B., Lawin, E. A., Coulibaly, O., and Ouedraogo, A. (2016). Forecasted changes in West Africa photovoltaic energy output by 2045. Climate, 4(4), 53. DOI: https://doi.org/10.3390/cli4040053

Fant, C., Adam Schlosser, C., and Strzepek, K. (2016). The impact of climate change on wind and solar resources in southern Africa. Applied Energy, 161, 556-564. DOI: https://doi.org/10.1016/j.apenergy.2015.03.042

Patchali, T. E., Ajide, O. O., Matthew, O. J., Salau, T. A. O., and Oyewola, O. M. (2020). Examination of potential impacts of future climate change on solar radiation in Togo, West Africa. SN Applied Sciences, 2(12), 1941. DOI: https://doi.org/10.1007/s42452-020-03738-3

Ohunakin, O. S., Adaramola, M. S., Oyewola, O. M., Matthew, O. J., and Fagbenle, R. O. (2015). The effect of climate change on solar radiation in Nigeria. Solar Energy, 116, 272-286. DOI: https://doi.org/10.1016/j.solener.2015.03.027

Pope, F. D., Braesicke, P., Grainger, R. G., Kalberer, M., Watson, I. M., Davidson, P. J., and Cox, R. A. (2012). Stratospheric aerosol particles and solar-radiation management. Nature Climate Change, 2(10), 713-719.

Amadi, S. O., andUdo, S. O. (2018). A Study of Multi-Annual Variability of Effective Sunshine Duration in Nigeria and Its Implications for Climate Forcing and Air Quality. Journal of Health and Environmental Studies, 2(2), 13-30.

Salby, M. L. (2012). Physics of the Atmosphere and Climate. Cambridge University Press.

Viana, M., Pey, J., Querol, X., Alastuey, A., de Leeuw, F., and Lükewille, A. (2014). Natural sources of atmospheric aerosols influencing air quality across Europe. Science of The Total Environment, 472, 825-833. DOI: https://doi.org/10.1016/j.scitotenv.2013.11.140

Bais, A. F., McKenzie, R. L., Bernhard, G., Aucamp, P. J., Ilyas, M., Madronich, S., & Tourpali, K. (2015). Ozone depletion and climate change: impacts on UV radiation. Photochemical & Photobiological Sciences, 14(1), 19-52.

Levy II, H., Horowitz, L. W., Schwarzkopf, M. D., Ming, Y., Golaz, J.-C., Naik, V., and Ramaswamy, V. (2013). The roles of aerosol direct and indirect effects in past and future climate change. 118(10), 4521-4532. DOI: https://doi.org/10.1002/jgrd.50192

Adams, P. J., Seinfeld, J. H., and Koch, D. M. (1999). Global concentrations of tropospheric sulfate, nitrate, and ammonium aerosol simulated in a general circulation model. 104(D11), 13791-13823. DOI: https://doi.org/10.1029/1999JD900083

Senf, F., Quaas, J., and Tegen, I. (2021). Absorbing aerosol decreases cloud cover in cloud-resolving simulations over Germany. 147(741), 4083-4100. DOI: https://doi.org/10.1002/qj.4169

Wu, D., Ding, X., Li, Q., Sun, J., Huang, C., Yao, L., Wang, X., Ye, X., Chen, Y., He, H., and Chen, J. (2019). Pollutants emitted from typical Chinese vessels: Potential contributions to ozone and secondary organic aerosols. Journal of Cleaner Production, 238, 117862. DOI: https://doi.org/10.1016/j.jclepro.2019.117862

Fu, T. M., & Tian, H. (2019). Climate change penalty to ozone air quality: review of current understandings and knowledge gaps. Current Pollution Reports, 5(3), 159-171.

Nwokolo, S. C., and Ogbulezie, J. C. (2018). A qualitative review of empirical models for estimating diffuse solar radiation from experimental data in Africa. Renewable and Sustainable Energy Reviews, 92, 353-393. DOI: https://doi.org/10.1016/j.rser.2018.04.118

DOI: http://dx.doi.org/10.17737/tre.2023.9.1.00150


  • There are currently no refbacks.

Copyright (c) 2023 Mfongang Erim Agbor, Sunday O. Udo, Igwe O. Ewona, Samuel Chukwujindu Nwokolo, Julie C. Ogbulezie, Solomon Okechukwu Amadi, Utibe Akpan Billy

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Creative Commons License This work is licensed under a Creative Commons Attribution 4.0 License.
Copyright @2014-2023 Trends in Renewable Energy (ISSN: 2376-2136, online ISSN: 2376-2144)