Accurate total solar irradiance estimates under irradiance measurements scarcity scenarios

Abstract

Accurate estimates of total global solar irradiance reaching the Earth’s surface are relevant since routine measurements are not always available. This work aimed to determine which of the models used to estimate daily total global solar irradiance (TGSI) is the best model when irradiance measurements are scarce in a given site. A model based on an artificial neural network (ANN) and empirical models based on temperature and sunshine measurements were analyzed and evaluated in Córdoba, Argentina. The performance of the models was benchmarked using different statistical estimators such as the mean bias error (MBE), the mean absolute bias error (MABE), the correlation coefficient (r), the Nash-Sutcliffe equation (NSE), and the statistics t test (t value). The results showed that when enough measurements were available, both the ANN and the empirical models accurately predicted TGSI (with MBE and MABE ≤ |0.11| and ≤ |1.98| kWh m−2 day−1, respectively; NSE ≥ 0.83; r ≥ 0.95; and |t values| < t critical value). However, when few TGSI measurements were available (2, 3, 5, 7, or 10 days per month) only the ANN-based method was accurate (|t value| < t critical value), yielding precise results although only 2 measurements per month were available for 1 year. This model has an important advantage over the empirical models and is very relevant to Argentina due to the scarcity of TGSI measurements.

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References

  1. Akinoglu, B. G., & Ecevit, A. (1990). Construction of a quadratic model using modified Ångström coefficients to estimate global solar radiation. Solar Energy, 45, 85–92.

    Google Scholar 

  2. Allen, R. G. (1997). Self-calibrating method for estimating solar radiation from air temperature. Journal of Hydrologic Engineering, 2, 56–67.

    Google Scholar 

  3. Almorox, J., Benito, M., & Hontoria, C. (2005). Estimation of monthly Ångström-Prescott equation coefficients from measured daily data in Toledo, Spain. Renewable Energy, 30, 931–936.

    Google Scholar 

  4. Almorox, J., Bocco, M., & Willington, E. (2013). Estimation of daily global solar radiation from measured temperatures at Cañada de Luque, Córdoba, Argentina. Renewable Energy, 60, 382–387.

    Google Scholar 

  5. Ampratwum, D. B., & Dorvlo, A. S. S. (1999). Estimation of solar radiation from the number of sunshine hours. Applied Energy, 63, 161–167.

    Google Scholar 

  6. Ångström, A. (1924). Solar and terrestrial radiation. Quarterly Journal of the Royal Meteorological Society, 50, 121–125.

    Google Scholar 

  7. Antonopoulos, V. Z., Papamichail, D. M., Aschonitis, V. G., & Antonopoulos, A. V. (2019). Solar radiation estimation methods using ANN and empirical models Author links open overlay panel. Computers and Electronics in Agriculture, 160, 160–167.

    Google Scholar 

  8. Bakirci, K. (2009a). Models of solar radiation with hours of bright sunshine: a review. Renewable and Sustainable Energy Reviews, 13, 2580–2588.

    Google Scholar 

  9. Bakirci, K. (2009b). Correlations for estimation of daily global solar radiation with hours of bright sunshine in Turkey. Energy, 34, 485–501.

    Google Scholar 

  10. Barron, M. G., Vivian, D. N., Yee, S. H., & Santavy, D. L. (2009). Methods to estimate solar radiation dosimetry in coral reefs using remote sensed, modeled, and in situ data. Environmental Monitoring and Assessment, 151, 445–455.

    Google Scholar 

  11. Basheer, I. A., & Hajmeer, M. (2000). Artificial neural networks: fundamentals, computing, design, and application. Journal of Microbiological Methods, 43, 3–31.

    CAS  Google Scholar 

  12. Besharat, F., Dehghan, A. A., & Faghih, A. R. (2013). Empirical models for estimating global solar radiation: a review and case study. Renewable and Sustainable Energy Reviews, 21, 798–821.

    Google Scholar 

  13. Bristow, K. L., & Campbell, G. S. (1984). On the relationship between incoming solar radiation and daily maximum and minimum temperature. Agricultural and Forest Meteorology, 31, 159–166.

    Google Scholar 

  14. Chen, R., Ersi, K., Yang, J., Lu, S., & Zhao, W. (2004). Validation of five global radiation models with measured daily data in China. Energy Conversion and Management, 45, 1759–1769.

    Google Scholar 

  15. Choubin, B., Zehtabian, G., Azareh, A., Rafiei-Sardooi, E., Sajedi-Hosseini, F., & Kişi, Ö. (2018). Precipitation forecasting using classification and regression trees (CART) model: a comparative study of different approaches. Environmental Earth Sciences, 77(8), 314.

    Google Scholar 

  16. Citakoglu, H. (2015). Comparison of artificial intelligence techniques via empirical equations for prediction of solar radiation. Computers and Electronics in Agriculture, 118, 28–37.

    Google Scholar 

  17. De Souza, J. L., Bastos Lyra, G., Dos Santos, C. M., Araujo Ferreira Junior, R., Tiba, C., Bastos Lyra, G., & Maringolo Lemes, M. A. (2016). Empirical models of daily and monthly global solar irradiation using sunshine duration for Alagoas State, Northeastern Brazil. Sustainable Energy Technologies and Assessments, 14, 35–45.

    Google Scholar 

  18. Donatelli, M., & Campbell, G. S. (1998). A simple model to estimate global solar radiation. Proceedings of the fifth European society of agronomy congress, Nitra, Slovak Republic (pp. 133–134).

  19. Duffie, J. A., & Beckman, W. A. (1991). Solar engineering of thermal processes. Hoboken: Wiley.

    Google Scholar 

  20. Elani, U. A. (2007). Distribution of ultraviolet solar radiation at Riyadh Region, Saudi Arabia. Environmental Monitoring and Assessment, 124, 235–241.

    CAS  Google Scholar 

  21. Hagan, M. T., & Menhaj, M. B. (1994). Training feed forward networks with the Marquardt algorithm. IEEE Transactions on Neural Networks, 5(6), 989–993.

    CAS  Google Scholar 

  22. Hargreaves, G. H., & Samani, Z. A. (1982). Estimating potential evapotranspiration. Journal of Irrigation and Drainage Engineering, 108, 223–230.

    Google Scholar 

  23. He, Z., Wen, X., Liu, H., & Du, J. (2014). A comparative study of artificial neural network, adaptive neuro fuzzy inference system and support vector machine for forecasting river flow in the semiarid mountain region. Journal of Hydrology, 509, 379–386.

    Google Scholar 

  24. Khosravi, A., Koury, R. N. N., Machado, L., & Pabon, J. J. G. (2018). Prediction of hourly solar radiation in Abu Musa Island using machine learning algorithms. Journal of Cleaner Production, 176, 63–75.

    Google Scholar 

  25. Liu, X., Li, Y., Zhong, X., Zhao, C., Jensen, J. R., & Zhao, Y. (2014). Towards increasing availability of the Ångström-Prescott radiation parameters across China: spatial trend and modeling. Energy Conversion and Management, 87, 975–989.

    Google Scholar 

  26. Marquardt, D. (1963). An algorithm for least-squares estimation of nonlinear parameters. SIAM Journal on Applied Mathematics, 11(2), 431–441.

    Google Scholar 

  27. Moreno-Sáez, R., & Mora-López, L. (2014). Modelling the distribution of solar spectral irradiance using data mining techniques. Environmental Modelling & Software, 53, 163–172.

    Google Scholar 

  28. Muzathik, A. M., Ibrahim, M. Z., Samo, K. B., & Wan Nik, W. B. (2011). Estimation of global solar irradiation on horizontal and inclined surfaces based on the horizontal measurements. Energy, 36, 812–818.

    Google Scholar 

  29. Newland, F. J. (1988). A study of solar radiation models for the coastal region of South China. Solar Energy, 31, 227–235.

    Google Scholar 

  30. Prescott, J. A. (1940). Evaporation from a water surface in relation to solar radiation. Transactions of the Royal Society of South Australia, 64, 114–118.

    Google Scholar 

  31. Quej, V. H., Almorox, J., Ibrakhimov, M., & Saito, L. (2016). Empirical models for estimating daily global solar radiation in Yucatán Peninsula, Mexico. Energy Conversion and Management, 110, 448–456.

    Google Scholar 

  32. Quej, V. H., Almorox, J., Arnaldo, J. A., & Saito, L. (2017). ANFIS, SVM and ANN soft-computing techniques to estimate daily global solar radiation in a warm sub-humid environment. Journal of Atmospheric and Solar - Terrestrial Physics, 155, 62–70.

    Google Scholar 

  33. Rafiei-Sardooi, E., Mohseni-Saravi, M., Barkhori, S., Azareh, A., Choubin, B., & Jafari-Shalamzar, M. (2018). Drought modeling: a comparative study between time series and neuro-fuzzy approaches. Arabian Journal of Geosciences, 11(17), 487.

    Google Scholar 

  34. Sajedi-Hosseini, F., Malekian, A., Choubin, B., Rahmati, O., Cipullo, S., Coulon, F., & Pradhan, B. (2018). A novel machine learning-based approach for the risk assessment of nitrate groundwater contamination. Science of the Total Environment, 644, 954–962.

    CAS  Google Scholar 

  35. Samani, Z. (2000). Estimating solar radiation and evapotranspiration using minimum climatological data. Journal of Irrigation and Drainage Engineering, 126, 265–267.

    Google Scholar 

  36. Samuel, T. D. M. A. (1991). Estimation of global radiation for Sri Lanka. Solar Energy, 47, 333–337.

    Google Scholar 

  37. Sharifi, S. S., Rezaverdinejad, V., & Nourani, V. (2016). Estimation of daily global solar radiation using wavelet regression, ANN, GEP and empirical models: a comparative study of selected temperature-based approaches. Journal of Atmospheric and Solar - Terrestrial Physics, 149, 131–145.

    Google Scholar 

  38. Sonmete, M. H., Ertekin, C., Menges, H. O., Hacıseferoğullari, H., & Evrendilek, F. (2011). Assessing monthly average solar radiation models: a comparative case study in Turkey. Environmental Monitoring and Assessment, 175, 251–277.

    Google Scholar 

  39. Urraca, R., Martinez-de-Pison, E., Sanz-Garcia, A., Antonanzas, J., & Antonanzas-Torres, F. (2017). Estimation methods for global solar radiation: case study evaluation of five different approaches in central Spain. Renewable and Sustainable Energy Reviews, 77, 1098–1113.

    Google Scholar 

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

    Google Scholar 

  41. Wacker, S., Gröbner, J., Zysset, C., Diener, L., Tzoumanikis, P., Kazantzidis, A., Vuilleumier, L., Stöckli, R., Nyeki, S., & Kämpfer, N. (2015). Cloud observations in Switzerland using hemispherical sky cameras. Journal of Geophysical Research – Atmospheres, 120, 695–707.

    Google Scholar 

  42. Walpole, R. E., Myers, R. H., Myers, S. L., & Ye, K. (2012). Probability & statistics for engineers & scientists. Boston: Prentice Hall.

    Google Scholar 

  43. Wang, J., Wang, E., Yin, H., Feng, L., & Zhao, Y. (2015). Differences between observed and calculated solar radiations and their impact on simulated crop yields. Field Crops Research, 176, 1–10.

    Google Scholar 

  44. Widén, J., Carpman, N., Castellucci, V., Lingfors, D., Olauson, J., Remouit, F., Bergkvist, M., Grabbe, M., & Waters, R. (2015). Variability assessment and forecasting of renewables: a review for solar, wind, wave and tidal resources. Renewable and Sustainable Energy Reviews, 44, 356–375.

    Google Scholar 

  45. Yorukoglu, M., & Celik, A. L. (2006). A critical review on the estimation of daily global solar radiation from sunshine duration. Energy Conversion and Management, 47, 2441–2450.

    Google Scholar 

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Acknowledgments

We thank Secretaría de Ciencia y Tecnología de la Universidad Nacional de Córdoba (UNC), Consejo Nacional de Investigaciones Científicas y Tecnológicas (CONICET), and Agencia Nacional de Promoción Científica (FONCYT) for their support.

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Correspondence to María Laura López.

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Highlights

• Performance of models to estimate total global solar irradiance (TGSI) is assessed.

• Frequency of measurements needed to calibrate models is analyzed.

• A minimum number of TGSI measurements per month are enough for ANN training.

• When TGSI measurements are scarce, empirical methods (EM) are not accurate.

• An ANN model is an overriding option with respect to the analyzed EM if TGSI measurements are scarce.

Appendix

Appendix

The tables presented in this section show the weights found for the ANN model when 2, 3, 5, 7, and 10 days per month were used for the calibration/training processes (Tables 6, 7, 8, 9, and 10, respectively).

Table 6 Weights of the ANN model when 2 days per month were used for the calibration/validation processes
Table 7 Weights of the ANN model when 3 days per month were used for the calibration/validation processes
Table 8 Weights of the ANN model when 5 days per month were used for the calibration/validation processes
Table 9 Weights of the ANN model when 7 days per month were used for the calibration/validation processes
Table 10 Weights of the ANN model when 10 days per month were used for the calibration/validation processes

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López, M.L., Olcese, L.E., Palancar, G.G. et al. Accurate total solar irradiance estimates under irradiance measurements scarcity scenarios. Environ Monit Assess 191, 568 (2019). https://doi.org/10.1007/s10661-019-7742-3

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Keywords

  • Artificial neural network
  • Scarce measurements
  • Solar energy
  • Solar radiation estimation