Skip to main content
SpringerLink
Log in

A new approach for estimating solar radiation using Gaussian distribution and developing new model

  • Research
  • Published:
Theoretical and Applied Climatology Aims and scope Submit manuscript

Abstract

The main aim of this study is to develop a new model using the Gaussian distribution in global solar radiation estimation. In this study, a new global solar radiation (SR) model was developed using the Matlab program, and the performance of this developed model was examined in different regions. With this newly developed model, the estimated values were compared with the actual measured values in the determined regions. When the literature is examined, it is seen that although many different methods and approaches have been used in SR estimation, no model has been developed with the Gaussian distribution. Thus, the performance of this new developed model was observed in detail in different regions. The performance of the developed model was examined in six different statistical error tests. The developed new model was compared with twenty different models. Global SR data used in this study were obtained from the Turkish State Meteorological Service. When the results are evaluated in general, it has been observed that the Gaussian model exhibited the best performance with RPE = 0.3574, MPE = 0.7794, R2 = 0.9848, MAPE = 6.7525, SSRE = 0.0997, and t-stat = 0.1913 resulting in the amongst all the models which were compared. In addition to these results, it was observed that the performance of the new model developed gave acceptable results in different regions. The findings of this study are expected to make significant contributions to the growing literature on advancing forecasting model development efforts to predict solar energy production.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on request.

Code availability

Not applicable.

Abbreviations

μ:

Mean of global SR

σ:

Variance of global SR

S:

Sunshine duration

S 0 :

Day length

H :

Daily total SR

H 0 :

SR coming out of atmosphere

W s :

Hour angle

∅:

Latitude of the site

δ :

Angle of solar declination

I sc :

Solar constant

mi:

Calculated value of SR

c i :

Measured value of SR

ma:

The mean calculated value of SR

ca:

The mean measured value of SR

References

  • Ağbulut Ü, Gürel AE, Biçen Y (2021) Prediction of daily global solar radiation using different machine learning algorithms: evaluation and comparison. Renew Sust Energ Rev 135:110114

    Google Scholar 

  • Akinoğlu BG, Ecevit A (1990) A further comparison and discussion of sunshine-based models to estimate global solar radiation. Energy 15(10):865–872

    Google Scholar 

  • Aksoy B (1997) Estimated monthly average global radiation for Turkey and its comparison with observations. Renew Energy 10(4):625–633

    Google Scholar 

  • Almorox JY, Hontoria C (2004) Global solar radiation estimation using sunshine duration in Spain. Energy Convers Manag 45(9):1529–1535

    Google Scholar 

  • Alsaad MA (1990) Characteristic distribution of global radiation for Amman, Jordan. Sol Wind Technol 7:261–266

    Google Scholar 

  • Aras H, Balli O, Hepbasli A (2006) Global solar radiation potential, Part 2: Statistical analysis. Energy Sources Part B-Economics Planning And Policy 1(3):317–326

    Google Scholar 

  • Atluri SN, Zhu T (1998) A new meshless local Petrov–Galerkin (MLPG) approach in compu-tational mechanics. Comput Mech 22(1998):117–127

    Google Scholar 

  • Bahel V, Srinivasan R, Bakhsh H (1986) Solar radiation for Dhahran, Saudi Arabia. Energy 11(10):985–989

    Google Scholar 

  • Bilbao J, Román R, Yousif C, Mateos D, de Miguel A (2014) Total ozone column, water vapour and aerosol effects on erythemal and global solar irradiance in Marsaxlokk, Malta. Atmos Environ 99:508–518

    Google Scholar 

  • Duffie JA, Beckman WA (2013) Solar radiation. Solar Engineering of Thermal Processes, Fourth Edition, pp 3–42

    Google Scholar 

  • El Genidy M (2019) Multiple nonlinear regression of the Markovian arrival process for estimating the daily global solar radiation. Communications in Statistics-Theory and Methods 48(22):5427–5444

    Google Scholar 

  • El Genidy MM, Abd El-Rahman DAE (2019) A New high accurate estimation method for evaluating the daily solar energy by nested percentiles algorithm. Asian Journal of Scientific Research 12(4):480–487

    Google Scholar 

  • El Genidy MM, Beheary MS (2022) Forecasting methods in various applications using algorithm of estimation regression models and converting data sets into Markov model. Complexity 2022:1–20

    Google Scholar 

  • El Genidy M, Megahed W, Mahfouz K (2022) Algorithms of solar energy prediction combined with percentile root estimation of three-parameters distributions. Appl Math 16(4):529–547

    Google Scholar 

  • Fan J, Wu L, Zhang F, Cai H, Ma X, Bai H (2019) Evaluation and development of empirical models for estimating daily and monthly mean daily diffuse horizontal solar radiation for different climatic regions of China. Renew Sust Energ Rev 105:168–186

    Google Scholar 

  • Feng Y, Hao W, Li H, Cui N, Gong D, Gao L (2020) Machine learning models to quantify and map daily global solar radiation and photovoltaic power. Renew Sust Energ Rev 118:109393

    Google Scholar 

  • Guermoui M, Gairaa K, Rabehi A, Djafer D, Benkaciali S (2018) Estimation of the daily global solar radiation based on the Gaussian process regression methodology in the Saharan climate. The European Physical Journal Plus 133(6):1–17

    Google Scholar 

  • Ikram RMA, Dai HL, Ewees AA, Shiri J, Kisi O, Zounemat-Kermani M (2022) Application of improved version of multi verse optimizer algorithm for modeling solar radiation. Energy Rep 8:12063–12080

    Google Scholar 

  • Jamil B, Bellos E (2019) Development of empirical models for estimation of global solar radiation exergy in India. J Clean Prod 207:1–16

    Google Scholar 

  • Jin Z, Yezheng W, Gang Y (2005) General formula for estimation of monthly average daily global solar radiation in China. Energy Convers Manag 46(2):257–268

    Google Scholar 

  • Kaplan YA (2018) A new model for predicting the global solar radiation. Environ Prog Sustain Energy 37(2):870–880

    Google Scholar 

  • Kaplan AG, Kaplan YA (2020) Developing of the new models in solar radiation estimation with curve fitting based on moving least-squares approximation. Renew Energy 146:2462–2471

    Google Scholar 

  • Kaplan YA, Saraç MS, Ünaldı GG (2022) Developing a new model in solar radiation estimation with genetic algorithm method. Environ Prog Sustain Energy 41(6):e13912

    Google Scholar 

  • Katiyar AK, Pandey CK (2010) Simple correlation for estimating the global solar radiation on horizontal surfaces in India. Energy 35(12):5043–5048

    Google Scholar 

  • Khorasanizadeh H, Mohammadi K, Mostafaeipour A (2014) Establishing a diffuse solar radiation model for determining the optimum tilt angle of solar surfaces in Tabass. Iran Energy Conversion and Management 78:805–814

    Google Scholar 

  • Li H, Ma W, Lian Y, Wang X, Zhao L (2011) Global solar radiation estimation with sunshine duration in Tibet, China. Renew Energy 36(11):3141–3145

    Google Scholar 

  • Louche A, Notton G, Poggi P, Simonnot G (1991) Correlations for direct normal and global horizontal irradiation on a French Mediterranean site. Sol Energy 46(4):261–266

    Google Scholar 

  • Makade RG, Chakrabarti S, Jamil B, Sakhale CN (2020) Estimation of global solar radiation for the tropical wet climatic region of India: a theory of experimentation approach. Renew Energy 146:2044–2059

    Google Scholar 

  • Mecibah MS, Boukelia TE, Tahtah R, Gairaa K (2014) Introducing the best model for estimation the monthly mean daily global solar radiation on a horizontal surface (Case study, Algeria). Renew Sust Energ Rev 36:194–202

    Google Scholar 

  • Menges HO, Ertekin C, Sonmete MH (2006) Evaluation of global solar radiation models for Konya, Turkey. Energy Convers Manag 47(18):3149–3173

    Google Scholar 

  • Notton G, Voyant C, Fouilloy A, Duchaud JL, Nivet ML (2019) Some applications of ANN to solar radiation estimation and forecasting for energy applications. Appl Sci 9(1):209

    Google Scholar 

  • Oztürk M, Ozek N, Berkama B (2012) Comparison of some existing models for estimating monthly average daily global solar radiation for Isparta. Pamukkale University Journal of Engineering Sciences 18(1):13–27

    Google Scholar 

  • Page JK (1961) The calculation of monthly mean solar radiation for horizontal and inclined surfaces from sunshine records for latitudes 40N-40S. UN conference on new sources of energy 4:378–390

    Google Scholar 

  • Qin W, Wang L, Lin A, Zhang M, Xia X, Hu B, Niu Z (2018) Comparison of deterministic and data-driven models for solar radiation estimation in China. Renew Sust Energ Rev 81:579–594

    Google Scholar 

  • Rahimi I, Bakhtiari B, Qaderi K, Aghababaie M (2012) Calibration of Angstrom equation for estimating solar radiation using Meta-Heuristic harmony search algorithm (Case study, Mashhad-East of Iran). Energy Procedia 18:644–651

    Google Scholar 

  • Raja IA, Twidell JW (1990) Diurnal variation of global insolation over five locations in Pakistan. Sol Energy 44(2):73–76

    Google Scholar 

  • Salcedo-Sanz S, Deo RC, Cornejo-Bueno L, Camacho-Gómez C, Ghimire S (2018) An efficient neuro-evolutionary hybrid modelling mechanism for the estimation of daily global solar radiation in the Sunshine State of Australia. Appl Energy 209:79–94

    Google Scholar 

  • Salhi H, Belkhiri L, Tiri A (2020) Evaluation of diffuse fraction and diffusion coefficient using statistical analysis. Appl Water Sci 10(6):1–12

    Google Scholar 

  • Salhi H, Hadjira A, Jamil B (2021) Statistical analysis of the solar diffuse fraction radiation using regression analysis of longitudinal data in India.

    Google Scholar 

  • Samuel TDMA (1991) Estimation of global radiation for Sri Lanka. Sol Energy 47(5):333–337

    Google Scholar 

  • Skeiker K (2006) Correlation of global solar radiation with common geographical and meteorological parameters for Damascus province, Syria. Energy Convers Manag 47(4):331–345

    Google Scholar 

  • Srivastava RC, Pandey H (2013) Estimating Angstrom–Prescott coefficients for India and developing a correlation between sunshine hours and global solar radiation for India. Renew Energy 1:11–17

    Google Scholar 

  • Tiris M, Tiris C, Erdalli Y (1997) Water heating systems by solar energy. In: Marmara Research Centre, Institute of Energy Systems and Environmental Research. Nato Tu-Coating, Gebze, Kocaeli, Turkey

    Google Scholar 

  • Togrul INT, Onat E (2000) A comparison of estimated and measured values of solar radiation in Elazig, Turkey. Renew Energy 20(2):243–252

    Google Scholar 

  • Togrul IT, Togrul H, Evin D (2000) Estimation of monthly global solar radiation from sunshine duration measurement in Elazig. Renew Energy 19(4):587–595

    Google Scholar 

  • Ulgen K, Hepbasli A (2002) Determination of Weibull parameters for wind energy analysis of Izmir, Turkey. Int J Energy Res 26(6):495–506

    Google Scholar 

  • Ulgen K, Hepbasli A (2004) Solar radiation models. Part 2: comparison and developing new models. Energy Sources 26(5):521–530

    Google Scholar 

  • Üstün İ, Üneş F, Mert İ, Karakuş C (2022) A comparative study of estimating solar radiation using machine learning approaches: DL, SMGRT, and ANFIS. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects 44(4):10322–10345

    Google Scholar 

  • Yang WY, Cao W, Tae SC, Moris J (2005) Applied numerical methods using MATLAB. John Wiley & Sons

    Google Scholar 

  • Yildiz M, Oz S (1994) Evaluation of the solar energy potential of Turkey. In Proceedings of the 6th National Energy Congress, pp 250–260

    Google Scholar 

  • Yohanna JK, Itodo IN, Umogbai VI (2011) A model for determining the global solar radiation for Makurdi, Nigeria. Renew Energy 36(7):1989–1992

    Google Scholar 

  • Zang H, Cheng L, Ding T, Cheung KW, Wang M, Wei Z, Sun G (2019) Estimation and validation of daily global solar radiation by day of the year-based models for different climates in China. Renew Energy 135:984–1003

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Energy Engineering, Osmaniye Korkut Ata University, 80000, Osmaniye, Turkey

    Yusuf Alper Kaplan

  2. Department of Mathematics, Osmaniye Korkut Ata University, 80000, Osmaniye, Turkey

    Ayse Gul Kaplan

Authors
  1. Yusuf Alper Kaplan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ayse Gul Kaplan
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Y.A.K. organised: Conceptualization, Writing- Reviewing and Editing A.G.K. prepared Writing- Reviewing and Editing. Y.A.K. and A.G.K. wrote the main manuscript text.

Corresponding author

Correspondence to Yusuf Alper Kaplan.

Ethics declarations

Ethics approval

Not applicable.

Consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kaplan, Y.A., Kaplan, A.G. A new approach for estimating solar radiation using Gaussian distribution and developing new model. Theor Appl Climatol 155, 1007–1017 (2024). https://doi.org/10.1007/s00704-023-04675-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00704-023-04675-y

Keywords

Search

Navigation