Table 1.

A summary of the studies regarding the prediction of solar radiation data using empirical models.

Location	Model	Input Parameters	Output Parameter	Data scale	Statistical Benchmarks	Key Findings	References
Ashanti, Owabide (Ghana)	Angstrom-Prescott and Hargreaves and Samani	Sunshine hours and air temperature	Global solar radiation	Five months from 2011: April, May, June, October, November	MBE, MPE, and RMSE	Proposed models using sunshine hours and air temperature compatible with measured solar radiation value.	[26]
Ghardaïa, Algeria	6 combined new models	Minimum and maximum temperature	Global solar radiation	365 days of 2006	RMSE, MBE, MAE, and MPE	GSR predicted well in all models, and MPE values found ±10%.	[27]
Yucatán Peninsula, Mexico	A novel empirical model (M5)	Average relative humidity, minimum temperature, maximum temperature, and transformed rainfall	Daily horizontal global solar radiation	From 6 different stations on different dates between 2000 and 2014.	MPE, MAPE, RMSE, MBE, MABE, and R2	The proposed model (M5) was calibrated using 12 existing models. If rainfall and relative humidity data are available, this model can be used.	[28]
India	32 empirical models in 4 different categories	Relative sunshine period, and clearness index	Global solar energy	1986–2000	MARE, MAE, RRMSE, RMSE, U95, t-stats, MPE, MBE, erMAX, r, and GPI	The power model with a clearness index shows great performance.	[29]
Tropical regions of China	6 temperature-based models (P1–P6)	Temperature, relative air humidity, vapor pressure deficit, transformed precipitation, and precipitation	Daily horizontal global solar radiation	1966–2015	R2, RMSE, NRMSE, and MBE	The second model (P2) has high accuracy when only air temperature is considered, but models 3 and 5 (P3 and P5) have higher accuracy when other variables (eg. precipitation and relative humidity) are considered for tropical regions of China.	[30]
Muğla, Türkiye	105 different regression models and set of new regression models	Sunshine duration, cloudless, and average sunshine duration	Global horizontal solar radiation	January 2007 to August 2015	MPE, MBE, MAPE, MABE, RMSE, and R2	7 new calibrated models were tested and found low error rates.	[31]
China	72 existing and developed empirical models	Meteorological and solar radiation data	Diffuse horizontal solar radiation	1966–2015	R2, RMSE, RRMSE, MAB, NRMSE, t-stat, U95, and GPI	In different categories, models were tested and developed.	[32]
India	Three Global Solar Radiation models (M-01, M-02, M-03)	Relative humidity, latitude, altitude, and sunshine duration	Global solar radiation	1986–2000	RMSE, MAE, R2, MPE, RMSRE MARE, MBE, t-stat, GPI, RRMSE, and U95	M-03 model contains 4 variables and can be applied with maximum 11.8935% MPE.	[33]
Morocco	Hybrid temperature-based models	Temperature	Daily global solar radiation	1996–2010	MBE, MSE, RMSE, R2, standard deviation, and performance score	4 ML models were used to optimize 42 temperature-based models and correlations (R2) increase.	[34]
China	Zone model	Surface meteorological measurements.	Daily global solar radiation	1970–2017	MABE, RMSE, and NSEC	With the zone method NSEC values greater than 0.8 and RMSE% less than 20% obtained.	[35]
Iran	Twenty-one sunshine-based empirical models	Number of days and sunshine	Daily solar radiation	2007–2017	R2, MAE, MBE, RRMSE, MAPE, RMSE, and MBE	21 different sunshine-based empirical models were compared and calibrated.	[36]
Adrar, Algeria	Proposed 6 temperature-based models	Daily air temperature	Daily average horizontal global solar radiation	4 years period	MBE, RMSE, and R2	Proposed M4 model shows best performance (R2 = 0.87).	[37]
Industrial City, the Kingdom of Saudi Arabia	Linear, Quadratic and Logarithmic	Relative humidity, ambient temperature, and sunshine duration	Global horizontal radiation	January–December 2016	r, R2, RMSE, MBE, MABE, and MAPE	3 different models were examined and compared, the quadratic model has the highest r and R2.	[38]
Eskişehir, Türkiye	Angström-Prescott model and improved versions of this model, also several typical models based on ambient temperature	Sun radiation, sunshine period, temperature, air pressure, wind speed, and relative humidity	Worldwide sun radiation	January 2011–December 2014	E, MPE, MAPE, SSRE, RSE, MBE, RMSE, t-sat, and R2	The author tested new model usage with 9 statistical techniques.	[39]
Peru	Multiple linear regression analysis	Temperature, precipitation, and relative humidity	Daily solar radiation	1990–2004 (calibration) and 2004–2010 (validation)	RMSE	Seven empirical models were employed for the prediction of daily solar radiation data.	[40]
Morroco	Temperature -Geographic factors model	Temperature- Geographic factors	Global solar radiation	August 2011–September 2015	r, nMAE, and nRMSE	22 empirical models and other machine learning methods were applied. Temperature-Geographic factors models recommend in all empirical models.	[41]
Iran	11 Newly Developed Empirical Models (NDEM)	Month number, solar declination, sunshine duration, RH, and cloud cover rank	Monthly, daily, and hourly diffuse solar radiation	January 2008 to December 2017	RMSE, NRMSE, and R2	11 newly developed models were tested. Errors do not exceed 10% for these models.	[42]
Ghana	Modified Angström-Prescot, modified Steyn-method, Ordinary kriging method	Sunshine duration	Global solar radiation, sky view factor, cloudiness index	2015–2018	r	Sky conditions were calculated by different methods for the 4 climate regions of Ghana.	[43]
China	Empirical PV power model, combined a sunshine-based model, and inverse distance weighting model	Minimum and maximum temperature, sunshine duration, relative humidity, and precipitation	Global solar radiation	1961 to 2018	RMSE, MAE, RRMSE, R2, and NS	New developed global solar radiation model can predict correctly.	[44]
Fiji island	20 empirical models	Sunshine duration, minimum, mean, and maximum temperatures, cloud cover, and relative humidity	Global solar radiation	1984 to 2018	ME, NSE, PME, RMSE, and r-value	20 models were analyzed by dividing into 3 different groups. Models with relative humidity in group 3 performed very well.	[45]
Irani (Ahvaz, BandarAbbas, and Kermanshah)	Eight Rs empirical models, (AP, GG, HS, S, An, Ch, Ba, Ab)	Extraterrestrial solar radiation, sunshine hours, air temperature, relative humidity, maximum possible sunshine hours, the function of daily range of air temperature, and station altitude	Solar radiation	2007 to 2017	RMSE, NMRSE, and R2	They compared 8 empirical models and SVM models. They do not recommend the use of empirical models instead of the SVM model, despite their high accuracy.	[46]