Mathematical expressions have been employed to estimate global solar radiation on horizontal from relative sunshine duration for two weather stations in the United Arab Emirates (UAE), which are Abu Dhabi and Al Ain. These expressions include the original Angstrom-Prescott regression function (linear), quadratic function, third-order function, single-term exponential function, power function, logarithmic, and linear-logarithmic function. The predicted values were compared to the measured values using number of statistical methods to validate the goodness of the fits, such as residual analysis and goodness of fit statistics. All the used mathematical models performed generally well in both cities of Abu Dhabi and Al Ain, with all values of the coefficient of determination (

Solar radiation is a primary factor in many applications, such as solar energy systems, architecture, agriculture, and irrigation. Despite the significance of solar radiation measurements, they are not yet available everywhere in the world. Due to the cost and maintenance and calibration requirements, this information is not readily available in many developing countries [

In [

The potential of solar radiation in UAE is significant, with an average annual solar hours of 3568 h (i.e., 9.7 h/day), which corresponds to an average annual solar radiation of approximately 2285 kWh/m^{2} (i.e., 6.3 kWh/m^{2} per day) [

UAE map showing the location of Abu Dhabi and Al Ain.

Several types of regression models have been proposed in the literature for predicting global solar irradiance on horizontal from the daily sunshine hours and extraterrestrial solar radiation. Table ^{2 }[

Regression models used in this paper.

Model (source) | Regression model |
---|---|

Linear (Angstrom-Prescott [ | |

Quadratic (Akinoglu and Ecevit [ | |

Third order (Samuel [ | |

Logarithmic (Ampratwum and Dorvlo [ | |

Linear-logarithmic (Newland [ | |

Exponential (Elagib and Monsell [ | ^{(bR)}_{S} |

Power (Coppolino [ |

As shown in Table

The main objective of this research work is to obtain the correlation coefficients for seven different regression models for Abu Dhabi and Al Ain. To produce the regression equations, daily weather data for Abu Dhabi (Latitude: 23.5°N, Longitude: 54.5°E, and Elevation: 6 m) and Al Ain (Latitude: 24°16′ N, Longitude: 55°36′ E, and Elevation: 250 m) were obtained from the National Center of Meteorology and Seismology (Abu Dhabi, UAE). The obtained weather data includes measured daily global solar radiation on horizontal and daily sun hours for an observation period of 13 years.

The proposed regression models (Table

MATLAB was used to compute the coefficients and to compare between the seven regression models statistically in order to find the best predictive model. Number of statistical methods was used to validate the accuracy and goodness of the fits. These methods included the residual analysis and goodness of fits statistics, such as the coefficient of determination (

Equation (

The coefficients of the seven regression models used in this work are reported in Table

Correlation coefficients.

Station | Model | ||||
---|---|---|---|---|---|

Abu Dhabi | Linear | 0.1833 | 0.5301 | ||

Quadratic | 0.1890 | 0.8450 | −0.3900 | ||

Cubic | 0.4201 | 0.5292 | − 0.7771 | 0.5211 | |

Exponential | 0.5399 | 0.1630 | |||

Logarithmic | 0.6290 | 0.1053 | |||

Linear-logarithmic | 0.7621 | −0.16268 | 0.08576 | ||

Power | −0.4698 | 0.034 | |||

Al Ain | Linear | 0.1833 | 0.6478 | ||

Quadratic | 0.6351 | 0.0966 | −0.0255 | ||

Cubic | 0.4411 | 0.8292 | − 0.9771 | 0.4211 | |

Exponential | 0.6416 | 0.099 | |||

Logarithmic | 0.6858 | 0.0153 | |||

Linear-logarithmic | 0.7081 | −0.01268 | 0.01276 | ||

Power | −0.4058 | 0.00014 |

Goodness of fit statistics for the used regression models.

Station | Model | ^{2} | MAPE | MBE | MABE | RMSE | SSR | SST |
---|---|---|---|---|---|---|---|---|

Abu Dhabi | Linear | 94% | 1.89 | −0.0035 | 0.1080 | 0.1330 | 17.751 | 18.862 |

Quadratic | 90% | 1.94 | 0.0094 | 0.1162 | 0.1529 | 16.979 | 18.863 | |

Cubic | 91% | 1.75 | 0.0006 | 0.1038 | 0.1324 | 17.209 | 18.861 | |

Exponential | 88% | 2.23 | 0.0370 | 0.1338 | 0.1742 | 16.628 | 18.878 | |

Logarithmic | 88% | 2.39 | 0.0148 | 0.1410 | 0.1777 | 16.687 | 18.864 | |

Linear-logarithmic | 87% | 3.11 | 0.0151 | 0.1799 | 0.2141 | 16.449 | 18.864 | |

Power | 88% | 2.52 | 0.0077 | 0.1474 | 0.1825 | 16.682 | 18.862 | |

Al Ain | Linear | 81% | 3.39 | −0.1341 | 0.1751 | 0.2173 | 16.328 | 20.766 |

Quadratic | 83% | 3.15 | −0.0068 | 0.1935 | 0.2134 | 16.610 | 19.919 | |

Cubic | 83% | 3.06 | 0.0016 | 0.1881 | 0.2078 | 16.497 | 19.918 | |

Exponential | 81% | 3.32 | 0.0053 | 0.2142 | 0.2592 | 16.166 | 19.919 | |

Logarithmic | 84% | 3.45 | 0.1040 | 0.2131 | 0.2332 | 16.794 | 20.048 | |

Linear-logarithmic | 83% | 3.07 | −0.0059 | 0.1896 | 0.2104 | 16.505 | 19.918 | |

Power | 74% | 4.10 | 0.2658 | 0.2781 | 0.3685 | 15.351 | 20.766 |

The residual analysis showed that the fitting error for the developed models are scattered randomly around zero, which indicates a good fit as illustrated in Figures

Residual analysis for Abu Dhabi.

Residual analysis for Al-Ain.

Regarding RMSE values, all models resulted in very small values of RMSE for both cities of Abu Dhabi and Al Ain. The cubic model (Samuel) gave the smallest MAPE for Abu Dhabi and Al Ain, 1.75 and 3.06, respectively.

The regression coefficients obtained for Abu Dhabi are different than those of Al Ain. The variations between the measured data of monthly average daily global radiation for Abu Dhabi and Al Ain and its calculated counterparts for the seven different regression models are shown in Figures

(a–g) Comparison between the measured and the calculated values of the monthly average daily global solar radiation using seven different regression models for Abu Dhabi, UAE.

(a–g) Comparison between the measured and the calculated values of the monthly average daily global solar radiation using seven different regression models for Al-Ain, UAE.

It is obvious that all regression models except the power (Coppolino) model performed almost with the same degree of accuracy in Al Ain. In order to come up with a more accurate regression models, several estimators (models) can be used to predict the monthly average daily global radiation on horizontal across the year. For example, the power model performed very well in the winter months (Dec, Jan, Feb, and Mar) in Al Ain as shown in Figure

Regarding the MBE, underestimation of the solar radiation on horizontal for the linear Angstrom-Prescott model was noted in both cities of Abu Dhabi and Al Ain. A negative value gives the average amount of underestimation in the predicted values and vice versa. The third-order model offered the lowest values of MBE compared to the other used models in both Abu Dhabi and Al-Ain stations, 0.0006 and 0.0016, respectively. Also the third-order model performed best regarding RMSE for both stations, with approximately 0.1324 in Abu Dhabi and 0.2078 in Al-Ain.

It can be noted that all regression models in Al-Ain failed to provide a value of

Many regression models that estimate global solar radiation using more readily meteorological data were proposed in literature. A number of sunshine duration regression models have been studied and analyzed to estimate monthly average daily global solar radiation on horizontal in both cities of Abu Dhabi and Al Ain, UAE. In general, all models performed well with minimum

Solar constant (W/m^{2})

Site latitude (deg)

Solar declination angle (deg)

Sun rise hour (deg)

Global solar radiation on horizontal (kWh/m^{2})

Extraterrestrial radiation (Wh/m^{2})

Number of the day in the year

Clearness index

Monthly average daily sun hours (h)

Monthly average maximum possible daily sun hours (h)

The sunshine hours ratio

Coefficient of determination (kWh/m^{2})

Measured monthly global solar radiation on horizontal (kWh/m^{2})

Calculated monthly global solar radiation on horizontal (kWh/m^{2})

Number of samples

Mean absolute percentage error (kWh/m^{2})

Root mean square error (kWh/m^{2})

Mean absolute bias error (kWh/m^{2})

Mean bias error (kWh/m^{2})

Sum of squares of the regression (kWh/m^{2})

Total sum of squares (kWh/m^{2}).

The authors would like to thank the National Center of Meteorology and Seismology (Abu Dhabi) for providing weather data. This work was financially supported by the UAE University under the Contract no. 07-04-7-11/09.