Calibration of two Solar Radiation Models and Development of two One-Parametric Solar Radiation Models Based on the Cloudiness in Mashhad, Iran

Surface solar radiation is an important parameter in hydrological, meteorological, climatological and crop yield models. Some parameters such as precipitation and temperature are widely available. By contrast, direct measurements of surface solar radiation are very sparse in most regions, especially in highland and mountainous regions. Lack of adequate observations on solar radiation has ever been a persistent problem in studies of land-surface processes. Hence, alternative techniques are required to estimate solar radiation. Apart from astronomical and geographical factors, incoming solar radiation is strongly modified by cloud cover, the underlying surface albedo, atmospheric turbidity, absorption and scattering. Empirical models which express global solar radiation as a function of these variables have been proposed by various investigators. Since most proposed empirical models are not flexible but rather restrictive in their application, their suitability for a particular location would largely depend on validation against actual measurements. Mashhad is located at latitude 36º 17ʹ 45ʺ -N, longitude59º 36ʹ 43ʺ -E and at 992 meters altitude. Because of its situation, the city experiences different air masses and has a specific changing climate. Considering the Average temperature and precipitation (14.1 °C and 255.2 mm, respectively), the city has a semi-arid climate based on Demartonne Method. The average sunshine hours and solar radiation intensity in the city are about 2892 hours/ year and 195 W/m2, respectively. In this study, we used temperature data, sunshine hours, relative humidity and precipitation to estimate the solar radiation (Rs). To compare the estimated and measured data, we used the measured solar radiation by Pyranometer that is available for 10 years (1994-2003). Extraterrestrial radiation (Ra) was calculated by the equation obtained by Allen and his colleagues (Allen et al., 1998). In this study we investigated two solar radiation models - Angstrom–Prescott and Garg and Garg models- and determined their coefficients for Mashhad. For this purpose, the least squares error method was applied. To calculate coefficients of both equations, we used the MATLAB programming language. We used the data sets of 1994-2000 for calibration and 2001- 2003 for validation. Some of the radiation models are based on the cloudiness. Therefore in this study we developed 2 new radiation models based on cloudiness data. These two models are generally presented as equation 11 and 12: In these equations N is fraction of cloudiness (octal) and A, B, C, K and M are constant coefficients. Based on available data from 1994-2000, coefficients of Angstrom–Prescott Model were determined as a=0.25 and b=0.42. High determination coefficient (R2of 0.87 and 0.89 for calibration and validation respectively, and low RMSE (2.46 and 5.15) and MBE (-0.14 and -4.63) confirm that the coefficients are acceptable. Also coefficients of Garg and Garg model were determined as X=0.27, Y=0.42 and Z=-0.0028.The amounts of R2 (0.87 and 0.89 for calibration and validation stages), RMSE (2.45 and 5.08) and MBE (-0.11 and -4.56) show that the coefficients of Garg and Garg model are acceptable too. As mentioned before, Cloudiness is one of the most important parameters for determination of solar radiation and many equations were developed based on this parameter. Therefore, in this study, two models were developed based on cloudiness. The first equation obtained using 1994-2000 data sets are as follow: For these equations, determination coefficient is equal to 0.84 and 0.82, respectively. Although water vapor is effective on solar radiation and Angstrum-Prescott model is better than Garg and Garg model, but there isnt much difference between these two models. So, because of requiring less meteorological data than Garg and Garg model, Angstrum-Prescott model is suggested. Of the two developed models in this study, equation 1 has more accuracy and validity than equation 2. Meanwhile, developed models have higher accuracy compared to Angstrom-Prescott and Garg & Garg models. Also, we should consider the fact that, Angstrom-Prescott model for calculating the radiation requires two parameters, which from these two parameters the N value can be obtained. Additionally, this value may not be accurate for the study area. Overall, using developed Model 1 cab is recommended for this research when only cloudiness parameter is known.