Developing Mathematical Models for Global Solar Radiation Intensity Estimation at Shakardara, Kabul
Hydrometeorology Department, Faculty of Geosciences, Kabul University, Kabul, Afghanistan.
Abstract
Solar energy properties such as Global Solar Radiation (GSR) intensity could be determined in either methods, experimentally or theoretically. Unfortunately, in most countries including Afghanistan, the first method which is more acceptable, but due to the high cost, maintenance and calibration requirements is not available. Therefore, an alternative widely used way is the second one which is model developments based on the meteorological (atmospheric) data; specially the sunny hours. The aim of this study at Shakardara area is to estimate atmospheric transparency percentage on 2017, determining the angstrom model coefficients and to introduce a suitable model for global solar radiation prediction. The hourly observed solar radiation intensity H (WHm-2) and sunshine hours data at Shakardara Snow Survey Station for a full year 2017 were used to determine the Angstrom model coefficients for a linear and a nonlinear correlation. Then, by the application of solver function in Excel, the residuals for all correlations were minimized to obtain our linear and nonlinear models coefficients. Finally, to show the accuracy of models, Root Mean Square Error (RMSE) and Mean Bias Error (MBE) indices for all models are calculated and the estimated H data of three models are compared with the observed one to provide a graphical picture of models’ accuracy. The results show an average value of 54% atmospheric transparency of sunny hours which was 2441 hours per year and 33% atmospheric transparency of monthly mean daily GSR which is 123.61 WHm-2. Moreover, the angstrom model’s coefficients found to be a=-0.1 and b=0.9 while for our linear model the same coefficients determined to be a=0 and b=0.6. Calculation of RMSE and MBE for each model showed that the suggested models for GSR predicting in Shakardara area could be ordered from most accurate to less one as our nonlinear model with 99.16%, angstrom modified model with 96.67% and our linear model with 95.56%.
Keywords:Solar Radiation, Angstrom Model, Transparency, Solar Constant, Shakardara.
1. Introduction
Energy is the unique power reason for all kind of developments in the present world. Hence, knowing some adequate, measured and trustable information about the solar power state of a region is a must essential. Solar energy properties (Global Solar Radiation (GSR) or Solar Radiation Intensity (SRI), sunshine duration hours, sunbeam incidence angle, sunrise/sunset hour angle and day lengths) could be determined in many ways: experimentally and theoretically. Unfortunately, in most developed countries the first method which is more acceptable, but due to the high cost, maintenance and calibration requirements is not available [1]. Moreover, because of different reasons; there is always some gaps in the observed GSR data series while for most of the solar based projects, a long period continuous GSR data set is required. Therefore, an alternative widely used way is the second one which is based on the meteorological (atmospheric) data; specially the sunny hours. Sunshine hours could be easily measured and is much more effective factor than other meteorological data on solar energy. Because of this, many empirical and mathematical models are developed, calibrated then adjusted and confirmed for specific areas and somehow worldwide. The inputs of most of these models is meteorological data sets such as air temperature, relative humidity, wind speed, sunshine hours and solar radiation which is easily available at many meteorological stations [2
]. Among many different models, the general form of Angstrom model is mostly famous to be used around the world. The operation of this model is based on sunshine hours data as input to find the GSR. This model correlates the ratio of solar energy and sunny hours on the top of atmosphere to the same two parameters on the ground level [3
]. It means that the Angstrom model is showing the clearness index of the atmosphere in a specific area. The main aim of this study is to determine the Angstrom’ model coefficients values firstly, and then to elaborate mathematical models for estimation of GSR from sunshine hours at the snow survey station (SSS) of Shakardara in Kabul province based on the general form of Angstrom model. Although, some similar studies were conducted in other countries, but there is no any empirical developed model to estimate the solar energy intensity for Afghanistan context yet. GSR has been determined either experimentally measurements or mathematically estimates in many countries. For instance, Aljawi, et al. [4
] have measured the solar ultraviolet radiation intensity at ground level in Bangi, Malaysia on 2014. Also, the total and spectral solar radiation irradiance (300–1100 nm) have been measured by Duay [5
] at the same region in Malaysia. He used in his experiment a fiber optic spectrometer (AvaSpec ULS 2048x64-USB- spectrometer) and has done the measurements for 18 days within Jan – Mar 2014 in the direction of zenith sky. These two studies were conducted to apply a direct measurement of the GSR intensity using AvaSpec spectrometer. The focused point for both studies were selected at the National University of Malaysia (UKM) with coordinates of 2.92oN, 101.7o E at 50 meters above the sea level. Moreover, Harees, et al. [6
]; at Iran, Togrul [7
] at Kyrgyzstan, Muzathik, et al. [8
], Muzathik, et al. [9
] at Terengganu, Malaysia, Taha at Egypt [10
] and Gana and Akpootu on 2013 at Nigeria [11
] have estimated the solar radiation intensity based on meteorological data using different mathematical models.
2. Materials and Method
Figure-1. Kabul province administrative map and Shakardara snow survey location.
In the first step, the components of Angstrom model were calculated to correlate the two different transparency indices based on the Angstrom (1924) model [9
]. The Angstrom model is given as:
2.1. Comparison Techniques
To show the accuracy of models’ operation and compare the estimated data of different models, some statistical quantities and indices for all models are calculated. Also, the estimated values of three models are graphically compared with the observed one to provide a pictorial insight of the models’ accuracy. In our case, the coefficient of correlation (r), the Mean Bias Error (MBE) and the Root Mean Square Error (RMSE) are calculated to test the models’ operation and to compare the models’ predicted values with those of measured.
The coefficient of correlation
The coefficient of correlation for both linear and nonlinear could be obtained as Yazdanpanah, et al. [3]:
As we can see RMSE, could have only positive values and a model with a best performance will have a value of RMSE, very close to zero. The more greater the value of RMSE, the poor accuracy of predicted value of H by the model.
3. Results and Discussions
Some solar properties for Shakardara SSS are calculated to establish the correlation between two transparency indices ( and ) and hence, to determine the angstrom model empirical constants and . Also, before creating the correlation, the monthly variation of the above indices is plotted to show the trend of model variables. The calculated solar properties and the trend of the transparency indices are presented in Table 1 and Figure 2, respectively.
As we can see in Table 1, the average value of the solar radiation that could penetrate to atmosphere and reaches to the ground surface at Shakardara area is around 33% of the solar extraterrestrial radiation. This is equivalent to 10.94 which is around third parts of the average value of the solar constant. Moreover, in an average day length of 11.99 hrs, the mean value of sunny hours is 6.67 hrs. This means that the average transparency rate of atmosphere based on sunshine hours in Shakardar is 53.79%.
Table-1. Some Solar Properties at Shakardara SSS in 2017.
Figure-2.Monthly Variation of Atmospheric Transparency at Shakardara SSS in 2017.
The monthly variation of atmospheric transparency indices in Figure 2 are closely parallel and hence, a pretty correlation could be established between them. Establishing a linear correlation between results in Angstrom model coefficients determination. The linear correlation between the aforementioned atmospheric transparency indices is plotted in Figure 3 (a). with
which is in the acceptable range of correlation coefficient. Also, a nonlinear correlation between
is created as in Figure 3 (b). to obtain a more accurate relation for monthly mean daily GSR estimation at Shakardar area.
Figure-3.(a) Linear Correlation between H/H0 and S/S0 and (b) nonlinear Correlation between H/H0 and S/S0.
Based on the linear correlation between S/S0 and H/H0. the angstrom model coefficients a and b are found to be -0.134 and 0.865 respectively. Moreover, this angstrom’s modified model was used to predicted the monthly mean value of daily GSR and the results were compared with those of measured one at Shakardara SSS. By applying the so called “residual minimization method” and using Solver Function of Excel, we have compared the measured and predicted values of angstrom modified model and the nonlinear model to obtain our linear and nonlinear models respectively. Some properties of the angstrom modified model and our linear and nonlinear models are presented in Table 2.
Table-2. Suggested parameters for different models to estimate the monthly mean daily GSR on horizontal surface at Shakardara SSS.
As it is obvious from Table 2, the RSME values range between 0.5 to 4.0 with the smallest value for our nonlinear polynomial model (=0.5) and the largest value is for our linear model. Hence, the most accurate monthly mean daily GSR data could be predicted using our curved model. Moreover, the values of MBE show that all models are predicting an overestimate of the observed data. However, our curved model predicts the monthly mean daily GSR with the smallest overestimates error. The statistical analysis and comparison of all models’ predicted data with that of observed one gives the reliability of model’s operation. As we can see in Table 2, the predicted data using our curved model is corresponding to the measured data with 99.16% accuracy.
Figure-5. Correlation between measured monthly mean daily GSR data and predicted radiation.
As we can see in Figure 4, the trend of all model’s predicted data is mostly parallel to that of observed data. The models work very well in the months with low values of GSR except in March and the most deviation of predicted data is occurred in the hot season especially in Jun. Moreover, Figure 5 illustrates that the most accurate GSR data is produced by our nonlinear model which is about 99.16% of the measured data and the most less accurate GSR data (about 96.67% of the measured data) is predicted by our linear model. However, both Figure 4 and 5 extremely recommend our nonlinear model to estimate the GSR based on sunshine duration hours in Shakardara areas.
4. Conclusion
This research was aimed to calculate the transparency rate and to elaborate some mathematical models for estimation of global solar radiation at horizontal ground surface in Shakardara area and anywhere with similar climate conditions. Hence, we have tried to determine the Angstrom model coefficients and elaborate two other mathematical models for solar radiation estimation based on sunny hour available data at Shakaradara district. The results show that Shakardara area is 54% sunny over the year and receiving around 33% of all incoming solar radiation energy on the top of atmosphere. Moreover, among three examined models, our polynomial model is highly recommended to be used for global solar radiation intensity based on sunshine hours data. This is helpful since most of the time the hydrometeorological stations are not equipped with actinometric instruments.
| DOI:10.53894/ijirss.v4i2.68 Funding: The author would like to thank the AFGSolar1 conference for providing financial support and to NWARA for providing the data. History: Received: 8 January 2021/Revised: 22 February 2021/Accepted: 16 March 2021/Published: 30 March 2021. Competing Interests: The authors declare that they have no conflict of interests. Transparency: The author confirms that the manuscript is an honest, accurate, and transparent account of the study was reported; that no vital features of the study have been omitted; and that any discrepancies from the study as planned have been explained Ethical: This study follows all ethical practices during writing |
References
[1] M. J. Ahmad and G. N. Tiwari, "Solar radiation models- review," International Journal of Energy and Engvironment, vol. 1, pp. 513-532, 2010.
[2] N. Adeniji, J. Adeniji, and O. Ojeikere, "Global solar radiation, sunshine-hour distribution, and clearness index: A case study of Sub-Sahara Region in Nigeria," Renewable Energy Research and Application, vol. 1, pp. 161-174, 2020.
[3] H. H. Yazdanpanah, R. Mirmujrebian, and H. Barqi, "Estimation of global solar radiation on horizontal ground surface at Esfahan," Geography and Environmental Planning, vol. 37, pp. 95 – 104, 2010.
[4] O. Aljawi, G. Geri, and A. B. Duay, Measurement of the solar ultraviolet radiation at ground level in Bangi. Malaysia: American Institute of Physics, 2015.
[5] A. B. Duay, Measurement of the solar radiation intensity in the zenith sky direction using a spectrometer in January– March 2014 at Bangi. Malaysia: Bangi, 2014.
[6] A. M. Harees, S. Zendparsa, A. Sepaskhowah, and M. J. Nazemossadat, "Assessment and development of solar radiation estimation models based on sunny hours and meteorological data," Agriculture and Natural Resources Sciences and Techniques, vol. 46, pp. 491-499, 2008.
[7] I. T. Togrul, "Estimation of solar radiation from Angstroms coefficients by using geographical and meteorological data in Bishkek, Kyrgyzstan," Journal of Thermal Science and Technology, vol. 29, pp. 99-108, 2009.
[8] A. M. Muzathik, W. M. N. W. Nik, K. Samo, and M. Z. Ibrahim, "Hourly global solar radiation estimates on a horizontal plane," Journal of Physical Science, vol. 21, pp. 51-66, 2010.
[9] A. Muzathik, W. Nik, M. Ibrahim, K. Samo, K. Sopian, and M. Alghoul, "Daily global solar radiation estimation based on sunshine hours," International Journal of Mechanical and Materials Engineering, vol. 6, pp. 75-80, 2011.
[10] H. A. T. Taha and T. Ahmed, "Estimation of hourly global solar radiation in Egypt using mathematical model," International Journal of Latest Trends in Agriculture & Food Sciences,, vol. 2, pp. 74-82, 2012.
[11] Daily Total, Daily total solar radiation and sunny hours recorded at automatic snow survey stations over 1 hour. Kabul, 2018.
[12] N. Gana and D. Akpootu, "Angstrom type empirical correlation for estimating global solar radiation in north-eastern Nigeria," The International Journal Of Engineering And Science, vol. 2, pp. 58-78, 2013.