Prediction of monthly mean daily diffuse solar radiation using artificial neural networks and comparison with other empirical models

An artificial neural network (ANN) model for estimating monthly mean daily diffuse solar radiation is presented in this paper. Solar radiation data from 9 stations having different climatic conditions all over China during 1995–2004 are used for training and testing the ANN. Solar radiation data from eight typical cities are used for training the neural networks and data from the remaining one location are used for testing the estimated values. Estimated values are compared with measured values in terms of mean percentage error (MPE), mean bias error (MBE) and root mean square error (RMSE). The results of the ANN model have been compared with other empirical regression models. The solar radiation estimations by ANN are in good agreement with the actual values and are superior to those of other available models. In addition, ANN model is tested to predict the same components for Zhengzhou station over the same period. Results indicate that ANN model predicts the actual values for Zhengzhou with a good accuracy of 94.81%. Data for Zhengzhou are not included as a part of ANN training set. Hence, these results demonstrate the generalization capability of this approach and its ability to produce accurate estimates in China.     

Computation of monthly mean daily global solar radiation in China using artificial neural networks and comparison with other empirical models

In this paper, an artificial neural network (ANN) model is developed for estimating monthly mean daily global solar radiation of 8 typical cities in China. The feed-forward back-propagation algorithm is applied in this analysis. The results of the ANN model and other empirical regression models have been compared with measured data on the basis of mean percentage error (MPE), mean bias error (MBE) and root mean square error (RMSE). It is found that the solar radiation estimations by ANN are in good agreement with the measured values and are superior to those of other available empirical models. In addition, ANN model is tested to predict the same components for Kashi, Geermu, Shenyang, Chengdu and Zhengzhou stations over the same period. Data for Kashi, Geermu, Shenyang, Chengdu and Zhengzhou are not used in the training of the networks. Results obtained indicate that the ANN model can successfully be used for the estimation of monthly mean daily global solar radiation for Kashi, Geermu, Shenyang, Chengdu and Zhengzhou. These results testify the generalization capability of the ANN model and its ability to produce accurate estimates in China.     

Empirical model development and comparison with existing correlations

This study utilized monthly mean daily values of global solar-radiation and sunshine duration at 41 locations in Saudi Arabia and developed an empirical correlation for the estimation of global solar radiation at locations where it is not measured. The paper also presents the comparison between the present correlation and other models developed under different geographical and varied meteorological conditions. The comparisons are made using standard statistical tests, namely mean bias error (MBE), root mean square error (RMSE), mean percentage error (MPE), and mean absolute bias error (MABE) tests. The errors are calculated using monthly mean daily measured and estimated values of global solar radiation at all 41 locations. The study found that the present correlation produced the best estimates of global solar radiation.     

Estimation of global and diffuse radiation at Tripoli

Different correlations were used to predict monthly average global and diffuse radiation on a horizontal surface at Tripoli. The estimated results are then compared with the experimental data for the year 1989–1990. Using statistical tests the RMSE, MBE and MABE to evaluate these correlations, it was found that the Dogeniaux-Lemoin, and the Erbs-Klein and Duffie correlations are the best to predict the global and the diffuse radiation respectively.     

Estimation of horizontal diffuse solar radiation with measured daily data in China

Three most widely used diffuse radiation models are calibrated using the daily data between January 1 1994 and December 31 1998 from 16 stations all over China. The second-degree polynomial relationship between R_D/R_G and n/N (Iqbal model) is suitable for diffuse radiation estimation in China. The averaged correlation coefficient R² is 0.84 and the maximum value is 0.93 at the 16 stations, and the Iqbal model works better in the eastern part of China than in the west. The A.A. El-Sebaii model could not be used to estimate diffused radiation accurately in China, with an averaged R²=0.47. The Liu and Jordan model could also be used for diffuse radiation estimation in China, and the averaged value of R² and parameter X₀ is 0.81 and 0.233, respectively. There is an evident linear relationship among the parameters X₀, a and b of the Liu and Jordan model.     

Estimation of daily diffuse solar radiation in China

Applying the measured global and diffuse solar radiation data from 78 meteorological stations in China, a countrywide general correlation model for calculating the daily diffuse radiation was derived on the basis of Liu and Jordan method. Two widely used statistics: root mean square error and mean bias error were used to assess the performance of the correlation. And the correlation shows good behavior when applied to most of the stations. Subsequently, with the measured data from the 78 stations, an analysis of geographical distribution of solar energy resource in China was also presented in the form of clearness index (the ratio of global solar radiation to extraterrestrial radiation) percentage frequency, and results show that the solar energy resource in western and northern China is relatively abundant.     

Estimation of monthly averaged direct normal solar radiation using elevation angle for any location

Light concentrators used in solar photovoltaic and solar thermal applications, and concentrates light by a factor of 10 or more, use only direct normal solar radiation, I_N. A new method, called elevation angle constant (EAC) method, is developed to determine the resource potential of I_N for different locations. This method is applicable to estimate the I_N at any location in the world. The EAC method is based on empirical relations. The method calculates the elevation angle constant (ε) for a given location and time. It uses readily available daily global and diffuse global radiation data to estimate the I_N. This is different from existing methods which invariably uses hourly global and diffuse radiation. The values of I_N are estimated for 12 locations across the world. The values of I_N obtained using the EAC method have been compared with values obtained using the model-based approach (Appendix-1). The comparison is also done with the measured values for some stations. Ninety percent of the estimated values of I_N using the EAC method for the stations like Angola, Egypt, Kuala Lumpur, Singapore, Brussels, Stuttgart, Ottawa, Birmingham, Los Angeles, Wellington, Perth and New Delhi are within ±5% of the values estimated by the model-based approach (Appendix-1).     

Estimation of monthly global solar radiation from sunshine duration measurement in Elazi

In this study, the relation between a and b terms and / was investigated to estimate the global solar radiation in Elazi by using different regression analyses. Equations which contain the whole year and two different periods, winter and summer, were developed. Eqs. (5)–(7) which represent second, third and fourth degree equations respectively, gave the best results in all of the equations having an error less than 1%. Contrary to expectations, the equations developed for summer and winter periods had higher errors than the others.     

Quality control and estimation of global solar radiation in China

Measurements of surface radiation in China are too sparse to meet demand for scientific research and engineering applications. Moreover, the radiation data often include erroneous and questionable values though preliminary quality-check has been done before the data release. Therefore, quality control of radiation data is often a prerequisite for using these data. In this study, a set of quality-check procedures were implemented to control the quality of the solar radiation measurements at 97 stations in China. A hybrid model for estimating global solar radiation was then evaluated against the controlled data. The results show that the model can estimate the global radiation with accuracy of MBE less than 1.5 MJ m⁻² and RMSE less than 2.8 MJ m⁻² for daily radiation and RMSE less than 2.0 MJ m⁻² for monthly-mean daily radiation at individual stations over most of China except at a few stations where unsatisfactory estimates were possibly caused by severe air pollution or too dense clouds. The MBE averaged over all stations are about 0.7 MJ m⁻² and RMSE about 2.0 MJ m⁻² for daily radiation and RMSE about 1.3 MJ m⁻² for monthly-mean daily radiation. Finally, this model was used to fill data gaps and to expand solar radiation data set using routine meteorological station data in China. This data set would substantially contribute to some radiation-related scientific studies and engineering applications in China.     

Estimation of monthly average daily global solar irradiation using artificial neural networks

This study explores the possibility of developing a prediction model using artificial neural networks (ANN), which could be used to estimate monthly average daily global solar irradiation on a horizontal surface for locations in Uganda based on weather station data: sunshine duration, maximum temperature, cloud cover and location parameters: latitude, longitude, altitude. Results have shown good agreement between the estimated and measured values of global solar irradiation. A correlation coefficient of 0.974 was obtained with mean bias error of 0.059 MJ/m² and root mean square error of 0.385 MJ/m². The comparison between the ANN and empirical method emphasized the superiority of the proposed ANN prediction model.     

Investigating different diffuse solar radiation models to analyse solar radiation on inclined surfaces in Oman

In this paper, a detailed analysis of the solar radiation on horizontal and tilted surfaces for six locations in Oman is presented. The locations are (from North to South): Majis/Sohar, Sur, Fahud, Masira, Marmul, and Salalah. These locations spread over Oman and cover different types of landscape. The method is validated through the use of measured data. The effect of tilt angle and orientation on the incident solar radiation is presented along with optimum surface tilt angles and directions for maximum solar radiation collection in these six locations. The solar radiation models used in this paper show good agreement with measured data. The results presented in this paper are extremely useful for quick estimation of solar radiation for calculations of buildings’ cooling load and solar collector system performance. This can be easily extended for other locations with similar landscapes and geographical conditions.     

Evaluation of sunshine duration from cloud data in Egypt

In this study, three empirical formulae have been deduced to estimate relative sunshine duration, n/N, using readily available observed data of cloud amount, C, in Egypt. The monthly mean values of n/N and C recorded at 34 stations during the period (1990–2005) have been used in the present study. The three deduced formulae have been verified for any locality in Egypt which lies above (zone 1) and below latitude 30° (zone 2) and for the whole country of Egypt. The agreement between measured and estimated values of the three deduced formulae were remarkable. It was found that the maximum possible error of estimated values, e (%), of the three deduced empirical formulae have not exceeded ±7.27% with mean percentage error (MPE) values range from −0.62% to +0.81%; meanwhile the values of statistical tests of main bias error (MBE) and root mean square error (RMSE) are very close to zero. It has been concluded that Egypt's deduced formula gives precise estimations for n/N and was recommended for use at any location in Egypt. The sunshine distribution and its percentage frequency over Egypt were also studied. The results revealed that latitudinal dependent of n/N. Egypt has minimum value of n/N (0.48) during January at the northern part of the country and maximum value (0.92) during June at the southern part.     

Estimation of monthly solar radiation distribution for solar energy system analysis

The concept of probability density frequency, which is successfully used for analyses of wind speed and outdoor temperature distributions, is now modified and proposed for estimating solar radiation distributions for design and analysis of solar energy systems. In this study, global solar radiation distribution is comprehensively analyzed for photovoltaic (PV) panel and thermal collector systems. In this regard, a case study is conducted with actual global solar irradiation data of the last 15 years recorded by the Turkish State Meteorological Service. It is found that intensity of global solar irradiance greatly affects energy and exergy efficiencies and hence the performance of collectors.     

Quality control of solar radiation data within the RMIB solar measurements network

Assessment of the solar resource is based upon measured data, where available. However, with any measurement there exist errors. Consequently, solar radiation data do not exhibit necessarily the same reliability and it often happens that users face time series of measurements containing questionable values though preliminary technical control has been done before the data release. To overcome such a situation, a major effort has been undertaken at the Royal Meteorological Institute of Belgium (RMIB) to develop procedures and software for performing post-measurement quality control of solar data from the radiometric stations of our in situ solar monitoring network. Moreover, because solar energy applications usually need continuous time series of solar radiation data, additional procedures have also been established to fill missing values (data initially lacking or removed via quality checks).     

Estimation of monthly-mean daily global solar radiation based on MODIS and TRMM products

Global solar radiation (GSR) is required in a large number of fields. Many parameterization schemes are developed to estimate it using routinely measured meteorological variables, since GSR is directly measured at a limited number of stations. Even so, meteorological stations are sparse, especially, in remote areas. Satellite signals (radiance at the top of atmosphere in most cases) can be used to estimate continuous GSR in space. However, many existing remote sensing products have a relatively coarse spatial resolution and these inversion algorithms are too complicated to be mastered by experts in other research fields. In this study, the artificial neural network (ANN) is utilized to build the mathematical relationship between measured monthly-mean daily GSR and several high-level remote sensing products available for the public, including Moderate Resolution Imaging Spectroradiometer (MODIS) monthly averaged land surface temperature (LST), the number of days in which the LST retrieval is performed in 1 month, MODIS enhanced vegetation index, Tropical Rainfall Measuring Mission satellite (TRMM) monthly precipitation. After training, GSR estimates from this ANN are verified against ground measurements at 12 radiation stations. Then, comparisons are performed among three GSR estimates, including the one presented in this study, a surface data-based estimate, and a remote sensing product by Japan Aerospace Exploration Agency (JAXA). Validation results indicate that the ANN-based method presented in this study can estimate monthly-mean daily GSR at a spatial resolution of about 5 km with high accuracy.     

Correlation of monthly-average daily global, diffuse and beam radiation with bright sunshine hours

Correlations between monthly-average daily radiation and bright sunshine hours for 11 Indian stations have been studied. It is found that the global radiation can be predicted to an accuracy of 0.5% by using the linear relation, G/G_ext = a + b (n/N). For diffuse radiation, three different correlations have been tried. For individual applications, any of the three correlations discussed in this paper can be used, but for collective applications, the correlation D/G_ext = a + b (n/N) gives better results. Beam radiation is found to be highly dependent upon the local conditions. To develop a single formula for 11 stations involves a large percentage of error. The Hay method [9] is comparable to the equation G/G_ext = a + b(n/N) for global radiation, but for diffuse radiation, the equation D/G_ext = a + b (n/N) is superior to the Hay method. The correlations for global and diffuse radiation are G/G_ext = 0.3156 + 0.4520(n/N) and D/G_ext = 0.3616 − 0.2123 (n/N), respectively.     

Analysis of experimental data on diffuse solar radiation in Athens,Greece, for building applications

Proper design and performance prediction of solar energy systems requires accurate information on the availability of solar radiation. The diffuse-to-total radiation correlation, originally developed by Liu and Jordan, has been extensively used as the technique and provided excellent results, although it was latitude dependent and not universally applicable. Thus, diffuse fraction correlations of this type have been developed by few other authors and for different location. This paper presents an analysis of hourly diffuse radiation on a horizontal surface. Hourly pyranometer data from Athens, Greece, are used to establish relationships between the diffuse fraction and the clearness index k _T for hourly and daily values. The results of the proposed equations are then compared with earlier equations. For the urban conditions of Athens the developed correlation fit to the empirical data.     

Evaluation and establishment of diffuse solar radiation models for Bursa,Turkey

The main objective of the present study is to evaluate the applicability of the diffuse solar radiation models from previous studies and establish new models for Bursa. Therefore, 35 regression models from previous studies in the literature are used and categorized as follows: (1) cloudness index is the function of clearness index; (2) cloudness index is the function of relative sunshine duration; (3) the diffuse coefficient is the function of the clearness index; and (4) the diffuse coefficient is the function of the relative sunshine duration. Also, new four diffuse solar radiation models were developed using 1968–2015 long-term global solar radiation and sunshine duration data. The new models are then compared with 35 empirical equations available in previous studies in terms of different statistical tests. Consequently, Models 6 and 8 are found as the most accurate and high-performance empirical models for estimation of the monthly mean diffuse solar radiation on a horizontal surface for Bursa, Turkey.     

Estimation of solar radiation components incident on Helwan site using neural networks

Field testing carried out for solar energy applications is costly, time consuming and depends heavily on prevailing weather conditions. Adequate security and weather protection must be provided at the test site. Measurements may also suffer from delays that can be caused by system failures and bad weather. To overcome these problems the need for accurate model becomes evermore important. To achieve such prediction task, an artificial neural network, ANN, model is regarded as a cost-effective technique superior to traditional statistical methods. In this paper, Levenberg optimization function is adopted to predict insolation data in different spectral bands for Helwan (Egypt) monitoring station. The predicted values were then compared with the actual values and presented in terms of usual statistics. The results hint that, the ANN model predicted infrared, ultraviolet, and global insolation with a good accuracy of approximately 95%, 93% and 96%, respectively. In addition, ANN model was tested to predict the same components for Aswan over an 11 month period. The predicted values of the ANN model compared to the actual values for Aswan produced an accuracy of 95%, 91% and 92%, respectively. Data for Aswan were not included as a part of ANN training set. Hence, these results demonstrate the generalization capability of this approach over unseen data and its ability to produce accurate estimates.     

Estimation of global solar radiation on horizontal surfaces in Jeddah, Saudi Arabia

The measured data of global solar radiation on a horizontal surface, as well as the number of sunshine hours, mean daily ambient temperature, maximum and minimum ambient temperatures, relative humidity and amount of cloud cover, for Jeddah (latitude 21° 42′37″N, longitude 39° 11′12″E), Saudi Arabia for the period 1996–2006 are analyzed. The data are divided into two sets. The sub-data set 1 (1996–2004) are employed to develop empirical correlations between the monthly average of daily global solar radiation fraction (H/H₀) and various meteorological parameters. The nonlinear Angström type model developed by Sen and the trigonometric function model proposed by Bulut and Büyükalaca are also evaluated. New empirical constants for these two models have been obtained for Jeddah. The sub-data set 2 (2005, 2006) are then used to evaluate the derived correlations. Comparisons between measured and calculated values of H have been performed. It is indicated that, the Sen and Bulut and Büyükalaca models satisfactorily describe the horizontal global solar radiation for Jeddah. All the proposed correlations are found to be able to predict the annual average of daily global solar radiation with excellent accuracy. Therefore, the long term performance of solar energy devices can be estimated.