Solar radiation models—A review

Solar radiation models for predicting the average daily and hourly global radiation, beam radiation and diffuse radiation on horizontal surface are reviewed in this article. Estimations of monthly average hourly global radiation from daily summations are discussed. It was observed that Collares‐Pereira and Rabl model as modified by Gueymard (CPRG) yielded the best performance for estimating mean hourly global radiation incident on a horizontal surface for Indian regions. Estimations of monthly average hourly beam and diffuse radiation are discussed. It was observed that Singh‐Tiwari and Jamil‐Tiwari both models generally give better results for climatic conditions of Indian regions. Therefore, their use is recommended for composite climate of Indian regions. Empirical correlations developed to establish a relationship between the hourly diffuse fraction and the hourly clearness index using hourly global and diffuse irradiation measurements on a horizontal surface are discussed. Fifty models using the Angstrom–Prescott equation to predict the average daily global radiation with hours of sunshine are considered. It was reported that Ertekin and Yaldiz model showed the best performance against measured data of Konya, Turkey. Copyright © 2010 John Wiley & Sons, Ltd.     

Global,direct and diffuse solar radiation on horizontal and tilted surfaces in Jeddah,Saudi Arabia

The measured data of global and diffuse solar radiation on a horizontal surface, the number of bright sunshine hours, mean daily ambient temperature, maximum and minimum ambient temperatures, relative humidity and amount of cloud cover for Jeddah (lat. 21°42′37′′N, long. 39°11′12′′E), Saudi Arabia, during the period (1996–2007) are analyzed. The monthly averages of daily values for these meteorological variables have been calculated. The data are then divided into two sets. The sub-data set I (1996–2004) are employed to develop empirical correlations between the monthly average of daily global solar radiation fraction (H/H₀) and the various weather parameters. The sub-data set II (2005–2007) are then used to evaluate the derived correlations. Furthermore, the total solar radiation on horizontal surfaces is separated into the beam and diffuses components. Empirical correlations for estimating the diffuse solar radiation incident on horizontal surfaces have been proposed. The total solar radiation incident on a tilted surface facing south H_t with different tilt angles is then calculated using both Liu and Jordan isotropic model and Klucher’s anisotropic model. It is inferred that the isotropic model is able to estimate H_t more accurate than the anisotropic one. At the optimum tilt angle, the maximum value of H_t is obtained as ∼36 (MJ/m² day) during January. Comparisons with 22 years average data of NASA SSE Model showed that the proposed correlations are able to predict the total annual energy on horizontal and tilted surfaces in Jeddah with a reasonable accuracy. It is also found that at Jeddah, the solar energy devices have to be tilted to face south with a tilt angle equals the latitude of the place in order to achieve the best performance all year round.     

An assessment of the solar radiation climate of the Cyprus environment

The solar radiation climate of Athalassa, Cyprus, is reported upon in detail. The database utilized in this analysis consisted of daily global and diffuse radiation on a horizontal surface, and global radiation on tilted surfaces, together with the calculated daily values of horizontal beam radiation. In addition, the data reported here include maximum and minimum temperature, relative humidity and percentage of possible sunshine. Monthly average hourly global and diffuse radiation for the time interval 5 a.m.–7 p.m. are reported and analyzed. The annual means of the daily global, diffuse and beam solar radiation on a horizontal surface are about 17.26, 5.75 and 12.35 MJ m⁻², respectively. The average monthly fraction of daily horizontal global radiation that is beam radiation varies from 0.61 in February to 0.77 in September. The average monthly clearness index varies from 0.636 in July to 0.491 in December, whereas the ratio of diffuse to global radiation varies from 0.494 in February to 0.257 in July. The solar radiation climate of the Cyprus environs has also been compared to those reported for two neighbouring countries. We conclude, based upon the above analysis, that Athalassa and its environs are characterized on average, by relatively high daily irradiation rates, both global and beam, and a relatively high percentage of clear days.     

DIFFUSE AND GLOBAL SOLAR RADIATION CORRELATIONS FOR JORDAN

Widely used correlations, for estimating both the monthly average global and diffuse radiations incident on a horizontal surface, have been statistically compared to recommend ones that best fit the measured radiation data in Jordan

The recommended correlations were further modified, by estimating the various coefficients of these correlations based on Jordanian data, to increase their accuracy in predicting both the global and diffuse radiation in Jordan. Finally a good agreement was obtained between the measured radiation data and the predicted data using the modified correlations.     

Correlations for estimating solar radiation using sunshine hours and temperature measurement in Osogbo,Osun State,Nigeria

In this study, the global solar radiation on horizontal surface in Osogbo, Osun state, Nigeria was analyzed using 11-year data (1997–2007). Correlations using linear and quadratic expressions were developed to relate the global solar radiation on horizontal surface based on relative sunshine hours and temperature measurements for evaluating the monthly average daily global solar radiation. The calculated monthly clearness index values indicate that the prevailing weather condition in Osogbo is heavily overcast. All the developed quadratic correlations gave better correlation coefficients (0.834, 0.872 and 0.823 respectively) than the linear models. However, the Hargreaves and Samani related based quadratic model gave the best among the three developed quadratic expressions and is therefore suggested for estimating the monthly global radiation in this site and its surroundings.     

Experimental and theoretical investigation of global and diffuse solar radiation in the United Arab Emirates

In the present study, the global, direct and diffuse components of solar radiation as well as temperature, relative humidity and wind speed have been continuously monitored and analysed on an hourly, daily and monthly basis. The monthly average daily total solar radiation varies from 2700 W h/m² in December to 8000 W h/m² in June with an average clearness index of 0.65. Experimental data are compared to the predictions of different theoretical models as functions of declination and hour angles. Correlations are obtained describing the variation of hourly, daily and monthly averages of total and diffuse solar radiation using polynomial expressions. Empirical correlations describing the dependence of the daily average diffuse to total radiation ratio on the clearness index are also obtained. Data for the daily diffuse to total radiation ratio are compared to correlations obtained by other investigators. The comparison shows a reasonable agreement with some scatter due to the seasonal dependence of the correlation. Comparison of calculations with experimental measurements under clear sky conditions show excellent agreement with a maximum error of 8%.     

Statistical comparison of correlations for estimation of global horizontal solar radiation

We evaluate the statistical performance of four correlations for estimating the monthly average daily horizontal global radiation. We have used bright sunshine and global radiation data for 140 locations around the world with varied meteorological conditions and geographical locations. The results show that Rietveld's equation generally gives the best estimates. Hay's correlation is next best, whereas the Glover-McCulloch relation gives the maximum error. The computations in this study are based on the most recently adopted solar constant.     

Analysis of the solar radiation data for Beer Sheva, Israel, and its environs

The solar radiation climate of Beer Sheva, Israel, is reported upon in detail. The database utilized in this analysis consisted of global radiation on a horizontal surface, normal incidence beam radiation, and global radiation on a south-facing surface tilted at 40°. Monthly-average hourly and daily values are reported for each of these three types of measured radiations, together with the calculated monthly-average daily values for the components of the global radiation, viz. the horizontal beam and diffuse radiations. The monthly-average hourly and daily clearness index values have also been calculated and analyzed. Monthly-average daily frequency distributions of the clearness index values are reported for each month. The solar radiation climate of Beer Sheva has also been compared to those reported for a number of countries in this region. The annual-average daily global radiation incident on a horizontal surface is 18.91 MJ/m² and that for normal incidence beam radiation is 21.17 MJ/m². The annual-average daily fraction of the horizontal global radiation that is beam is 0.72. The annual-average daily value for the clearness index is 0.587 and the average frequency of clear days annually is 58.6%. We conclude, based upon the above analysis, that Beer Sheva and its environs are characterized by relatively high, average-daily irradiation rates, both global and beam, and a relatively high frequency of clear days.     

Statistical comparison of correlations for estimation of the diffuse fraction of global radiation

We compare the statistical performance of eight correlations for estimating the diffuse fraction of the monthly daily global horizontal radiation with predicted monthly values of diffuse insolation for 40 locations in 15 countries with varied meteorological conditions and geographical locations. A new useful correlation is presented based on measured diffuse insolation records for selected stations. The correlations of Collares-Pereira and Rabl, Hay, and Page yield good estimates.     

Correlations between monthly average global solar radiation on horizontal surfaces and relative duration of sunshine in Yunnan Province, China

With measured data of global solar radiation and the relevant data of geographic and meteorological parameters at 7 meteorological stations in Yunnan Province, the correlations between monthly average global solar radiation on horizontal surfaces and relative duration of sunshine are developed in this special region which has significantly varying climates. It is believed that the two correlations developed in this work are applicable for estimating monthly global solar radiation on horizontal surfaces at any site in Yunnan Province, China.     

Solar radiation incident on tilted flat surfaces in Barcelona, Spain

Monthly averages of hourly irradiances upon a surface tilted toward the south in Barcelona, Spain, have been calculated from the global and diffuse average hourly solar irradiance on a horizontal surface computed over a period of three years (1973–1975). Similarly, daily irradiation on a monthly average and total annual irradiation for several inclinations were computed. Optimum slopes corresponding to a maximum incident energy were calculated from the annual average of daily solar irradiation, summer and winter, in the same way as the values of the inclination for which annual irradiation is maximum and minimum.     

Global solar radiation estimation with sunshine duration in Tibet,China

Eight models using only the sunshine duration for estimating the global solar radiation on a horizontal surface are evaluated at Changdu, Geer, Lasa and Naqu stations in Tibet, China against the measured meteorological data during 1994–2008. Based on statistical error tests, results show that the simple linear Ångström–Prescott model is reasonably accurate in practice, and the modifications with complex expression are not necessary in Tibet. Then, two general Ångström–Prescott models for estimating the daily and monthly average daily global solar radiation respectively in Tibet are proposed.     

Models of diffuse solar radiation

For some locations both global and diffuse solar radiation are measured. However, for many locations, only global is measured, or inferred from satellite data. For modelling solar energy applications, the amount of radiation on a tilted surface is needed. Since only the direct component on a tilted surface can be calculated from trigonometry, we need to have diffuse on the horizontal available. There are regression relationships for estimating the diffuse on a tilted surface from diffuse on the horizontal. Models for estimating the diffuse radiation on the horizontal from horizontal global that have been developed in Europe or North America have proved to be inadequate for Australia [Spencer JW. A comparison of methods for estimating hourly diffuse solar radiation from global solar radiation. Sol Energy 1982; 29(1): 19–32]. Boland et al. [Modelling the diffuse fraction of global solar radiation on a horizontal surface. Environmetrics 2001; 12: 103–16] developed a validated model for Australian conditions. We detail our recent advances in developing the theoretical framework for the approach reported therein, particularly the use of the logistic function instead of piecewise linear or simple nonlinear functions.Additionally, we have also constructed a method, using quadratic programming, for identifying values that are likely to be erroneous. This allows us to eliminate outliers in diffuse radiation values, the data most prone to errors in measurement.     

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.     

Solar constant values for estimating solar radiation

There are many solar constant values given and adopted by researchers, leading to confusion in estimating solar radiation. In this study, some solar constant values collected from literature for estimating solar radiation with the Ångström-Prescott correlation are tested in China using the measured data between 1971 and 2000. According to the ranking method based on the t-statistic, a strategy to select the best solar constant value for estimating the monthly average daily global solar radiation with the Ångström-Prescott correlation is proposed.     

Direct and diffuse solar radiation correlations for tilted surfaces in Athens, Greece

The solar energy available in the Athens, Greece area was determined in a previous publication by a processing of hourly measurements corresponding to a period of 20 years. Here, the same measurements are employed in conjunction with appropriate models for analysing total radiation in direct and diffuse components and for estimating the energy incident on tilted surfaces. Results include instant (kW/m²) and integrated (kJ/m² per day, month or year) values of the average direct, diffuse and total energy incident on tilted surfaces. These quantities are presented in the form of algebraic correlations having as independent variable time (hour, day, month), surface azimuth and angle of inclination to the horizontal plane.     

Solar radiation on Adana, Turkey

Measured monthly mean daily global radiation data for Adana (Lat. 37° 00′ N, Long. 35° 20′ E) has been used for estimating global horizontal solar-radiation. Hourly global, diffuse and direct solar-radiations on a horizontal surface in Adana have been determined.     

Calculation of monthly average insolation on tilted surfaces

Several simplified design procedures for solar energy systems require monthly average meteorological data. Monthly average daily totals of the solar radiation incident on a horizontal surface are available. However, radiation data on tilted surfaces, required by the design procedures, are generally not available. A simple method of estimating the average daily radiation for each calendar month on surfaces facing directly towards the equator has been presented by Liu and Jordan [1]. This method is verified with experimental measurements and extended to allow calculation of monthly average radiation on surfaces of a wide range of orientations.     

Solar radiation on tilted south oriented surfaces: validation of transfer-models

Three transfer-models in use for estimating solar radiation on tilted surfaces are tested. A 12 year series of hourly global, diffuse, and reflected solar irradiation measured with horizontal pyranometers as well as hourly global solar irradiation measured with tilted south oriented pyranometers is available. One model uses daily irradiation, the other two use hourly irradiation. The models converting hourly solar irradiation on a horizontal surface to a tilted surface yield better results than that using daily irradiation. The best results are gained if pairs of hourly global and diffuse solar irradiation are available. The root mean square errors exceed 10% only if the sky is covered by more than 85% with clouds or if the solar elevation angle is less than 10°.     

Measurement of solar energy radiation in Abu Dhabi,UAE

This paper presents data on measurement of actual solar radiation in Abu Dhabi (24.43°N, 54.45°E). Global solar radiation and surface temperatures were measured and analyzed for one complete year. High resolution, real-time solar radiation and other meteorological data were collected and processed. Daily and monthly average solar radiation values were calculated from the one-minute average recorded values. The highest daily and monthly mean solar radiation values were 369 and 290 W/m², respectively. The highest one-minute average daily solar radiation was 1041 W/m². Yearly average daily energy input was 18.48 MJ/m²/day. Besides the global solar radiation, the daily and monthly average clearness indexes along with temperature variations are discussed. When possible, global solar energy radiation and some meteorological data are compared with corresponding data in other Arab state capitals. The data collected indicate that Abu Dhabi has a strong potential for solar energy capture.