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.     

Evaluation of cloudiness/haziness factor for composite climate

In this communication, an attempt has been made to evaluate the cloudiness/haziness factor for the composite climate of New Delhi (latitude: 28.58° N; longitude: 77.02° E; elevation: 216 m above msl). To estimate the hourly variation of beam and diffuse radiation on a horizontal surface for any day, atmospheric transmittances for beam and diffuse radiation have been introduced to take into account the uncertain behaviour of atmospheric conditions. For the present study, the hourly data of global and diffuse solar radiation on a horizontal surface for a period of 10 years (1989–1998) have been used and analyzed using linear regression analysis. The data have been obtained from the Indian Meteorological Department, Pune, India. It has been observed that there is about 15% maximum deviation between predicted and observed values of hourly varying beam and diffuse radiation for clear (blue sky) weather condition.     

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.     

Statistical comparison of solar radiation correlations Monthly average global and diffuse radiation on horizontal surfaces

For most solar energy applications, it is necessary to predict the amount of global and diffuse radiation arriving on a horizontal surface at any specified location. Scientists have developed methods to achieve this using different input parameters. The purpose of this study is to compare statistically correlations for estimating the monthly average daily global/diffuse radiation incident on a horizontal surface and to recommend one in each catagory that best fits measured data from a number of locations chosen and is the simplest to use. The effects of using the new solar constant of 1367 W⁻² in these correlations are also investigated. As a result, Rietveld's and Page's correlations are recommended for estimating monthly average daily global and diffuse radiation incident on a horizontal surface, respectively. In addition, these correlations seem to be just as accurate with the new solar constant.     

Experimental testing of models for the estimation of hourly solar radiation on vertical surfaces at Arcavacata di Rende

More than 55,000 data of hourly solar radiation on a horizontal surface and on vertical surfaces exposed to the south, west, north and east, measured at Arcavacata di Rende (CS), were compared with hourly radiation data calculated by various calculation models.Erbs, Reindl et al. and Skartveit et al. correlations for the split of hourly global radiation in the diffuse and beam components were used together with the isotropic sky model and three anisotropic sky models.The agreement between experimental and calculated data is generally good.     

Estimation of symmetric and asymmetric hourly global and diffuse radiation from daily values

The validity of the correlations[1–3] to estimate the hourly global and diffuse solar radiation components for an independent dataset of fourteen locations is examined in this article. The correlations for the diffuse component[2,3] are found to be in rather poor agreement with the data. An improved correlation for the diffuse component that includes a daily diffuse fraction as a parameter is developed. The influence of this improved correlation on estimating the beam radiation component is examined. A convenient form of describing asymmetry for these three components of solar radiation distribution is proposed and validated.     

Evaluation of hourly tilted surface radiation models

This study investigates the performance of the isotropic and four anisotropic hourly tilted surface radiation models by using monthly average hourly utilizable energy as a standard of measure. Utilizable energy is the radiation above a specified threshold level. Differences between the utilizable energy measured and the utilizable energy predicted are observed for various surface slope/azimuth orientations and critical radiation levels. Normalized root mean square difference and normalized mean bias difference statistics are formed to quantify the ability of each model to estimate the utilizable energy on a tilted surface. The influence of horizontal diffuse radiation on tilted surface model performance is examined by comparing the predicted utilizable energy on a tilted surface using both measured horizontal diffuse and estimated horizontal diffuse found from diffuse fraction correlations. On an overall basis, the isotropic sky model showed the poorest performance and is not recommended for estimating the hourly radiation on a tilted surface. The anisotropic models have comparable performance to each other. There was no significant degradation of tilted surface model performance when the diffuse radiation is estimated from a diffuse fraction correlation rather than obtained from measurements.     

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.     

The assessment of four different correction models applied to the diffuse radiation measured with a shadow ring using global and normal beam radiation measurements for Beer Sheva, Israel

The measurement of the diffuse radiation incident on a horizontal surface, a priori a straightforward task, is fraught with difficulties. It is possible to measure the diffuse radiation by three different techniques: two of which measure it directly and the third indirectly. The most accurate is the indirect one, which is based upon the concurrent measurements of the horizontal global and the normal incidence beam radiation. The disadvantage of this being the relatively expensive tracking system required for measuring the latter. The diffuse radiation can be measured directly with a pyranometer outfitted with either an occulting disk or shadow ring, which prevent the beam radiation from impinging on the pyranometer sensor. The occulting disk can provide accurate measurements of the diffuse radiation but it requires a relatively expensive sun tracking system in the east–west axis. The shadow ring is a stationary device with regard to the east–west axis and blocks the beam radiation component by creating a permanent shadow on the pyranometer sensor. The major disadvantage of the shadow ring is that it also blocks that portion of the diffuse radiation obscured by the shadow ring. This introduces a measurement error that must be corrected to account for that portion of the sky obscured by the shadow band. In addition to this geometric correction factor there is a need to correct for anisotropic sky conditions. Four correction models have been applied to the data for Beer Sheva, Israel and the results have been evaluated both graphically and statistically. An attempt has been made to score the relative performance of the models under different sky conditions.     

Correlation for estimation of diffuse fraction of daily global radiation

We present seasonally dependent correlations to estimate the daily ratio of diffuse to total radiation received by a horizontal surface using insolation measurements made at Dhahran, Saudi Arabia. Comparisons with existing models for daily diffuse radiation show good agreement.     

Mapping global, diffuse and beam solar radiation over Zimbabwe

A database for long-term monthly radiation over Zimbabwe is developed. The meteorological raw data inputs are long-term monthly average records of pyranometer-measured hemispherical radiation, monthly average sunshine records, and satellite-measured hemispherical records over a 2-year period. The sunshine records are incorporated into the database by use of Angstrom-type correlations developed for Zimbabwe, and the short-term satellite data are ‘cultured to long-term ground-measurement basis by means of an empirically derived correlation’ and a ‘time series factor’. Diffuse radiation values are generated from the resulting hemispherical radiation database by a locally developed correlation of the monthly average diffuse fraction of hemispherical radiation with monthly average clearness index. Normal beam radiation is computed from the hemispherical and diffuse radiation using two different methods. The two methods are found to agree generally to within 7%. The results are presented as country-border-contained isolines of radiation. The sensitivity of beam radiation to the accuracy of estimating diffuse radiation is inspected. The sensitivity is quite high, about 1:1 for months and locations with very low clearness. This translates to an almost equal sensitivity of insolation available to tracking tilted apertures, underscoring the importance of developing a local diffuse fraction-clearness index correlation rather than relying on a correlation developed elsewhere.     

Analysis of monthly average solar radiation and bright sunshine for different thresholds at Cape Canaveral, Florida

Data for beam, global horizontal, and global normal radiation measured at Cape Canveral were analyzed for the period 1986–1991. Some empirical correlations between these parameters are proposed. A detailed analysis of the beam irradiance data also led to the derivation of sunshine fractions corresponding to different radiation thresholds. It is shown that the current WMO threshold of 120 W/m² corresponds to optimal radiation/sunshine correlations. Finally, improved monthly irradiation empirical fits using sunshine data are proposed.     

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.     

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.     

Contribution to the study of the solar radiation climate of Lisbon

Based upon a statistical analysis of available data, this paper offers relationships permitting the determination of the direct, diffuse and global radiation intensities, on a horizontal surface and on clear days, and it establishes linear correlations between those three components. Daily sums of diffuse and global radiation, on a horizontal surface and on cloudy days, are found to be correlated with one another and they both can be determined from the knowledge of the insolation fraction. This paper also analyses the contribution of the direct and diffuse components to the daily sum of global radiation on the ground, with emphasis to the contribution of diffuse radiation from the cloudy regions of the sky, and infers some global characteristics of the clouds. Finally, it is shown that four regression parameters alone are enough to make fair predictions of all the statistical relationships involving daily sums of solar radiation.     

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.     

A method for characterization and inter-comparison of sites with regard to solar energy utilization by statistical analysis of their solar radiation data as performed for three sites in the Israel Negev region

A method for the characterization and inter-comparison of sites with regard to their suitability for utilization of solar energy based upon the statistical analysis of their solar radiation intensities is presented. In this method each monthly data set of the daily global, horizontal beam and diffuse radiation intensities was analyzed and the following parameters were determined: monthly average daily radiation intensity, coefficient of variation, skewness and kurtosis. The values of the skewness and kurtosis have been applied, using generally accepted rules, to describe the distribution curves for each of the radiation intensity data sets. In addition, the same type of statistical analysis was applied to the monthly average daily ratios of the horizontal beam to global radiation, diffuse to global and the clearness index for the three sites. In this investigation, this statistical analysis method has been applied to the global and beam radiation measured at three sites located in the southern, Negev region of Israel, viz., Beer Sheva, Sde Boker and Eilat. The southern region of Israel is characterized by relatively high average daily irradiation intensities for both global and normal incidence radiation. They have been characterized with regard to the distribution of their intensity levels and a site inter-comparison has also been performed. An inter-comparison of the results of these analyses for the three sites has been performed on a monthly basis. The results of this analysis are used both to characterize and compare the composition of the solar radiation at the three sites under investigation. The results of this study will be presented in detail.     

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.     

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.