A MULTIPLE LINEAR CORRELATION FOR DIFFUSE RADIATION FROM GLOBAL AND SUNSHINE DATA

Several years of measured data of global and diffuse radiation together with sunshine duration, for five locations in Spain are used to establish empirical relationships to connect monthly mean daily diffuse irradiation with clearness index and relative sunshine duration. A correlation connecting sky radiation with both clearness index and percent possible sunshine together is found to be most accurate for locations in Spain and Portugal. When clearness index and relative sunshine duration are combined together, it is observed that the accuracy of the estimated diffuse radiation data is better than when they are used separately.     

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.     

Effect of sunshine and solar declination on the computation of monthly mean daily diffuse solar radiation

Several years of measured data for 17 European locations have been used to develop models for estimating monthly mean daily values of diffuse radiation (Hd) from combinations of the following: clearness index, sunshine fraction, and solar declination. Two models giving the highest correlation coefficients and the lowest standard errors of estimation are tested with data for 10 European locations not used in their development. From consideration of the MBE and RMSE values, a model which estimates Hd values from clearness index, relative sunshine duration and solar declination is found to be the most accurate. Comparison with Hd values predicted with the European Community solar radiation model (ECM) confirms this conclusion.     

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.     

Diffuse solar radiation estimates from sunshine hours and clearness index for Karachi, Pakistan

Correlations for the estimation of monthly average daily diffuse solar radiation as a function of the sunshine hours and clearness index have been obtained from Karachi. Generally, two types of correlations are used: (a) diffuse radiation as a function of relative sunshine hours and extraterrestrial radiation, and (b) diffuse radiation as a function of global and extraterrestrial radiation. These correlations are mostly first- and second-order polynomials in the sunshine hours and clearness index, indicating the presence of the diffuse solar radiation component. The diffuse solar radiation shows a peak value during the monsoon months of July–August. The diffuse to global ratio is found to be 0.32 from the analysis, and the diffuse to extraterrestrial radiation ratio is nearly 0.19 throughout the year. Among the established relations, Iqbal and Stanhill overestimate the radiation value, while Liu and Jordan underestimate it.     

Correlations for the estimation of the diffuse radiation component in greece

Correlations for calculation of the diffuse component of the daily and monthly average solar irradiation in terms of the clearness index are obtained from available data at both rural and urban locations in Greece. These correlations are mostly of first and occasionally second order in the clearness index and strongly reflect the higher levels of diffuse radiation present in Greece. No evidence of significant seasonal variation has been found, while air pollution in the urban areas is seen to play a small role only in the summer months and at high clearness index values.     

Estimating monthly average daily diffuse solar radiation with multiple predictors: A case study

Solar radiation measurements are not easily available, especially for the diffuse solar radiation. In this study, two models for estimating the diffuse solar radiation are proposed based on multiple predictors including the clearness index, relative sunshine duration, ambient temperature and relative humidity. One of them aims to increase the estimation accuracy, and the other aims to estimate the diffuse solar radiation direct from other meteorological elements in the absence of the global solar radiation. For a case study, the performance of the proposed models is validated by comparing with eight existing models selected from literature against the measured data at Guangzhou station in China. Through the analysis based on statistical error tests, results show that the two models can estimate the monthly average daily diffuse solar radiation with good accuracy.     

Contribution to the study of solar radiation in Abu Dhabi

Measurements of global solar radiation for 10 yr in Abu Dhabi are used to examine the suitability of a method of prediction of global solar radiation. It shows a good degree of accuracy. A correlation between the clearness index, H/H₀, and the fraction of maximum possible number of sunshine hours is obtained and found to be H/H₀ = 0.307 + 0.312n/N. The diffuse solar radiation is predicted by two methods which show almost similar results. Correlation between the diffuse solar radiation as a fraction of the global radiation, H_d/H, and the fraction possible number of sunshine hours, n/N, is established using both methods, for comparison sake, since measurements of diffuse solar radiation are not available. The comparison shows a good agreement between the two correlations. The relation between the diffuse solar radiation as a fraction of the global radiation H_d/H, and the clearness index, H/H₀, is established and compared with those obtained elsewhere in order to justify their use, since direct measurements are not available. The relation shows a latitude dependency.     

Correlation between hourly diffuse and global radiation for New Delhi

Estimation of hourly insolation on tilted surfaces is required in simulation of solar energy systems. This necessitates splitting of hourly global horizontal insolation into diffuse and direct components. Many models have been developed for this purpose, and the aim of this study is to develop a correlation between hourly diffuse ratio and clearness index for New Delhi. The correlation is developed on the basis of measured data for two years. The performance of this correlation was checked by calculating the difference between computed and measured diffuse radiation. The correlation proved to perform quite well. A comparison of the present correlation with those for other locations showed that such correlations are location dependent.     

An analysis of thermal and solar zone radiation models using an Angstrom–Prescott equation and artificial neural networks

The correlation between the clearness index and sunshine duration is useful in the estimation of the solar radiation for areas where measured solar radiation data are unavailable. Regression techniques and artificial neural networks were used to investigate the correlations between daily global solar radiation (GSR) and sunshine duration for different climates in China. Measurements made during the 30-year period (1971–2000) from 41 measuring stations covering 9 thermal and 7 solar climate zones and sub-zones across China were gathered and analysed. The performance of the regression and the ANN models in the thermal and solar zones was analysed and compared. The coefficient of determination (R²), Nash–Sutcliffe efficiency coefficient (NSEC), mean bias error (MBE) and root-mean-square error (RMSE) were determined. It was found that the regression models in both the thermal and the solar climate zones showed a strong correlation between the clearness index and sunshine duration (R²=0.79–88). There appeared to be an increasing trend of larger MBE and RMSE from colder climates in the north to warmer climates in the south. In terms of the thermal and solar climate zone models, there was very little to choose between the two models.     

Discourses on solar radiation modeling

All solar energy applications require readily available, site-oriented and long-term solar radiation data. A typical database comprises of global, direct and diffuse solar irradiance, duration of sunshine and complementary data like cloud cover, atmospheric turbidity, humidity, temperature, etc. However, most of these stations do not provide complete if any information on solar data, chiefly due to the capital and maintenance costs that measuring instruments incur. For instance, global radiation is the most frequently measured parameter, its two components, i.e. diffuse and direct irradiance are often not measured.Improvements have been made to the meteorological radiation model MRM which, had been developed by Muneer et al. as a simple broadband irradiance estimation model based on synoptic information, by incorporating the sunshine information in the model's regressions. The result of the improvement of the model is a considerable reduction in biases and scatter in the comparison between estimated and measured data. The improved meteorological radiation model, IMRM is more accurate, by up to 70% in some cases, than its predecessor in estimating, global and diffuse horizontal irradiance.When sunshine, atmospheric pressure and temperature are not measured by a nearby station, yet cloud information is recorded, radiation estimation models based on cloud cover, CRM, can be used. Three CRMs have been compared to newly proposed models. It was found that models with locally fitted coefficients gave a more accurate estimation of the solar radiation than CRMs with generalized coefficients. The newly proposed model performed better that the older generation models.The third section of the article deals with estimation of diffuse radiation and possible improvements in its modeling. In this section, apart from clearness index (k_t), influence of the synoptic parameters of sunshine fraction (SF), cloud cover (CC) and air mass (m) on diffuse fraction of global radiation (k) is studied both qualitatively and quantitatively. It is found that, SF shows a strong bearing on the k–k_t relationship followed by CC and then m. As a next step, a series of models are developed for k as a polynomial function of k_t, SF, CC and m. After an extensive evaluation procedure, a regression model is selected such that the diffuse radiation can be estimated with reasonable accuracy without making the model overtly complex. It was found that among all the models, the composite model involving all parameters provides the most accurate estimation of diffuse radiation. The site-specific models are further investigated for any appreciable correlations between different locations and their possible attributions. It was also found that a single model could more than adequately estimate the diffuse radiation for the locations within a given region. Three optimum models are also recommended for each region, in view of the fact that information on all parameters is not necessarily available for all sites. This study reveals a significant improvement from the conventional k–k_t regression models to the presently proposed models, therefore, leading to more accurate estimation of diffuse radiation by approximately 50%.     

Study of hourly solar radiation data in Istanbul

This paper presents a study of the solar radiation data measured in Istanbul (41.1°N, 29.0°E) during 1992 and 1993. The monthly and annual average values of total solar radiation and clearness index are analysed. The monthly averages of daily total radiation are 1.23 kW h m⁻² day⁻¹ for January and 6.55 kW h m⁻² day⁻¹ for July. The annual average value of daily total radiation is 3.81 kW h m⁻² day⁻¹. The monthly averages of clearness index for January and July are 0.28 and 0.50, respectively. The annual average value of clearness index is 0.38. In the second part of the study, the seasonal relative frequency of hourly total radiation and clearness index is studied. 46% of the annual data corresponds to a value greater than 300 W m⁻². The annual average frequency of clear hours is 24%. The analysis points to the conclusion that solar radiation will be efficient and useful between April and September for heating purposes. A polynomial relationship is developed between hourly clearness index and hourly fractional sunshine duration. Some statistical tests are used to check this relationship for four different ranges of optical air mass.     

A multiple correlation between different solar parameters in Medina, Saudi Arabia

The purpose of this work is to give the potential of solar energy in Medina (Kingdom of Saudi Arabia). We develop a correlation between the different parameters of solar energy. We have used a database available at the National Renewable Energy Laboratory (NREL) website for five years since 1998 until 2002. Also, a typical meteorological year (TMY) has been built from this database. By using the correlations model obtained from these database, we can estimate the global and diffuse irradiation with good agreement in Medina. The correlation connecting diffuse irradiation with both clearness index and sunshine (SS) duration is found to be applicable in Medina site. A linear correlation between ambient temperature and global irradiation data is found from sunrise until midday with a good agreement. A polynomial correlation is given between temperature and global irradiation data from midday until sunset.     

Estimates of the Linke turbidity factor over Zimbabwe using ground-measured clear-sky global solar radiation and sunshine records based on a modified ESRA clear-sky model approach

This paper describes a procedure that can be used to calculate values for Linke atmospheric turbidity factors at air mass 2 (TL2) over Zimbabwe. Ground measured daily global solar radiation on clear days over 3years is used to evaluate TL2 for those stations that measure global radiation. The evaluation makes use of the clear-sky model of the European Solar Radiation Atlas (ESRA) combined with a diffuse transmittance model developed in the study. For those stations that do not measure global radiation but have sunshine duration records, global radiation values are generated through Angstrom type regression coefficients between the clearness index and relative sunshine duration. The TL2 values that are generated from the ESRA model are higher than those obtained from the study model (root mean square error (RMSE) up to 1.0 Turbidity Units). When compared to TL2 values from this study, the worldwide database SoDA, give significantly higher TL2 values (RMSE up to 2.2 Turbidity Units), underlining the value addition obtained in using measurement derived values in place of SoDA values.The values obtained from the study may be used to yield better estimates of clear-sky solar radiation for Zimbabwe. A better estimate of the clear-sky solar radiation will in turn improve the accuracy of the global radiation estimates from satellite based methods.     

Analysis of monthly average daily global radiation and monthly average sunshine duration at two tropical locations

The diffuse radiation falling on a horizontal surface at Madras, India has been analysed and the results presented. Five years of data have been used for the analysis and a correlation has been established between the daily average diffuse radiation with the monthly average clearness index. It has also been shown that there is an appreciable difference in the ratio of monthly average hourly diffuse to the monthly average daily diffuse radiation with respect to day length.     

Solar radiation maps for Iraq

As measured solar radiation data for all parts of Iraq is not available, it has to be estimated using other weather variables. A number of correlations which use dry bulb temperature, relative humidity and sunshine duration were tried. Finally a correlation using sunshine duration was selected as it gave most accurate estimation of solar radiation. Constants for the correlation for three stations representing three climatic regions in Iraq were determined. Monthly and yearly solar radiation maps were drawn using sunshine duration data from 24 stations from all over the country.     

Correlation between daily diffuse and global radiation for India

Solar radiation characteristics have been studied in various countries and many correlations developed. In the absence of such studies, the same correlations are applied in other countries. Since radiation records are now available in most developing countries, it is possible to perform similar studies for these regions. The purpose of this study is to use daily global and diffuse radiation data for 13 stations in India to establish a correlation between the daily diffuse ratio and the clearness index. Plotting individual values of the daily diffuse ratio against the clearness index for all Indian Stations showed the existence of a definite relationship between them, confirming the validity of Liu and Jordan approach. It was found that a cubic equation provides a fairly accurate fit for this relationship. Comparison with other studies showed that no single correlation is applicable to all regions, and that each region possesses its own characteristics. Although the stations considered had diverse latitude, climate and geographical variations, the study showed that none had any effect on the correlation.     

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%.     

Estimation of the diffuse radiation fraction for hourly,daily and monthly-average global radiation

Hourly pyrheliometer and pyranometer data from four U.S. locations are used to establish a relationship between the hourly diffuse fraction and the hourly clearness index k_T. This relationship is compared to the relationship established by Orgill and Hollands and to a set of data from Highett, Australia, and agreement is within a few percent in both cases. The transient simulation program TRNSYS is used to calculate the annual performance of solar energy systems using several correlations. For the systems investigated, the effect of simulating the random distribution of the hourly diffuse fraction is negligible. A seasonally dependent daily diffuse correlation is developed from the data, and this daily relationship is used to derive a correlation for the monthly-average diffuse fraction.     

Prediction of hourly and daily diffuse fraction using neural network,as compared to linear regression models

For most of the locations all over Egypt the records of diffuse radiation in whatever scale are non-existent. In case that it exists, the quality of these records is not as good as it should be for most purposes and so an estimate of its values is desirable. To achieve such a task, an artificial neural network (ANN) model has been proposed to predict diffuse fraction (K_D) in hourly and daily scale. A comparison between the performances of the ANN model with that of two linear regression models has been reported. An attempt was also done to describe the ANN outputs in terms of first order polynomials relating K_D with clearness index (K_T) and sunshine fraction (S/S₀). If care is taken in considering the corresponding regional climatic differences, these correlations can be generalized and transferred to other sites. The results hint that the ANN model is more suitable to predict diffuse fraction in hourly and daily scales than the regression models in the plain areas of Egypt.