Study of the corrective factor involved when measuring the diffuse solar radiation by use of the ring method

By comparing the diffuse solar radiation on a horizontal plane as continuously measured in Geneva over a full year by using both a fixed ring and a moving disk, we conclude that the ring corrective factor can be evaluated on the basis of simple models, but with a daily uncertainty of the order of 5 per cent. In this study, the isotropy of the diffuse radiation can be used as a reasonable approximation, even if this assumption is not fully verified. More precise measurements would require the use of a disk.     

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.     

Computation of diffuse solar radiation

A technique for computing the spectral and angular (both the zenith and azimuthal) distribution of the solar energy reaching the surface of earth and any other plane in the atmosphere has been developed. Here the computer code LOWTRAN is used for getting the atmospheric transmittances in conjunction with two approximate procedures: one based on the Eddington method and the other on van de Hulst's adding method, for solving the equation of radiative transfer to obtain the diffuse radiation in the cloud-free situation. The aerosol scattering phase functions are approximated by the Hyeney-Greenstein functions. When the equation of radiative transfer is solved using the adding method, the azimuthal and zenith angle dependence of the scattered radiation is evaluated, whereas when the Eddington technique is utilized only the total downward flux of scattered solar radiation is obtained. Results of the diffuse and beam components of solar radiation received on surface of earth compare very well with those computed by other methods such as the more exact calculations using spherical harmonics and when atmospheric conditions corresponding to that prevailing locally in a tropical location (as in India) are used as inputs the computed values agree closely with the measured values.     

A method to calibrate a solar pyranometer for measuring reference diffuse irradiance

Accurate pyranometer calibrations, traceable to internationally recognized standards, are critical for solar irradiance measurements. One calibration method is the component summation, where the pyranometers are calibrated outdoors under clear sky conditions, and the reference global solar irradiance is calculated as the sum of two reference components, the diffuse and subtended beam solar irradiances. The beam component is measured with pyrheliometers traceable to the World Radiometric Reference, while there is no internationally recognized reference for the diffuse component. In the absence of such a reference, we present a method to consistently calibrate pyranometers for measuring the diffuse component with an estimated uncertainty of ±(3% of reading+1 W/m²). The method is based on using a modified shade/unshade method, and pyranometers with less than 1 W/m² thermal offset errors. We evaluated the consistency of our method by calibrating three pyranometers four times. Calibration results show that the responsivity change is within ±0.52% for the three pyranometers. We also evaluated the effect of calibrating pyranometers unshaded, then using them shaded to measure diffuse irradiance. We calibrated three unshaded pyranometers using the component summation method. Their outdoor measurements of clear sky diffuse irradiance, from sunrise to sundown, showed that the three calibrated pyranometers can be used to measure the diffuse irradiance to within ±1.4 W/m² variation from the reference irradiance.     

A comparison of methods for estimating hourly diffuse solar radiation from global solar radiation

Four methods of estimating hourly diffuse irradiation from hourly global irradiation are compared, using global and diffuse irradiation data from the Australian Bureau of Meteorology for five widely separated Australian locations. A development of one of these methods with constants derived from the data for each place is found to perform best when judged on a criterion of absolute error, and this performance in maintained when constants averaged over the five locations are used. The derived constants are also given for all other Australian locations for which both global and diffuse data are available, and a method is suggested for deriving suitable values of the constants for places situated between 20° and 45° S for which only global radiation data are available. A previously reported dependence of the proportion of diffuse radiation on latitude is demonstrated.     

MEO shadowring method for measuring diffuse solar irradiance: Corrections based on sky cover

The present paper deals with atmospheric corrections factors proposed as a function of the atmospheric transmissivity in order to correct the diffuse solar irradiance measured with the Melo-Escobedo-Oliveira Shadowring Measuring Method (MEO shadowring Method). Global irradiance was measured by an Eppley-PSP pyranometer; direct normal irradiance by an Eppley-NIP pyrheliometer fitted to a ST-3 sun tracking device and diffuse irradiance by an Eppley-PSP pyranometer fitted to a MEO shadowring. The Solar Radiometric Laboratory at Sao Paulo State University provided the measurements during the years 1996–2005. Two correction models for diffuse solar irradiance were proposed: All Sky Correction Model (ASC Model) and Sky Cover Correction Model (SCC Model). The MBE and RMSE statistical indicators performed the validations. The correction models showed results in the same order of magnitude: ASC Model showed 0.81% deviation, while SCC Model showed 0.66% deviation. Therefore, the correction models proposed as a function of the sky covering (atmospheric transmissivity) were efficient to correct the isotropic diffuse irradiance, approaching the measured and reference diffuse irradiance less than 1%. Corrections show dependence on sky coverage and seasonality. The results presented that the sky cover corrections improve the MEO shadowring method, allowing the generation of a reliable global, direct and diffuse radiation database without high financial investments.     

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.     

On the estimation for clear skies of the spectral distribution of diffuse solar radiation on a horizontal surface from global and diffuse broadband solar radiation

Using experimental data collected at Uccle (Belgium) in 1980, new relations are proposed which allow the spectral density distribution of diffuse solar radiation on a horizontal surface to be estimated for clear skies, as a function of the commonly measured broadband global and diffuse solar irradiances.     

Characterization of sky conditions by the use of solar radiation data

A method is proposed to characterize the sky and cloud conditions (SCC) by using ground based global/diffuse irradiance data. The term SCC is defined for the purpose of this paper as the bulk effect of clouds, and other atmospheric constituents on the values of the diffuse fraction of solar radiation (), the ratio between, the global to extra terrestrial radiation (K_T) and the transmissivity T_r measured at the earth's surface. However, there is a difficulty in using the measured values of K_T and () for describing the SCC since these values depend on the solar zenith angle and not only on meteorological factors. This difficulty is overcome by the use of a simple semi-empirical procedure by which one can eliminate the seasonal and latitudinal variations (due to variations in the solar zenith angle) in and K_T, or similar relations, leaving only variations due to SCC. The procedure is based on a paper by Zangvil and Aviv on the effect of latitude and season on the relation between the diffuse fraction of solar radiation and the ratio of global to extraterrestrial radiation, Solar Energy39, 321–327 (1987) where a numerical simulation of the seasonal and latitudinal (zenith angle dependent) changes of positions of points representing different simulated SCC on a diagram was performed. The method is demonstrated on monthly mean relations calculated from three years of global and diffuse irradiance measured at Sede Boker, Israel. Results show that the large scatter of the original data points on a diagram is, to a considerable extent due to a seasonal effect (variations of the solar zenith angle). After these effects are removed by the use of the proposed technique the transformed monthly data points have much less scatter and they describe the observed seasonal variations of sky and cloud conditions correctly.     

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.     

Transmission coefficient of the transparent insulation of flat diffuse solar radiation heating systems

A method is proposed for calculating the transmission coefficient of the transparent insulation of the diffuse solar radiation heating systems in terms of the equivalent value of the direct solar radiation ray incidence angle.     

The diffuse fraction of hourly solar radiation for Amman/Jordan

This paper presents various correlations of the hourly clearness index K_t with the hourly diffuse fraction K_d on a horizontal surface for Amman/Jordan. The first correlation is based on Orgill and Hollands method, but using weighted averages. The second correlation is based on hourly integrated values of K_t's and K_d's without any grouping. A refinement of the latter correlation is attempted by including a random shock.     

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.     

Prediction of hourly diffuse solar radiation from measured hourly global radiation on a horizontal surface

A statistical procedure has been employed to develop correlations between the hourly global horizontal radiation and its diffuse component. Several years', hourly radiation data from three Canadian stations and two French stations have been employed for this purpose. The relationships have been developed in dimensionless form which predict for particular solar altitudes when is given.Under heavily cloudy conditions or when the sky is completely covered ( ), diffuse radiation increases linearly with the global radiation. In this region, solar altitude has no bearing on the fraction of diffuse radiation.As goes beyond 0.35, the effect of solar altitude begins to appear and the region immediately following this may be considered as partly-cloudy-skies conditions. In the beginning of this region, the diffuse component increases briefly with the increase in global radiation and then begins to decrease as the partly cloudy skies become clearer. At particular solar altitudes, a minimum value of the diffuse radiation is reached. The value of where reaches its minimum value varies with solar altitude.The region beyond which a minimum value of is reached may be considered as mainly-clear-sky conditions. In this region, increases again with , lower solar altitudes giving a higher percentage of diffuse radiation.Under partly cloudy skies and under clear skies, solar altitudes lower than 30° had a marked effect on the fraction of diffuse radiation. However, solar altitudes greater than 30° had minimal influence on the fraction of diffuse radiation.     

Interrelationships between total, direct, and diffuse solar radiation in the tropics

Formulas that directly yield intensities of direct and diffuse radiation on horizontal surfaces from measurements of hourly total radiation only have been developed. Alternatively, atmospheric turbidity and solar altitude can also yield similar results. These formulas result in obtaining relations similar to those given by Parmelee from data collected in the United States. The data for New Delhi have also been shown to agree with these correlations.

Computed values of direct solar radiation on a horizontal surface or at normal incidence, are expressed by a mathematical expression that is shown to agree closely with the computed values obtained by Rao and Seshadri.

Correlation between hourly direct and total transmission factors has been shown to depend on the solar altitude, in addition to the atmospheric turbidity.