Circumsolar Radiation Research Articles

The transmissivity of E-W aligned models of a conventional and clerestory greenhouse under natural winter irradiance

Computer model predictions of the winter light transmission characteristics of conventional symmetric-roofed and vertical south roofed (clerestory) multispans have been substantially verified by measurements on small glass models of the two multispan houses. Good correlations were found between the predicted and measured diffuse and direct light transmissions across a central span, after correcting for absorption by joints at the apices and troughs of each span. Errors at the extreme edges of the span still occur, however, but plausible explanations can be found for these. The average transmission difference between the two models over the winter period was found to be 4%, compared with a predicted value of 5%. Somewhat lower levels of direct and circumsolar radiation than expected may account for part of the difference.

The transmissivity of E−W aligned models of a conventional and clerestory greenhouse under natural winter irradiance

Computer model predictions of the winter light transmission characteristics of conventional symmetric-roofed and vertical south roofed (clerestory) multispans have been substantially verified by measurements on small glass models of the two multispan houses. Good correlations were found between the predicted and measured diffuse and direct light transmissions across a central span, after correcting for absorption by joints at the apices and troughs of each span. Errors at the extreme edges of the span still occur, however, but plausible explanations can be found for these. The average transmission difference between the two models over the winter period was found to be 4%, compared with a predicted value of 5%. Somewhat lower levels of direct and circumsolar radiation than expected may account for part of the difference

Calibration of a sunphotometer by simultaneous measurements of direct-solar and circumsolar radiations

A new method is proposed for the calibration of the sunphotometer. Well-known difficulties of the usual Langley-plot method when applied to unsteady turbidity conditions can be avoided by monitoring the circumsolar radiation. To realize this idea, an alternate of the Langley-plot method is developed, in which the logarithm of the sunphotometer reading is plotted against the ratio of intensity of singly scattered circumsolar radiation to that of direct solar radiation instead of the optical air mass in the usual Langley-plot method. Results of numerical simulations and field tests with a newly developed instrument show that the rms error of the calibration constant could be reduced to 1/5–1/10 of the usual method for wavelengths larger than 500 nm.

Total cloudiness and high-cloud frequency on eastern sicily

High clouds are the main responsibles for the increase of collimated radiation coming from the circumsolar corona. It is, therefore, required a quantitative evaluation of such a radiation in order to know whether it is convenient to use low focusing systems in the mirror solar plants. For this purpose we have analysed the diurnal evolution (from 7 a.m. to 7 p.m.) of the cloud cover and of the high-cloud frequency over eastern Sicily in which the EURELIOS solar plant is located. The results show that 1) the high-cloud frequency over the Adrano area exceeds of (50÷100)% that observed in other stations of eastern Sicily; 2) with the exception of summer months, in which the cloud cover is scanty, the high-cloud frequency increases with the solar elevation. So far, it has not been possible to quantify the circumsolar radiation (which varies from a few to 30% of the direct one) as a function of clouds of different kind and thickness.

Circumsolar radiation calculated for various atmospheric conditions

The circumsolar radiance and irradiance is discussed taking into account all relevant optical parameters. The decrease of the radiance from the limb of the sun to an angular distance of 10° from the sun's center is mainly determined by the optical depth of the atmosphere and the size distribution of scattering particles. Thin cirrus clouds have the strongest effect. In this case the radiance at 0.5° angular distance may reach about 2 per cent of the radiance of the direct sun. In the case of aerosol scattering alone, the radiance at 0.5° does not reach more than 0.1 per cent. Therefore a field of view larger than the angular size of the sun only gives rise to a significant increase in the total (solar plus circumsolar) irradiance if a thin cirrus layer is present.

Effect of Circumsolar Radiation on Performance of Focusing Collectors

Circumsolar radiation is one of several factors, along with optical errors (contour, tracking, etc.), that determine the size and shape of the solar image at the receiver of a concentrating collector. The sensitivity of a collector to circumsolar radiation depends on insolation conditions and on collector parameters; it increases with geometrical concentration ratio and decreases with threshold. In this paper the Lawrence Berkeley Laboratory (LBL) circumsolar data are used to calculate the effect of circumsolar radiation on both the instantaneous and the long-term average performance of focusing collectors. To speed up the computations, the optical properties of the concentrator are expressed in terms of an angular acceptance function. The angular acceptance function and the brightness distribution of the sun are then convoluted, a procedure which requires, for each circumsolar scan, only 56 multiplications and additions (one for each of the angular intervals at which the brightness has been measured by the LBL circumsolar telescope). While the formalism is applicable to all focusing collectors, only parabolic troughs and dishes are evaluated explicitly in this paper. The instantaneous performance corresponding to particular circumsolar scans is of interest for the analysis of test results of collectors with high concentration. For most predictions of long-term average performance a far simpler approach will, however, be adequate. For this purpose a standard synthetic circumsolar scan has been developed that describes the brightness distribution of the solar disk (“limb darkening”) and of the circumsolar region. The radiation intercepted by a receiver is calculated once for the solar portion and once for the circumsolar portion of this standard sun shape. The long-term average radiation intercepted by the receiver is then obtained by averaging the solar and the circumsolar intercept factors, weighted according to the long-term average circumsolar ratio for the location and period under study. Tested against hour-by-hour simulations, this simple approach was found to have an rms error of only 0.2 percent, negligible compared to typical uncertainties in system performance calculations. This analysis points out the usefulness of the long-term average circumsolar ratio as a simple measure of circumsolar radiation.

Six-gaussian representation of the angular-brightness distribution for solar radiation

The angular distribution of circumsolar radiation varies with changing atmosphere and influences the solar irradiance at the receiver of a concentrating system. In order to facilitate calculation of this irradiance, five typical sunshapes are chosen from the widest to the narrowest shape in the Lawrence Berkeley Laboratory data and are approximated by a sum of 6 gaussian distributions. An effective sunshape can then be obtained by convolution with error-cone distributions that represent a statistical description of uncertainties encountered in an optical concentrating system. Convolution of circular-normal error cones first with the sum of gaussians and then with actual sunshape indicates good agreement whenever the error-cone dispersion is greater than 0.0012. Thus the analytic convolution can replace more costly (in time and computer storage) numerical calculation. A simple prescription indicates how each of the analytic representations may be transformed to approximate sunshapes appropriate for slightly different atmospheric conditions.

A method for determining the circumsolar sky function

In 1980 a new pyrheliometric scale (World Radiometric Reference) will be introduced. This scale will be realized with higher accuracy than the previous one, therefore the accuracy of the transfer of the new scale could also be increased. In this paper a method is described for determining the circumsolar sky function which could be used to significantly decrease the systematic error caused by the circumsolar radiation during calibration of geometrically different pyrheliometers. DOI: 10.1111/j.2153-3490.1980.tb00961.x

The diffuse solar irradiance of slopes under cloudless skies

The diffuse irradiance of slopes relative to the diffuse irradiance of a horizontal surface is calculated by integrating the mean radiance distributions of cloudless skies in Britain for a wide range of solar elevations, azimuths and slope angles. There is reasonable agreement with measurements reported from a number of stations; discrepancies are probably due to errors in measurements and to the influence of aerosol on the radiance distributions. A simple model of the diffuse irradiance of slopes, which takes account of circumsolar radiation, is proposed, and agrees well with integrated values of irradiance.

The diffuse solar irradiance of slopes under cloudless skies

AbstractThe diffuse irradiance of slopes relative to the diffuse irradiance of a horizontal surface is calculated by integrating the mean radiance distributions of cloudless skies in Britain for a wide range of solar elevations, azimuths and slope angles. There is reasonable agreement with measurements reported from a number of stations; discrepancies are probably due to errors in measurements and to the influence of aerosol on the radiance distributions. A simple model of the diffuse irradiance of slopes, which takes account of circumsolar radiation, is proposed, and agrees well with integrated values of irradiance.

A comparison of compound parabolic and simple parabolic concentrating solar collectors

The compound parabolic and simple parabolic solar collectors are analyzed and compared for their ability to accept non-direct radiation and for their respective reflector arc-lengths. The simple parabolic concentrator (SPC) can make use of some non-direct solar radiation if the absorber tube is intentionally enlarged so as to intercept defocussed radiation. A principal advantage of collecting non-direct radiation with a SPC rather than with a compound parabolic concentrator (CPC) is the reduced materials use in the construction of the reflector, but a principal disadvantage is the reduction of acceptance angle to about 1 3 that of the CPC. However, a SPC with concentration ratio less than 10 can still collect most of the circumsolar non-direct radiation.

Pyrheliometric and circumsolar sky radiation measurements by the Smithsonian Astrophysical Observatory from 1923 to 1954

Pyrheliometric and circumsolar sky radiation measurements by the Smithsonian Astrophysical Observatory from 1923 to 1954

Single and multiple scattering contributions to circumsolar radiation

Single and multiple scattering contributions to the circumsolar radiation along the almucantar and sun vertical have been computed by a Gauss-Seidel solution to the radiative transfer equation. In the near forward direction, the multiple scattering contributions are significant for optical depths of the order of 0.4. However, the shape of the angular distribution of almucantar radiance up to 10 degrees appears less sensitive to multiple scattering. The results have been compared against an existing radiative transfer code.

Atmospheric turbidity and the circumsolar radiation

We investigate the possibility of determining the turbidity from the intensity of the circumsolar radiation and find that such a connection can be made only when the size distribution of the aerosol particles is known. However, measurements of both the turbidity and the aureole intensity can give useful information about the size distribution.

Circumsolar Radiation as a Measure of the Turbidity of the Atmosphere Part 2

The paper is theoretical, based on experimental data. It treats field measurements of the circumsolar radiation in order to derive from them the variations of the turbidity of the atmosphere at the high level stations Table Mountain and Montezuma. A single relationship is derived for the circumsolar radiation as a function of the coefficient of turbidity beta.

Circumsolar Sky Radiation and Turbidity of the Atmosphere

A statistical treatment of field measurements carried out by the Astrophysical Observatory of the Smithsonian Institution is presented. The brightness of a band of sky 10 degrees wide, concentric with the sun, has been determined. Measurements were obtained at two high altitude stations (Table Mountain and Montezuma) with the aid of a pyranometer constructed by C. G. Abbot and L. B. Aldrich. The primary object was to obtain an idea of the integral scattering of the sun's radiation by the atmospheric aerosol. Results have been used to determine long-periodic changes in the scattering properties of the atmosphere and their relation to other phenomena.

An effect of the circumsolar sky radiation on the Ångström Pyrheliometric scale

According to the basic equation of the Angstrom pyrheliometer, the heating power of the compensation electric current is directly proportional to the incident radiation intensity. However, as Anders Angstrom pointed out, this direct ratio needs two corrections; the “edge effect” correction and the correction for heat conduction in the black paint thickness. This work directs attention to the existence of a third correction arising from the non-uniform illumination of the strips. In cases of pyrheliometers having no edge effect, this inhomogeneity is due to circumsolar sky radiation. The value of this correction can be determined by applying Angstrom's theory using an irradiation term depending on distance measured from the midpoint of the strip. For simplicity a linear illumination distribution was used, even though the real distribution of the energy coming from the sun's aureole is not quite linear along the strip. The incident radiation flux can be exactly determined by applying Pastiel's theory. When calculating a reliable value for the correction in question, the sensitivity distribution along the strip should be taken into consideration. This can be determined on the basis of Angstrom's theory. For the pyrheliometer A529, in mean Budapest circumsolar sky conditions, the correction due to non-uniform irradiation is 0.5%. This correction is nearly compensated by the correction for heat conduction in the black paint. DOI: 10.1111/j.2153-3490.1973.tb00623.x

An effect of the circumsolar sky radiation Ion the Ångstrom Pyrheliometric scale

According to the basic equation of the àgström pyrheliometer, the heating power of the compensation electric current is directly proportional to the incident radiation intensity. However, as Anders àngström pointed out, this direct ratio needs two corrections; the “edge effect” correction and the correction for heat conduction in the black paint thickness. This work directs attention to the existence of a third correction arising from the non-uniform illumination of the strips. In cases of pyrheliometers having no edge effect, this inhomogeneity is due to circumsolar sky radiation. The value of this correction can be determined by applying àngström's theory using an irradiation term depending on distance measured from the midpoint of the strip. For simplicity a linear illumination distribution was used, even though the real distribution of the energy coming from the sun's aureole is not quite linear along the strip. The incident radiation flux can be exactly determined by applying Pastiel's theory. When calculating a reliable value for the correction in question, the sensitivity distribution along the strip should be taken into consideration. This can be determined on the basis of àngström's theory. For the pyrheliometer A529, in mean Budapest circumsolar sky conditions, the correction due to non-uniform irradiation is 0.5%. This correction is nearly compensated by the correction for heat conduction in the black paint.DOI: 10.1111/j.2153-3490.1973.tb00623.x

Circumsolar Radiation and the International Pyrheliometric Scale

Issue is taken with the ascription of the 2% discrepancy in values of solar irradiance at the surface of the earth, found between the measurements performed by the absolute radiometers of Kendall and Wilson and those obtained by Eppley-Angstrom pyrheliometers, to the possibility that the two types of instruments might collect different amounts of circumsolar radiation. It is shown that this explanation is very unlikely.

Calculated Circumsolar Radiation as a Function of Aerosol Type, Field of View, Wavelength, and Optical Depth

Get PDF Email Share Share with Facebook Tweet This Post on reddit Share with LinkedIn Add to CiteULike Add to Mendeley Add to BibSonomy Get Citation Copy Citation Text H. Grassl, "Calculated Circumsolar Radiation as a Function of Aerosol Type, Field of View, Wavelength, and Optical Depth," Appl. Opt. 10, 2542-2543 (1971) Export Citation BibTex Endnote (RIS) HTML Plain Text Citation alert Save article