A simple model for computing diffuse solar radiation

In this paper a very simple model for predicting the daily diffuse solar radiation at any Italian location using as input few extensively measured meteorological parameters is proposed. In fact the daily diffuse radiation D, MJ.m⁻².day⁻¹, here is correlated with only the relative sunshine duration s/S and the noon altitude of the sun on the 15th of the month h_n, degrees, by the following equation:

D=7(s/S⁻(sinh_n)^1.55

.

The validity of this formula is verified using monthly mean daily data from four Italian stations displaced at various latitudes or altitudes or geographical situations (inland or coastal site). The test results show that the deviations between the measured and the computed values of D are generally low; the maximum standard per cent error of estimate Φ (%) is less than 10. Moreover a comparison of the values of D computed for each tested station by the present formula and the others considered correlations with experimental data is showed. This comparison points out that the standard per cent error of estimate Φ (%) referring to the present equation is better than ones obtained for the other considerd correlations for Adrano, Palermo and Genova whereas it is almost equal for Macerata. Consequently the very simple model herein proposed results independent of the latitude, the altitude and the geographical situation of the place and reasonably it can be considered valid and useful to predict the daily diffuse solar radiation at all Italian locations lacking in data records of diffuse radiation with good reliability.     

An atmospheric model for computing direct and diffuse solar radiation

This paper proposes an atmospheric model, which extends the computation of the direct radiation given by Cole's model to the cloudy sky and shows a method to calculate the diffuse radiation.Therefore the monthly average values of the global radiation incident on a horizontal surface at Palermo are computed by this method. These values are compared with the experimental data provided by the Istituto di Idraulica Agraria, Università di Palermo and generally exhibit a mean deviation not more than 10 per cent. The deviations become lower than 8 per cent taking into account the effect of the underlying surface albedo.In order to better verify the validity of the proposed method, it should be suitable to extend its application to other locations provided with actinometric stations. This should allow to use this method with more realibility to predict the radiation incident on the locations lacking in actinometric data.     

A model for calculating direct and diffuse solar radiation

A new model is presented for computing both direct and diffuse solar radiation for a cloudy sky, based on the model of King and Buckius for the direct component for a clear sky. The model is employed to calculate the daily global insolation incident on a horizontal surface at Ibadan for the year 1977. The results are presented in the form of both weekly and monthly averages, and compared with the experimental data provided by the International Institute of Tropical Agriculture (I.I.T.A.), Ibadan. Two values of cloudiness coefficient k (= 1.0 and 0.75) are used in the calculations, with the case of k = 0.75 being superior and for which the deviations from the data do not exceed 15 per cent.     

A simple, solar spectral model for direct-normal and diffuse horizontal irradiance

A spectral model for cloudless days that uses simple mathematical expressions and tabulated look-up tables to generate direct-normal and diffuse horizontal irradiance is presented. The model is based on modifications to previously published simple models and comparisons with rigorous radiative transfer codes. This model is expected to be more accurate than previous simple models and applicable to a broader range of atmospheric conditions. The primary significance of this model is its simplicity, which allows it to be used on small desk-top computers. The spectrum produced by this model is limited to 0.3–4.0 μm wavelength with an approximate resolution of 10 nm.     

Experimental validation of a spectral direct solar radiation model

A model of spectral direct radiation of the sun at the ground compared with the spectral measurements performed by a monochromator has evidenced a satisfactory agreement. However, some discrepancies, mainly in the shorter wavelength range, have been evaluated. In order to point out the causes of these discrepancies, long series of data of direct integral radiation, water vapour content, aerosol turbidity together with standard meteorological data have been performed. These causes are defined by means of a statistical analysis.     

A simple model for estimating the transmittance of direct solar radiation through clear atmospheres

The clear-day all-wavelength transmittance τ of solar radiation directly through the 1962 standard atmosphere to a surface at altitude A is found to fit a simple mixed-gray-gas model (1 black, 1 gray, 1 clear) with a maximum error of 0.4 per cent. The relation is τ= a_o+a₁e^{k/cos z} where z is the zenith angle of the sun. The constant a₀, a₁ and k are functions only of altitude and of haze model (visibility range). Allowance is made for the effect of four climate types (tropical, midlatitude summer and winter, and subarctic summer) by modifying the 3 constants by ratios which depend on climate type only (not on altitude or haze model) and which lie between 0.92 and 1.04. This simple model should be capable of being combined with sunshine or cloud records, plus generalizations covering diffuse radiation, to yield predictions of insolation for use in design optimizations.     

A simple clear skies model for the luminous efficacy of diffuse solar radiation on inclined surfaces

In the present work we study the luminous efficacy of diffuse solar radiation incident on vertical surfaces for a clear sky and mean hourly values of diffuse irradiance and diffuse illuminance. We develop a model easy to use, similar to a model previously obtained for horizontal surfaces. To develop the present model for vertical surfaces we assume that the slope of the surface influences diffuse illuminance and diffuse irradiance in the same way. As a consequence of this hypothesis, the luminous efficacy of diffuse solar radiation is assumed to be the same for both horizontal and inclined surfaces.     

A simple model for computing the spectral radiance of clear skies

From standard and observed atmospheric profiles, the spectral sky radiance is computed on the basis of the Lowtran-6 numerical code. Then, a simple model for its calculation is built, based on Bliss—Kondrat'yev theoretical considerations. Some comparisons of spectral sky radiances are shown. At last, the total sky emissivity ε is obtained, and the function ε = f(t_dew) is discussed, where t_dew is the dewpoint temperature.     

Applicability of a simple model for computing diffuse solar radiation to locations of the European, African, Asian and North American areas

It is tested if the correlation type D = K(s/S)^−0.25 (sin h_n)^1.55, 0.2 s/S 0.9 previously proposed by Coppolino for Italian locations using K = 7.0, allows a reliable estimation of the monthly mean daily diffuse solar radiation D (MJ m⁻² day⁻¹), from only the monthly mean daily relative sunshine s/S and the noon altitude of the sun on the 15th of the month h_n (degrees) at locations of the European, African, Asian and North American areas. The test is performed at 14 stations in the above areas displaced at various latitudes L, elevations above sea level E and geographical situations, using K = 7.0 for the stations where 0.48 (s/S)_m, 0.63, K = 8.5 for those where 0.40 (s/S)_m < 0.48 or (s/S)_m > 0.63, and K = 10.0 for those where (s/S)_m < 0.40; (s/S)_m is the yearly mean value of s/S. K = 7.0 is chosen for five stations provided only with sunshine measurements and for three of the other nine stations provided with diffuse radiation measured data as well. K = 8.5 is chosen for five of the above nine stations and K = 10.0 for the remaining one. Moreover the prediction validity of the tested correlation is compared with that of two equations commonly quoted in literature: one of D = f(K_t, G) type and the other of D = f (s/S, G) type, where K_t = G/G₀. G and G₀ are the global and extraterrestrial monthly mean daily solar radiation, respectively. The test results point to a good agreement between the measured data of D and values from the above (D = f(s/S, h_n)) equation for eight of the above nine stations (i.e. with the exception of one with E = 2210 m), and deviations are generally low among D-values from the three considered equations, respectively, for the other five stations. Consequently the tested D = f(s/S, h_n) equation, with K-value chosen by the above guidelines, can be considered applicable, with good reliability, to all locations of the above areas provided 30°S < L < 55°N and E < 2000 m.     

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.     

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.     

Computing diffuse fraction of global horizontal solar radiation: A model comparison

For simulation-based prediction of buildings’ energy use or expected gains from building-integrated solar energy systems, information on both direct and diffuse component of solar radiation is necessary. Available measured data are, however, typically restricted to global horizontal irradiance. There have been thus many efforts in the past to develop algorithms for the derivation of the diffuse fraction of solar irradiance. In this context, the present paper compares eight models for estimating diffuse fraction of irradiance based on a database of measured irradiance from Vienna, Austria. These models generally involve mathematical formulations with multiple coefficients whose values are typically valid for a specific location. Subsequent to a first comparison of these eight models, three better performing models were selected for a more detailed analysis. Thereby, the coefficients of the models were modified to account for Vienna data. The results suggest that some models can provide relatively reliable estimations of the diffuse fractions of the global irradiance. The calibration procedure could only slightly improve the models’ performance.     

A method for spectral analysis of concentrated solar radiation

In the year 1994 the DLR in Cologne inaugurated a 20 kW solar furnace for technological and scientific experiments. One of the main applications of the solar furnace is the research on photochemical reactions using concentrated sunlight. For this purpose exact knowledge of the spectral composition and its local distribution is essential. The evaluation of experiments and the validation of computer codes rely on these informations.The solar radiation that is concentrated to high flux densities (up to 4 MW/m²) shows short-time fluctuations and therefore a special measurement technique is required.It is shown how to use the imaging properties of a Czerney-Turner monochromator in combination with video camera detection to achieve a fast spectral analysis. This measurement is actually done along an intersection line through the focus. Moreover the calibration is described and first test pictures are analysed.     

A simple hourly clear-sky solar radiation model based on meteorological parameters

An hourly solar radiation model, based on observed meteorological data, was developed and tested. As a means of comparison, the Watt and Bird models and the Solmet regression models were also tested. Several conclusions were drawn about the parameterization of solar radiation-depleting parameters. It was determined that a reasonable estimate of lower layer aerosol extinction can be determined using humidity, visibility, and mixing height. The parameterization of water vapor absorption obtained by atmospheric rather than laboratory observations was found to give better model results.     

A simple hourly all-sky solar radiation model based on meteorological parameters

An hourly solar radiation model for cloudy skies, based on meteorological data, was developed andtested. As a means of comparison, the SOLMET regression and Watt models were also tested. The present model was examined for individual cloud types using measured solar radiation to judge the effectiveness of the model in the presence of particular clouds.     

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.     

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.