Predicting the spectral and broadband aerosol transmittance in the atmosphere for solar radiation modelling

Calculations of the spectral transmittance of the atmospheric aerosol, using Mie theory, for wavelengths between 0 and 40 μm is presented. The chemical composition of the aerosol particles has been modelled in order to correspond to the atmospheric conditions of medium and large coastal or near coastal cities with important industrial and other anthropogenic emission sources. Individual size distributions and optical properties for each aerosol constituent have been considered.Based on the detailed aerosol model, and using parameterization techniques, analytical broadband aerosol transmission functions for the absorption and total attenuation are obtained. The accuracy of the proposed expressions are verified with various tests, using data from the National Observatory of Athens (NOA). The proposed broadband aerosol transmission functions can be incorporated directly into solar radiation models to predict accurately the beam, diffuse and global solar radiation at a given place.     

Concentration of the solar radiation in a solar furnace

Energy concentration in a solar furnace is greatly influenced by the optical accuracy of the reflecting surface of the mirror. The highest density of a heat flux on the heating surface of a specimen is determined by its concentration and by the reflectivity of the mirror.

Since the apparent diameter of the moon is almost equal to that of the sun and the illumination of the moon may be adapted to the photographic determination of flux density, the rate of energy concentration in the authors' solar furnace was studied by the moon's image projected upon the heating zone in place of that of the sun.

As a result, about 300 watts per cm was obtained as the highest possible density of the heat flux in this solar furnace. This figure also agreed with the results of an optical analysis based on the practical finishing of the present mirror surface. With a heat flux of 300 watts per sq cm, in accordance with Stefan-Boltzmann's law of radiation, the highest temperature attainable is estimated to be approximately 2700°K. Besides the above, in actual experiment, approximately 2300°C was obtained in observing the melting points of binary mixtures, e.g., MgO---CoO and MgO---Cr₂O₃. Thus, the above-mentioned three approaches to the problem are in fairly good agreement.     

Effects of changes in the atmosphere on solar insolation

A review of the nature of solar radiation and the spectral distribution of its energy is presented. The attenuation of solar radiation by scattering and absorption and the effects of atmospheric pollutants on radiation attenuation with an estimate of the long-term effects of pollutants is discussed.     

Some factors affecting the absorption of solar radiation in solar stills

The performance of a solar still can be affected to a significant degree by the build-up of reflecting layers of salt on the water surface and basin liner. This paper presents a method of quantitatively assessing the effect of these salt layers, taking into account the band absorption characteristics of water. A revised curve of the absorption of the solar spectrum in water is given.     

Analysis of solar radiation measurements at Athens Observatory and estimates of solar radiation in Greece

In this paper measurements of Global (G) Solar Radiation on a horizontal surface at Athens during the 16 yr period 1960-75 are analysed. Mean annual, monthly and daily totals, the diurnal variation, frequency distribution of daily totals, frequency of occurrence of daily totals of Global Radiation less than 8.5, 17, and 34 MJ/m² for 2, 3, 4 and 5 successive days are computed and discussed.Direct Solar Radiation at normal incidence (I) is computed and analysed in a similar manner to that of Global Radiation, for the same period. Components of direct radiation of normal incidence have been computed from spot value observations at times when sky conditions permitted.Annual values of global radiation were estimated from sunshine measurements (1960-73) widely distributed throughout Greece. It is considered that this analysis of measurements should closely represent the radiation climatology of Greece.     

Absorption of solar radiation in ponds

Analysis is presented to predict the local rate of solar energy absorption in a pond using the radiative transfer theory. The physical model considers absorption and scattering by the water and internal reflection of radiation from the air-water interface as well as the bottom. A forward scattering approximation and a discrete-coordinate approximation of the radiative transfer equation are discussed. Numerical results for the local volumetric rate of solar energy absorption in the water are presented in the paper for a range of parameters of physical interest. The effects of the directional distribution of solar radiation incident on the water surface, the attenuation of solar radiation by the atmosphere during the diurnal cycle and the modification of the spectral radiation characteristics of water by impurities and additives on the absorption and distribution of the absorbed energy in the pond are investigated.     

Measurement of solar radiation by silicon solar cell

Investigations into the use of a silicon solar cell to measure solar radiation intensity are described. The effect of optical path length ratio and atmospheric constituents are discussed. A survey is made of other photovoltaic devices. It is concluded that, on presently available data, the silicon cell is the most suitable for the purpose.

Comparisons are made between the signals obtained from a silicon-solar-cell radiometer and a Kipp thermopile type solarimeter used as a standard. One set of comparisons is made for 30-minute intervals on clear days and is analysed so that known effects due to angle of incidence are allowed for and variations in the signals caused by spectral quality of the radiation can be separated. This set of comparisons shows an extreme spread of ±13 percent on a reference constant determined for midday clear sky. This extreme spread includes variations of +6.5 to −3 percent at midday together with variations during the course of any one day.

A second set of comparisons made during whole days or long periods, during which conditions were stable, gave rise to two calibration constants, one for clear-sky and one for overcast-sky conditions.

If an over-all calibration constant is desired for all conditions, then a value of 15.79 mA cm⁻² min/Langley is obtained with a probable error of to percent. The skew effect here is because more readings were taken for clear-sky conditions, thus favoring the lower constant for these conditions.     

Global solar radiation estimation

This paper presents the comparison between the observed and estimated values of global solar radiation on horizontal surfaces obtained from the linear Angstrom type of correlation of Rehman and Halawani [1] for 52 cities spread in 11 countries; viz. India, Egypt, Sri Lanka, Spain, Zimbabwe, Yemen, Sudan, Italy, Zambia, Hong Kong, and Malaysia. The comparisons are also made with the local linear models wherever available. The estimated values are compared with the measured values in terms of percent error, mean bias error (MBE), mean absolute bias error (MABE), root mean square error (RMSE), and mean percent error (MPE). This study finds that the model of Rehman and Halawani [1] is capable of giving estimates within an acceptable mean percent error of 5% and less for 33% of cities and between 5–10% for 50% of cities.     

The solar radiation resource

We discuss the characteristics of solar radiation which are most useful for the assessment of solar technologies. Graphs are presented which show the total annual insolation incident on the principal tracking and non-tracking collectors. Additional graphs are developed for the latitudinal and seasonal variations of solar radiation in the absence of an atmosphere. These are then compared with measurements averaged over the U.S. SOLMET sites to provide an understanding of the role of atmospheric effects on the seasonal variations of solar radiation.     

On the random nature of solar radiation

The correlation of beam and global radiation is examined on an hourly, monthly and yearly basis from analysis of nearly 3000 days of simultaneous hourly horizontal global and normal beam radiation measurements for Bet Dagan, Israel. One-to-one beam-global correlations are obtained by appropriately averaging over the correlation matrices, and these results are compared with the corresponding correlation functions that are based on U.S. radiation data. The accuracy of predicting yearly collectible energy for solar collector systems from hourly global data plus an hourly beam-global correlation function is determined in a form whose results may be of more general value than could be obtained with computer simulations.     

Spatial-temporal forecasting of solar radiation

We apply the CARDS solar forecasting tool, developed at the University of South Australia, to forecasting of solar radiation series at three sites in Guadeloupe in the Caribbean. After performing the model estimates at each individual site, forecast errors were tested for cross correlation. It was found that on an hourly time scale, there was small but significant correlation between sites, and this was taken into account in refining the forecast. Cross correlation was found to be insignificant at the ten minute time scale so this effect was not included in the forecasting. Also, the final error series in each case was tested for an ARCH effect, finding that to construct prediction intervals for the forecast a conditional heteroscedastic model had to be constructed for the variance. Note that cross correlation between sites has to be included for this procedure as well as in the forecasting of the radiation.     

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.     

Investigating different diffuse solar radiation models to analyse solar radiation on inclined surfaces in Oman

In this paper, a detailed analysis of the solar radiation on horizontal and tilted surfaces for six locations in Oman is presented. The locations are (from North to South): Majis/Sohar, Sur, Fahud, Masira, Marmul, and Salalah. These locations spread over Oman and cover different types of landscape. The method is validated through the use of measured data. The effect of tilt angle and orientation on the incident solar radiation is presented along with optimum surface tilt angles and directions for maximum solar radiation collection in these six locations. The solar radiation models used in this paper show good agreement with measured data. The results presented in this paper are extremely useful for quick estimation of solar radiation for calculations of buildings’ cooling load and solar collector system performance. This can be easily extended for other locations with similar landscapes and geographical conditions.     

Short-term variability of solar radiation

This paper presents a study of the variability of solar radiation in the minute-long time range. The solar climate in Northern Europe is classified in this paper as being either stable, or highly variable, due to stochastic cloud cover inducing fluctuations of the solar irradiance. In general, solar radiation exhibits both positive and negative increments in the radiation during any period. The distribution functions of these increments with respect to their magnitude and duration are investigated, as well the distribution functions of stable intervals during generally variable radiation. The distribution functions are found to be a superposition of two exponential functions with different exponents, which depend on the magnitude of the radiation increments.     

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.     

Records on solar radiation in Chile

After a short introduction of a historical nature, the institutions that at present carry out measurements of solar radiation in Chile are named and information regarding the equipping of the National Archive of Solar Evaluations, in order to have a “National Standard”, is presented. Also included are the first results of the coordinated measurements, and, after a short summary of the first Chilean publications regarding this subject, a comparison between the values measured and Black's Isopleth's Map are given. The paper calls attention to the phenomenon of seasonal displacement of maximum solar radiation over the South American Continent.     

Solar radiation absorption in solar ponds

The local rate of absorption of the solar radiation in a solar pond is determined for the direct component at angles of incidence from 0° to 75° with 15° intervals as well as for the diffuse component by the exact treatment of the radiation problem. The effects of bottom reflection, the pond depth, the type of radiation on the thermal performance of the pond are examined, and a new rigorous approach is presented for treating diffuse radiation as a direct beam. The fraction of the solar radiation absorbed within the first 10 cm of water is determined under various conditions. The local rate of solar energy absorption at any depth and at any incidence angle can readily be computed from a fourth-degree polynomial expression, the coefficients of which are tabulated for different incidence angles and bottom reflectivities.