REST2: High-performance solar radiation model for cloudless-sky irradiance, illuminance, and photosynthetically active radiation – Validation with a benchmark dataset

REST2, a high-performance model to predict cloudless-sky broadband irradiance, illuminance and photosynthetically active radiation (PAR) from atmospheric data, is presented. Its derivation uses the same two-band scheme as in the previous CPCR2 model, but with numerous improvements. Great attention is devoted to precisely account for the effect of aerosols, in particular.Detailed research-class measurements from Billings, OK are used to assess the performance of the model for the prediction of direct, diffuse and global broadband irradiance. These measurements were made in May 2003 during a sophisticated radiative closure experiment, which involved the best radiometric instrumentation currently available and many ancillary instruments. As a whole, these exceptional measurements constitute the only known modern benchmark dataset made specifically to test the intrinsic performance of radiation models. Using this dataset as reference, it is shown that REST2 performs better than CPCR2 for irradiance, illuminance or PAR predictions. The availability of the turbidity data required by REST2 or other similar models is also discussed, as well as the effect that turbidity has on each component of broadband irradiance, PAR irradiance and illuminance, and on the diffuse/global PAR ratio.     

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.     

Investigations of solar radiation detectors using a laboratory test facility for solar radiation meteorological instruments

A laboratory test facility for solar radiation detectors has been built and is in operation at the Aerological Station of the Swiss Meteorological Institute (SAP/SMI). This installation is conceived as a universal test bed for solar radiation exposed meteorological instruments, and consists of a commercially available solar simulator, a laser alignment system, a translation mechanism with instrument mounts, and an adjustable projection mirror. The solar simulator produces a well characterized radiation beam which can be filtered to match the terrestrial or outer space solar spectrum with an irradiance of up to one solar constant (1367 Wm⁻²). The instrument mounts and a HeNe laser beam provide a precise and easy alignment of the reference and the test instruments in the radiation beam, allowing for incident angles in the range of 15°–75°. The measurement is based on a comparison of the response of an active cavity absolute radiometer PMO6 with the signal of the test instrument.Detailed investigations of the Haenni Solar 111B type heliometer have revealed important irregularities in the sunshine threshold irradiance angular distribution. Measurements performed with and without the protection glass cover prove the exceedingly high threshold values at large declination angles to be a consequence of enhanced reflections due to the incident angle and inhomogeneities in the glass cover.Very satisfactory results have also been obtained on characterization measurements of pyranometers showing the mean values of the responsivity to be within 0.8% of the calibration values measured at the world radiation center (WRC) at Davos.     

Photocatalysis and radiation absorption in a solar plant

Recently, many papers have appeared in literature about photocatalytic detoxification. However, progress from laboratory data to the industrial solar reactor is not easy. Kinetic models for heterogeneous catalysis can be used to describe the photocatalytic processes, but luminic steps, related to the radiation, have to be added to the physical and chemical steps considered in heterogeneous catalysis. Thus, the evaluation of the radiation, and its distribution, inside a photocatalytic reactor is essential to extrapolate results from laboratory to outdoor experiments and to compare the efficiency of different installations. This study attempts to validate the experimental set up and theoretical data treatment for this purpose in a Solar Pilot Plant. The procedure consists of the calibration of different sunlight radiometers, the estimation of the radiation inside the reactor, and the validation of the results by actinometric experiments. Finally, a comparison between kinetic constants, for the same reaction in the laboratory (artificial light) and field conditions (sun light), is performed to demonstrate the advantages of knowing the radiation inside a large photochemical reactor.     

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.     

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.     

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.     

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.     

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.     

Hydrogen production using solar radiation

Various water-splitting methods using solar energy are reviewed and compared to each other. Direct thermal method has the highest efficiency, however it poses difficulties because of the need for heat-resisting materials. Thermochemical method becomes promising if corrosion-resisting materials are found. Electrolytic method is straightforward and conventional. However, a hybrid system combining electrolytic method with thermochemical and/or photochemical methods looks promising and is believed to result in optimum conversion efficiencies in the near future. Photolysis and biochemical methods are environmentally most acceptable, but are of low conversion efficiencies presently.     

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%.     

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.     

Computation of solar radiation distribution in a solar still with internal and external reflectors

A model that calculates the distribution of solar radiation inside a basin-type solar still with plane reflectors has been proposed. In this model, both surface finish and optical view factors are taken into consideration in the computation of solar radiation that effectively reaches the surface of saline water in the distillation system. The model was applied to a conventional solar still and an advanced solar still with separate condenser. The conventional solar still was tested at New Delhi (28°35′N, 77°12′E) in previous work while the advanced distillation system was developed in this investigation and it comprised three basins with saline water. Basin 1 was fitted horizontally in the evaporator chamber, with the condenser chamber housing basins 2 and 3. The top part of the evaporator unit was covered with glass to allow solar radiation to reach water in basin 1. In addition, the internal surfaces of the walls of the evaporator and external surface of the front wall of the condenser unit reflected part of the incoming solar radiation onto the surface of saline water in basin 1. The distillation system was tested outdoors at the Malawi Polytechnic (15°48′S, 35°02′E). Under the prevailing meteorological conditions, it is found that the computed solar load on the surface of saline water in the evaporator basin is lower than that observed on a horizontal plane outside each energy system. The new model exhibited a higher degree of accuracy than the previous one. Other results are presented and discussed in this paper.     

Study of solar radiation stability of modern polymer materials on a large solar furnace

The testing of modern polymer insulators designed for transmission facilities for light stability under the action of solar radiation is considered. The technique of accelerated testing including irradiation of the samples with ultraviolet radiation using a large solar furnace has been proposed.