Models of solar radiation with hours of bright sunshine: A review

In the design and study of solar energy, information on solar radiation and its components at a given location is very essential. Solar radiation data are required by solar engineers, architects, agriculturists and hydrologists for many applications such as solar heating, cooking, drying and interior illumination of buildings. For this purpose, in the past, several empirical correlations have been developed in order to estimate the solar radiation around the world. The main objective of this study is to review the global solar radiation models available in the literature. There are several formulate which relate global radiation to other climatic parameters such as sunshine hours, relative humidity and maximum temperature. The most commonly used parameter for estimating global solar radiation is sunshine duration. Sunshine duration can be easily and reliably measured and data are widely available.     

Global,direct and diffuse solar radiation on horizontal and tilted surfaces in Jeddah,Saudi Arabia

The measured data of global and diffuse solar radiation on a horizontal surface, the number of bright sunshine hours, mean daily ambient temperature, maximum and minimum ambient temperatures, relative humidity and amount of cloud cover for Jeddah (lat. 21°42′37′′N, long. 39°11′12′′E), Saudi Arabia, during the period (1996–2007) are analyzed. The monthly averages of daily values for these meteorological variables have been calculated. The data are then divided into two sets. The sub-data set I (1996–2004) are employed to develop empirical correlations between the monthly average of daily global solar radiation fraction (H/H₀) and the various weather parameters. The sub-data set II (2005–2007) are then used to evaluate the derived correlations. Furthermore, the total solar radiation on horizontal surfaces is separated into the beam and diffuses components. Empirical correlations for estimating the diffuse solar radiation incident on horizontal surfaces have been proposed. The total solar radiation incident on a tilted surface facing south H_t with different tilt angles is then calculated using both Liu and Jordan isotropic model and Klucher’s anisotropic model. It is inferred that the isotropic model is able to estimate H_t more accurate than the anisotropic one. At the optimum tilt angle, the maximum value of H_t is obtained as ∼36 (MJ/m² day) during January. Comparisons with 22 years average data of NASA SSE Model showed that the proposed correlations are able to predict the total annual energy on horizontal and tilted surfaces in Jeddah with a reasonable accuracy. It is also found that at Jeddah, the solar energy devices have to be tilted to face south with a tilt angle equals the latitude of the place in order to achieve the best performance all year round.     

Models for obtaining solar radiation from other meteorological data

The application of solar energy requires a knowledge of long-term solar radiation and daylight data. Because of the limited availability of measured data, various formulae have been derived to compute the solar irradiance using other, more commonly available, weather data. In this article two such models are presented, MRM (meteorological radiation model) and CRM (cloud-cover radiation model). MRM requires hourly data for sunshine duration, dry- and wet-bulb temperature; while CRM requires only cloud amount. Both models can generate hour-by-hour data for horizontal global, diffuse, and beam irradiance. A brief comparison of the two models is presented. Results showed that MRM has the advantage over CRM, on account of its consistency with the measured data. Both models are now available via the Internet in the form of electronic spreadsheets.     

A software to process daily solar radiation data

This work presents one software developed to process solar radiation data. This software can be used in meteorological and climatic stations, and also as a support for solar radiation measurements in researches of solar energy availability allowing data quality control, statistical calculations and validation of models, as well as ease interchanging of data.     

Analysis of experimental data on diffuse solar radiation in Athens,Greece, for building applications

Proper design and performance prediction of solar energy systems requires accurate information on the availability of solar radiation. The diffuse-to-total radiation correlation, originally developed by Liu and Jordan, has been extensively used as the technique and provided excellent results, although it was latitude dependent and not universally applicable. Thus, diffuse fraction correlations of this type have been developed by few other authors and for different location. This paper presents an analysis of hourly diffuse radiation on a horizontal surface. Hourly pyranometer data from Athens, Greece, are used to establish relationships between the diffuse fraction and the clearness index k _T for hourly and daily values. The results of the proposed equations are then compared with earlier equations. For the urban conditions of Athens the developed correlation fit to the empirical data.     

Estimation of global solar radiation on horizontal surfaces in Jeddah, Saudi Arabia

The measured data of global solar radiation on a horizontal surface, as well as the number of sunshine hours, mean daily ambient temperature, maximum and minimum ambient temperatures, relative humidity and amount of cloud cover, for Jeddah (latitude 21° 42′37″N, longitude 39° 11′12″E), Saudi Arabia for the period 1996–2006 are analyzed. The data are divided into two sets. The sub-data set 1 (1996–2004) are employed to develop empirical correlations between the monthly average of daily global solar radiation fraction (H/H₀) and various meteorological parameters. The nonlinear Angström type model developed by Sen and the trigonometric function model proposed by Bulut and Büyükalaca are also evaluated. New empirical constants for these two models have been obtained for Jeddah. The sub-data set 2 (2005, 2006) are then used to evaluate the derived correlations. Comparisons between measured and calculated values of H have been performed. It is indicated that, the Sen and Bulut and Büyükalaca models satisfactorily describe the horizontal global solar radiation for Jeddah. All the proposed correlations are found to be able to predict the annual average of daily global solar radiation with excellent accuracy. Therefore, the long term performance of solar energy devices can be estimated.     

Comparative study of various correlations in estimating hourly diffuse fraction of global solar radiation

Proper design and performance predictions of solar energy systems require accurate information on the availability of solar radiation. The diffuse-to-global solar radiation correlation, originally developed by Liu and Jordan, has been extensively used as the technique providing accurate results, although it is latitude dependent. Thus, in the present study, empirical correlations of this type were developed to establish a relationship between the hourly diffuse fraction (k_d) and the hourly clearness index (k_t) using hourly global and diffuse irradiation measurements on a horizontal surface performed at Athalassa, Cyprus. The proposed correlations were compared against 10 models available in the literature in terms of the widely used statistical indicators, rmse, mbe and t test. From this analysis, it can be concluded that the proposed yearly correlation predicts diffuse values accurately, whereas all candidate models examined appear to be location-independent for diffuse irradiation predictions.     

The assessment of different models to predict the global solar radiation on a surface tilted to the south

Global and diffuse solar radiation intensities are, in general, measured on horizontal surfaces, whereas stationary solar conversion systems (both flat plate solar collector and PV) are tilted towards the sun in order to maximize the amount of solar radiation incident on the collector surface. Consequently, the solar radiation incident on a tilted surface must be determined by converting the solar radiation intensities measured on a horizontal surface to that incident on the tilted surface of interest. There exist a large number of models designed to perform such a conversion. 11 such models have been tested utilizing data measured in Beer Sheva, Israel. The data consist of hourly global and diffuse solar radiation on a horizontal surface, normal incidence beam and global radiation on a south-oriented surface tilted at 40°. The horizontal diffuse radiation measured using a shadow ring was corrected using four different correction models. This resulted in 44 model permutations. The individual model performance is assessed by an inter-comparison between the calculated and measured solar global radiation on the south-oriented surface tilted at 40° using both graphical and statistical methods. The relative performance of the different models under different sky conditions has been studied. Different grading systems have been applied in an attempt to score the relative performance of the models.     

Correlation between hourly diffuse and global radiation for New Delhi

Estimation of hourly insolation on tilted surfaces is required in simulation of solar energy systems. This necessitates splitting of hourly global horizontal insolation into diffuse and direct components. Many models have been developed for this purpose, and the aim of this study is to develop a correlation between hourly diffuse ratio and clearness index for New Delhi. The correlation is developed on the basis of measured data for two years. The performance of this correlation was checked by calculating the difference between computed and measured diffuse radiation. The correlation proved to perform quite well. A comparison of the present correlation with those for other locations showed that such correlations are location dependent.     

Calculation of monthly average insolation on tilted surfaces

Several simplified design procedures for solar energy systems require monthly average meteorological data. Monthly average daily totals of the solar radiation incident on a horizontal surface are available. However, radiation data on tilted surfaces, required by the design procedures, are generally not available. A simple method of estimating the average daily radiation for each calendar month on surfaces facing directly towards the equator has been presented by Liu and Jordan [1]. This method is verified with experimental measurements and extended to allow calculation of monthly average radiation on surfaces of a wide range of orientations.     

Performance of low temperature solar rankine power generation system

The overall performance of a solar thermal electrical power generation system is governed by the performance of the energy collection system and the power conversion unit. Any system operating under given meteorological and solar radiation conditions has a unique energy collection temperature for which the electrical output of the system will be a maximum. An engineering analysis of the system was carried out to obtain general correlations which can be used for determining such an optimum temperature. Factual experience on the design and operation of a Rankine system, using flat plate collectors and the climatological data, was used to obtain numerical estimates for the net energy conversion capability of such systems operating in Kuwait.     

Evaluation of decomposition models of various complexity to estimate the direct solar irradiance over Belgium

Solar energy production is directly correlated to the amount of radiation received at a given location. Appropriate information on solar resources is therefore very important for designing and sizing solar energy systems. Concentrated solar power projects and photovoltaic tracking systems rely predominantly on direct normal irradiance (DNI). However, the availability of DNI measurements from surface observation stations has proven to be spatially too sparse to quantify solar resources at most potential sites. Satellite data can be used to calculate estimates of direct solar radiation where ground measurements do not exist. Performance of decomposition models of various complexity have been evaluated against one year of in situ observations recorded on the roof of the radiometric tower of the Royal Meteorological Institute of Belgium in Uccle, Brussels. Models were first evaluated on a hourly and sub-hourly basis using measurements of global horizontal irradiance (GHI) as input. Second, the best performing ground-based decomposition models were used to extract the direct component of the global radiation retrieved from Meteosat Second Generation (MSG) images. Results were then compared to direct beam estimations provided by satellite-based diffuse fraction models and evaluated against direct solar radiation data measured at Uccle. Our analysis indicates that valuable DNI estimation can be derived from MSG images over Belgium regardless of the satellite retrieved GHI accuracy. Moreover, the DNI retrieval from MSG data can be implemented on an operational basis.     

Calculation of monthly mean solar radiation for horizontal and inclined surfaces

The use of daily rather than hourly time intervals in the calculation of the monthly mean values of solar radiation for both horizontal and inclined surfaces has for long been a desirable objective due to a reduction in the required computational effort and more general availability of daily data. This paper presents a method for such calculations, with bright sunshine hours and surface albedo being the only required input data. The incorporation of the effects of multiple reflection between the ground and atmosphere results in relationships used to calculate the diffuse and total solar radiation for a horizontal surface which are largely independent of season and location.The present paper shows that, despite the use of a daily time interval, the solar radiation incident on both horizontal and south-facing surfaces may be calculated with an accuracy generlly associated with instrumental measurements. This result is achieved without the necessity of arbitrarily varying the empirical coefficients to account for variations in climatological conditions at the stations being studied.     

Measurement of solar energy radiation in Abu Dhabi,UAE

This paper presents data on measurement of actual solar radiation in Abu Dhabi (24.43°N, 54.45°E). Global solar radiation and surface temperatures were measured and analyzed for one complete year. High resolution, real-time solar radiation and other meteorological data were collected and processed. Daily and monthly average solar radiation values were calculated from the one-minute average recorded values. The highest daily and monthly mean solar radiation values were 369 and 290 W/m², respectively. The highest one-minute average daily solar radiation was 1041 W/m². Yearly average daily energy input was 18.48 MJ/m²/day. Besides the global solar radiation, the daily and monthly average clearness indexes along with temperature variations are discussed. When possible, global solar energy radiation and some meteorological data are compared with corresponding data in other Arab state capitals. The data collected indicate that Abu Dhabi has a strong potential for solar energy capture.     

Correlations between monthly average global solar radiation on horizontal surfaces and relative duration of sunshine in Yunnan Province, China

With measured data of global solar radiation and the relevant data of geographic and meteorological parameters at 7 meteorological stations in Yunnan Province, the correlations between monthly average global solar radiation on horizontal surfaces and relative duration of sunshine are developed in this special region which has significantly varying climates. It is believed that the two correlations developed in this work are applicable for estimating monthly global solar radiation on horizontal surfaces at any site in Yunnan Province, China.     

A simple formula for estimating global solar radiation in central arid deserts of Iran

Over the last two decades, using simple radiation models has been an interesting task to estimate daily solar radiation in arid and semi-arid deserts such as those in Iran, where the number of solar observation sites is poor. In Iran, most of the models used so far, have been validated for a few specific locations based on short-term solar observations. In this work, three different radiation models (Sabbagh, Paltridge, Daneshyar) have been revised to predict the climatology of monthly average daily solar radiation on horizontal surfaces in various cities in central arid deserts of Iran. The modifications are made by the inclusion of altitude, monthly total number of dusty days and seasonal variation of Sun–Earth distance. A new height-dependent formula is proposed based on MBE, MABE, MPE and RMSE statistical analysis. It is shown that the revised Sabbagh method can be a good estimator for the prediction of global solar radiation in arid and semi-arid deserts with an average error of less than 2%, that performs a more accurate prediction than those in the previous studies. The required data for the suggested method are usually available in most meteorological sites. For the locations, where some of the input data are not reported, an alternative approach is presented.     

Atmospheric aerosol influence on the Brazilian solar energy assessment: Experiments with different horizontal visibility bases in radiative transfer model

The radiative transfer model BRASIL-SR is used by Brazilian Institute for Space Research for the assessment of the solar irradiation in Brazil. The model parameterizes the influence of aerosols in the solar radiation transmittance using climate averages of horizontal visibility, which does not represent the actual atmospheric condition in Brazil, especially during dry season. In clear sky conditions, aerosols are a major source of bias in solar radiation models. Their concentration have large spatial and temporal variability particularly in the Brazilian Midwestern region from April until October, due to forest fires, and in Southeastern region due to pollution from megacities. In this study, meteorological data from METAR comprising the years of 2006, 2007 and 2008 were analyzed to evaluate the seasonal variability of the horizontal visibility in Brazil to better represent the influence of aerosols on the model estimations of surface solar irradiation. New horizontal visibility values was generated to each month simulated, to provide input data to the BRASIL-SR model and site specific ground data were used to validate the model estimates. The global, direct beam and diffuse solar irradiation estimates obtained by making use of the new horizontal visibility data presented an overall lower BIAS and RMSE deviations.     

Model evaluation and optimum collector slope for a tropical country

Various models proposed in the literature, viz. the Beam method, proposed by Morse & Czarnecki; two methods proposed by Liu & Jordan, using hourly values and average daily values of solar radiation: and Klucher's method are compared in this paper using measured hourly values of global and diffuse radiation on a horizontal surface and the total radiation on a tilted surface. It was observed that the model proposed by Klucher estimates the radiation more consistently with the experimental observations for clear as well as cloudy sky conditions.

This method was used for predicting the year round radiation availability on (i) a fixed collector inclined at an optimum tilt, (ii) a partially tracking collector in which the slope is fixed but following the sun's azimuth angle, and (iii) a fully tracking collector. In this analysis, measured values of hourly global and diffuse solar radiation on a horizontal plane for four widely separated Indian stations, viz. Delhi (28°38′N), Poona (18°29′N), Calcutta (22°36′N), and Madras (13°8′N) as per India Meteorological Department classification for climatic analysis, have been used.

With the model proposed, the radiation availability on different slopes for all the twelve months of the year for a fixed and partially tracking collector have been evaluated and optimum tilts for various seasons of a year for different solar energy applications for all the four Indian stations have been determined. For a typical winter month at New Delhi in the semi-arid zone of India, a fixed collector, a partially tracking collector and a fully tracking collector receive 60, 80 and 95% more radiation compared to that received on a horizontal plane respectively. Another observation is that the variation of the insolation received on inclined surfaces is not at all sensitive to the angle of tilt in the neighbourhood of the optimum angle of operation.     

Analysis of short-term solar radiation data

Solar radiation data are available for many locations on an hourly basis. Simulation studies of solar energy systems have generally used these hourly values to estimate long-term annual performance, although solar radiation can exhibit wide variations during an hour. Variations in solar radiation during an hour, such as on a minute basis, could result in inaccurate performance estimates for systems that respond quickly and non-linearly to solar radiation. In addition, diffuse fraction regressions and cumulative frequency distribution curves have been developed using hourly data and the accuracy of these regressions when applied to short-term radiation has not been established. The purpose of this research is to investigate the inaccuracies caused by using hourly rather than short-term (i.e., minute and 3 min) radiation data on the estimated performance of solar energy systems. The inaccuracies are determined by examination of the frequency distribution and diffuse fraction relationships for short-term solar radiation data as compared to existing regressions and by comparing calculated radiation on tilted surfaces and utilizability based on hourly and short-term radiation data.     

Solar radiation estimations over India using Meteosat satellite images

India is endowed with good solar energy resource due to its geographic position in the equatorial Sun Belt of the earth, but its atmosphere can have eventual large presence of aerosols with the subsequent negative feedback to the solar radiation available. Therefore, solar resource assessment studies over India are of high interest for potential solar energy applications. In this work daily estimations of global horizontal and direct normal irradiation are presented for six locations in India covering the years from 2000 till 2007. These computations have been performed with IrSOLaV/CIEMAT method for computing solar radiation components from Meteosat images with a spatial resolution of less than 5 × 5 km. A brief assessment exercise of the model output have been made with ground measurements available from the World Radiation Data Centre database, which consists only of daily sums of global horizontal irradiation. The daily global horizontal irradiation estimated by the model has shown a general positive bias with the ground measurements in the range of 5%, being the root mean square deviation around 12%, excepting for Trivandrum location where there are evidences of higher uncertainty in the ground measurements. In addition, the dynamical behavior of daily global irradiation is quite well reproduced by the model as a consequence of adding to the input the daily turbidity values estimated from MODIS Terra satellite information. Estimations of direct normal irradiation are also exposed but no assessment was made due to the lack of ground measurements. The importance and need of accurate daily aerosol data with high spatial resolution for solar radiation estimations is pointed out in this work.