- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Journal of Energy
Volume 2013 (2013), Article ID 305207, 8 pages
Solar Radiation: Models and Measurement Techniques
Department of Applied Sciences, Institute of Engineering & Technology, Gautam Buddh Technical University, Lucknow 226021, India
Received 19 December 2012; Revised 11 April 2013; Accepted 12 April 2013
Academic Editor: Mattheos Santamouris
Copyright © 2013 C. K. Pandey and A. K. Katiyar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
In order to grasp the significance of the work accomplished by the author, it is necessary to keep abreast of the present developments in this field. The research work reported in the paper is an attempt to get knowledge to assess the solar energy potential for practical and efficient utilization in India. Our work is centered on estimating realistic values of solar (global and diffuse) radiation on horizontal and tilted surfaces using measured meteorological data and geographical and geometrical parameters for India.
The sun is the driving force for all atmospheric processes. Solar radiant intensity is the expression of that input of energy upon the planet. Therefore, the ability to understand and quantify its value and distribution accurately is important in the initial understanding and modeling of any other thermodynamic or dynamic process in the earth-ocean-atmosphere system. Unfortunately, however, too little is known about the spatial and temporal distribution of incoming solar radiation. A more complete and precise description of that distribution will prove usefulness to many fields of study that rely on atmospheric energy input, such as agricultural , architectural , and engineering  planning. For these reasons, analysis of the solar radiation distribution in India—a state with a relatively high loading of input radiation and relatively high spatial and temporal variability—is both important and relevant.
2. Renewable Energy
From the beginning of 19th century, dwelling of fossil fuels is increasing continually toward the development of industrialization and modern life style. The fossil fuels are being used from domestic to industrial applications on the cost of pollution, health hazards, and ecology of earth. Excessive exploitation of conventional fuels directly and indirectly assist in global warming and many more factors which drive the planet towards dark future.
To overcome the dependency on conventional fuels, researchers and many organizations are working on alternative fuels, which should be commercially viable, easy to use, less pollutant, and must be abundant in nature. In this direction, renewable energies, like solar energy, tidal energy, wind energy, biofuels, and so forth, are more suitable than conventional sources of energy. These nonconventional forms are not only renewable but also maintain ecology and environment as they are ecofriendly and do not contribute to global warming and production of green house gases and so forth.
In context of India and developing countries, it is awful condition, because most of the Indian families exploit forest and fossil fuels for their domestic uses, which directly and indirectly not only affect growth of country but also health of user. Quest for energy security and sustainable development depend on the ability to get energy from renewable sources, and to use it optimistically to meet growing and diverse needs of India.
India is blessed with an abundance of nondepleting and environment friendly renewable energy resources such as solar, wind, biomass and hydro, and so forth. The Uttar-Pradesh, where solar energy and wind energy are profusely available throughout the year in comparison to the rest of India, has higher potential to exploit renewable energies for domestic and industrial applications.
3. Need for Renewable Energy
Increasing rate of energy consumption is essential for progress of our civilization and therefore main problem is how we produce energy. Extensive use of fossil fuels and nuclear energy has created bad impact on environmental, social, and sustainability problems. So we need such energy sources that will forever and can be used without pollution. Furthermore, conventional energy systems using fossil resources, especially old ones in numerous and small scale, are found to be major contributors to atmosphere pollution and greenhouse effect. In this sense the earth is already showing many signs of worldwide climate change (http://www.geosunnrg.com/) as follows.(i)Average temperatures have climbed 1.4 degrees Fahrenheit (0.8 degree Celsius) around the world since 1880, much of this in recent decades, according to NASA’s Goddard Institute for Space Studies.(ii)The rate of warming is increasing. According to a number of climate studies, the last two decades of 20th century were the hottest in 400 years and possibly the warmest for several millennia. The UN’S Intergovernmental Panel on Climate Change (IPCC) reports that 11 of the past 12 years are among the dozen warmest since 1850. (iii)The Arctic is feeling atmosphere pollution and greenhouse effect the most. Average temperatures in Alaska, western Canada, and eastern Russia have risen twice the global average, according to the multinational Arctic Climate Impact Assessment report compiled between 2000 and 2004.(iv)Arctic ice is rapidly disappearing, and the region may have its first completely ice-free summer by 2040 or earlier. Polar bears and indigenous cultures are already suffering from the sea-ice loss.(v)Glaciers and mountain snows are rapidly melting; for example, Montana’s Glacier National Park now has only 27 glaciers versus 150 in 1910. In the Northern Hemisphere, thaws also come a week earlier in spring and freezes begin a week later.(vi)Coral reefs, which are highly sensitive to small changes in water temperature, suffered the worst bleaching—or die off in response to stress—ever recorded in 1998, with some areas seeing bleach rates of 70 percent. Experts expect these sorts of events to increase in frequency and intensity in the next 50 years as sea temperatures rise.(vii)The IPPC, in a 2007 report, claims that humans are “very likely” behind global warming. The report, based on the work of some 2,500 scientists in more than 130 countries, concluded that humans have caused all or most of the current planetary warming. Human-caused global warming is often called anthropogenic climate change.(viii)Industrialization, deforestation, and pollution have greatly increased atmospheric concentrations of water vapor, carbon dioxide, methane, and nitrous oxide, all greenhouse gases that help to trap heat near Earth’s surface.(ix)Humans are pouring carbon dioxide into the atmosphere much faster rate than absorbing rate of plants and oceans.(x)These gases persist in the atmosphere for years, meaning that even if such emissions were eliminated today, it would not immediately stop the global warming.(xi)Some experts point out that the natural cycles in Earth’s orbit can alter the planet’s exposure to sunlight, which may explain the current trend. Earth has indeed experienced warming and cooling cycles roughly every hundred thousand years due to these orbital shifts, but such changes have occurred over the span of several centuries. Today’s changes have taken place over the past 100 years or less.
4. Renewable Energy Future
Clearly, human kind has to set a different course in its need for energy, one that involves less intrusive sources such as solar, wind, and geothermal energy. There are energy sources that do not harm the planet and will never run out. The clock is ticking down but there is still time. Humankind has proven to be resourceful and prudent in the past. It needs to be again in the crucial areas of energy and the environment in order to assure sustainability for future generations (http://www.geosunnrg.com/).
5. Renewable Energy in India
India in 2006 had a population of 1.1 billion with a Gross Domestic Product of Rupees 33 trillion (728 billion US$) (http://indiabudget.nic.in/es2006-07/esmain.htm; 2006-2007). A breakup of India’s primary commercial energy shows that more than 80% is supplied from fossil fuels. If we also consider traditional fuels and biomass, India’s total primary energy consumption was about 20 EJ in 2004-2005 (an average of 18 GJ/capita/year). Figure 1 shows the share of different kind of energy sources in total India’s primary energy supply (Government of India, Planning Commission; 2006). Fossil fuels account for about 64% of the total primary energy while traditional biomass accounts for about 33%. The India’s population accounts for 17% of the world’s total population; however, energy consumption is only 4% of the total world’s primary energy consumption. The modern renewable energy accounts for only small portion of the total energy mix. India is the only country in the world that has a separate Ministry of New and Renewable Energy (MNRE), earlier known as the Ministry of Non-Conventional Energy Sources.
In view of the scarce fossil fuel reserves, energy security, and climate change concerns, it is expected that renewable energy will play a significant role in India’s future energy mix. Figure 2 provides an overview of the different renewable energy sources. Renewable energy can be used for the entire spectrum of end-uses as given in Figure 3 .
6. Modeling Techniques
In the literature, there exist several methods for modeling solar radiation components (global, beam, and diffuse) on the ground of parametric models and decomposition models. Parametric models like Iqbal, Gueymard and ASHRAE models [5–7], require detailed information of atmospheric conditions. Meteorological parameters frequently used as predictors include the type, amount, and distribution of clouds or other observations, such as the fractional sunshine, atmospheric turbidity, and perceptible water content . On other hand, decomposition models usually use information only on global radiation to predict the beam and sky components. These relationships are usually expressed in terms of the irradiations which are the time integrals of the radiant flux or irradiance. Decomposition models which are based on the correlations between the clearness index (it is the ratio of global to the extraterrestrial solar radiation) and the diffuse fraction (it is the ratio of diffuse to the global solar radiation), diffuse coefficient (it is the ratio of diffuse to the extraterrestrial solar radiation) or the direct transmittance (it is the ratio of beam to the extraterrestrial solar radiation) as an example Orgill and Hollands, Erbs et al., Reindle et al. and Liu and Jordan models [9–12] developed to estimate direct and diffuse radiations from global radiation. Instead of these two methods nowadays empirically method [13–15] and the artificial neural network method (which constitutes a widely accepted novel approach offering an alternative way to synthesize complex problems) can also be used for the determination of global and diffuse components of solar radiation [16, 17].
7. Measurement Techniques of Radiation
To asses the availability of solar radiation at different locations, measurements of global radiation, diffuse radiation, beam radiation, sun shine hours, bright sun shine hours, maximum and minimum temperature, humidity, pressure, visibility, wind speed and direction, gust speed, water precipitation, and air mass are very important parameters.
To measure the abovementioned parameters we require a big laboratory and group of skilled fellows. Although it is a difficult task to maintain and run such a laboratory but the quality and reliability of data of the site then can only be ensured. However there is a wide network of Indian meteorological department which provides wide variety of data that includes radiation and meteorological and pollution data. But the radiation data are scared. World Radiation Centre also provides data of global, beam, and diffuse radiation of cities of the world.
The direct measurement of solar radiation and its components (direct and diffuse) is done in two basic ways as well. The values are measured either by using ground-based instrumentation as pyranometers, or remotely with satellites. These methods are often used in combination to validate one another [18–20]. In general, pyranometer data from adequately maintained instruments provide an accurate description of the solar radiation values in the immediate area. It has been suggested that extrapolation of daily values beyond the discrete point represented by the location of the pyranometer can result in the misrepresentation of the extrapolated areas. Suckling  found that, for areas in the Tennessee Valley Authority region, permissible extrapolation distances of daily solar radiation values were ~200 km, but that these distances may vary by season. However, Younes and Muneer  claimed that “…for a given location that is, farther than 50 km from the measurement station the use of the respective measurement station’s data is obsolete in the assessment of solar energy applications.” In his study of solar radiation variability in San Diego County, California, Aguado  suggested that the relative proximity of two points to the coast further complicates the abilities of researchers to extrapolate beyond the discrete points at which solar radiation was measured.
Global and diffuse solar radiation can be measured with the help of a thermoelectric pyranometer. Basically pyranometer is consisting of a thin-blackened surface supported inside a relatively massive well-polished case. When solar radiation falls on this surface, the temperature of the surface rises until its rate of loss of the heat by all causes is equal to the rate of gain of heat by radiation. This rise in temperature sets up a thermal e.m.f. which is measured on a recording millivoltmeter or recorder. Each pyranometer is calibrated and a certificate is provided by the manufacturer. For quality data of solar radiation pyranometer have to be calibrated at regular intervals and required proper maintenance.
Instrument used for measuring the intensity of direct solar radiation, that is, beam radiation is called pyrheliometer. The Ångström compensation pyrheliometer is a standard instrument for the measurement of direct solar radiation, in which the sensor is fixed at the lower end of a tube provided with a diaphragm so that when the tube is directed towards the sun, the sensing surface is normal to the line joining the sun to the receiver, and only radiation from the sun and a narrow annulus of the sky is received by the sensor. The alignment is done by means of a sighting device called the diopter.
In pyrheliometer the absorption of the radiant energy by a blackened metal strip, exposed to the sun’s ray, is determined by measuring the electric current necessary to heat an identical shielded strip to the same temperature. Since both strips are mounted similarly and are at the same temperature and the heat exchange of the strips with surroundings is identical, the rate of generation of heats in shielded strip due to electric current is equal to the rate of absorption of radiant energy by the exposed strip. The equivalence or otherwise of the temperature of the two strips is determined by two fine thermocouples attached to the back of the strips, connected in series with a sensitive galvanometer. The current through the shielded strip is determined with an accurate digital milliammeter. The advantage of the instrument is that the equilibrium current through the shielded strip is not affected by change in the rate of heat loss from the strips, provided that the changes affect both the strips equally.
Such an instrument in theory is an absolute instrument as all the relevant factors required for the calculation of the radiation intensity can be measured:
let = the intensity of direct solar radiation in watts/cm2 = area of the strip = absorption of the strip = heating current in amperes.Then we have ,where is a constant for the instrument and depends upon resistance, length, breath, and absorptance of the strip. The constant of the instrument is actually determined by comparison with other standard instrument with constant traceable to the group of standards maintained at the World Radiation Centre in Switzerland.
For a study of the intensity of solar radiation in different regions, Scott glass filter OG1, RG2, and RG8 are used. The transmission of the filters is given below: OG1 transmits from 0.525 μ to 2.800 μ RG2 transmits from 0.630 μ to 2.800 μ RG8 transmits from 0.700 μ to 2.800 μ.
8. Estimation of Radiation
It is generally accepted that models for solar radiation prediction are necessary, because in most cases the density and number of solar radiation measuring stations cannot describe the necessary variability . It is then understandable that new models and improvements to existing modeling techniques are continually proposed which intend to improve estimates of solar radiation values with the use of more readily available meteorological variables [22, 25, 26].
8.1. Estimation of Solar Radiation on Horizontal Surface
Ångström  proposed first theoretical model for estimating global solar radiation based on sunshine duration. Page  and Prescott  reconsidered this model in order to make it possible to calculate monthly average of the daily global radiation (MJ/m2 day) on a horizontal surface from monthly average daily total insolation on an extraterrestrial horizontal surface as per the following relation: where is the monthly average daily extraterrestrial radiation (MJ/m2 day), is the monthly average daily bright sunshine hours, is the maximum possible monthly average daily sunshine hours or the day length, and and are constants.
Although a number of correlations included more parameters and have been developed by different workers [12, 30–32], one has been found to be very convenient, applicable to a large number of locations, and is the most widely used correlation [15, 33–37].
Solar radiation coming through the atmosphere is partially absorbed or reflected by its constituents (aerosol particles cause diffuse radiation) which actually reduces the beam component and affects the performance of energy systems. Therefore, knowledge of diffuse irradiation on a horizontal surface is also important in designing the various energy utilization systems. Many researchers have presented empirical correlations to estimate daily diffuse radiation. Two of the most widely used correlations are due to Liu and Jordan  and Page  to which the irradiation data fitted are given as where is daily mean diffuse radiation and , the clearness index.
A third type approach has been proposed by Iqbal  to find a correlation between and the ratio of bright sunshine () to the day length () given as where and are the constants.
Gopinathan  used the above models, estimated the radiation, and suggested that the applicability of the correlations to locations in various parts of the word is to be tested. Therefore, an extensive work has to be done in this area [25, 39–41]. Recently some others researchers [13, 14, 42–51] have also reported new developments in solar energy.
Orgill and Holland , Erbs et al. , and Collars-Pareira and Rabl  have all related the diffuse fraction of global radiation to an index of the atmospheric clarity on hourly basis. Elminir  examined the correlations of Orgill and Hollands  and Erbs et al.  and recommended then later for computing hourly diffuse fraction. Ahmad and Tiwari  presented modified version of ASHRAE  model for New Delhi station. Katiyar , Gueymard , Jacovides et al. , Katiyar et al. 2010 [36, 37], and Chen et al.  have also reported new developments in solar energy, which could be used to estimate long-term global, direct, and diffuse radiation.
8.2. Estimation of Solar Radiation on Tilted Surfaces
Most of the solar energy systems of interest redesigned with tilted collected surfaces. Therefore, it is necessary to have knowledge about the availability of solar radiation on tilted surfaces.
The total amount of radiation incident on an inclined plane is composed of beam , sky-diffuse , and ground reflected components: The daily beam radiation received on the tilted surface can be expressed as Under isotropic conditions, the global radiation on inclined surface can be written as where is the ground albedo, is the surface slope from the horizontal (degree), and and are monthly mean daily total and diffuse radiation on horizontal surface, respectively.
The estimation of solar radiation on tilted surfaces has been made by different authors. Recently, Mefti et al.  gave the hourly solar radiation model for inclined surfaces using sunshine duration data. An extensive work has to done in this area [13, 14, 58–63].
9. Present Trends in Correlation
Ångström-Prescott correlation has served as a basic approach to estimate global radiation for long time. Simplicity of Ångström-Prescott equation has dominated over its several demerits. Coefficients in Ångström-Prescott equation are site dependent. Yeboah-Amankwah and Agyeman  believed that “” and “” are time dependent and so developed a differential Ångström model with a set of coefficients which vary with time. Sahin and Sen  proposed a method to dynamically estimate the coefficients. These works do not include radiation damping process when solar rays pass through the atmosphere. Some researchers [66, 67] are employing a damping structure to calculate global solar radiation in clear sky. Their models consider physical process in detail, so the effect of latitude, elevation, and other factors are taken into account automatically. However damping spectrums are very irregular and hence numerical integration is indispensable. To overcome all these difficulties Yang et al.  proposed a “Hybrid model” which considers the physical process but still maintains the simplicity of the Ångström equation. The author tested their hybrid model with data of Japan and found that it needs greater turbidity when applied to urban areas due to air pollution; otherwise, global radiation may be estimated. Also, the estimation under completely cloudy sky is still difficult. Hybrid model assumed that global radiation has linear relationship with effective beam radiation and diffuse radiation as well as fractional sunshine time. Yang and Koike  also proposed a model to calculate solar radiation from upper air humidity. This could be used to predict numerical weather prediction (NWP).
Lingamgunta and Veziroglu  proposed a universal relationship for estimating clear sky insolation. This relation predicts annual mean daily clear sky insolation and is a function of latitude and altitude only. The author claimed that relation (the author called it as Lingamgunta-Veziroglu relation) predicts radiation that fairly accurate over conventional methods.
Suehrcke  proposed an entirely new relation between relative sunshine duration and global radiation. This relation, unlikely Ångström-Prescott equation, is nonlinear and it does not require any empirical constants. The local atmospheric conditions are considered through the value of the average daily clear index. Further fractional sunshine can be calculated from Suehrcke relation, and Suehrcke’s sunshine radiation relationship has been verified by Driesse and Thevenard  using a global data sheet.
Recently there have been emphases [73–76] on empirical correlation using satellite images. Most estimation of daily global radiation values from satellite images requires the useof models which allow us to calculate these values from a small number of images per day (usually three). Different methodologies have been developed in this regard.
Atmospheric pollutants and aerosols absorb and scatter shortwave solar radiations. The interactions have resultant impacts on atmospheric radiative energy transfer and balance. If the pollution increases, then diffuse component of global solar radiation will also increase. Spectral and diffuse radiation study of global solar radiation has now gained importance as reflected in recent literature [77–79]. There has been another area of modeling gaining importance which is estimation of solar radiation potential using artificial neural network [16, 60, 80–82].
This paper presents a brief account of the general introduction, principle, experimental technique, measurements of solar radiation data, and review of literature of solar radiation models and describes present trend of solar energy modeling which is of major interest to solar energy engineers, architects, designing building, and thermal devices for optimum and efficient utilization of this nonconventional energy resource.
- S. A. Changnon and D. Changnon, “Importance of sky conditions on the record 2004 Midwestern crop yields,” Physical Geography, vol. 26, no. 2, pp. 99–111, 2005.
- Z. Yang, X. H. Li, and Y. F. Hu, “Study on solar radiation and energy efficiency of building glass system,” Applied Thermal Engineering, vol. 26, no. 8-9, pp. 956–961, 2006.
- E. H. Amer and M. A. Younes, “Estimating the monthly discharge of a photovoltaic water pumping system: model verification,” Energy Conversion and Management, vol. 47, no. 15-16, pp. 2092–2102, 2006.
- I. R. Pillai and R. Banerjee, “Renewable energy in India: status and potential,” Energy, vol. 34, no. 8, pp. 970–980, 2009.
- M. Iqbal, An Introduction to Solar Radiation, Academic Press, Toronto, Canada, 1983.
- C. Gueymard, “Critical analysis and performance assessment of clear sky solar irradiance models using theoretical and measured data,” Solar Energy, vol. 51, no. 2, pp. 121–138, 1993.
- American Society of Heating Refrigeration and Air-Conditioning Engineers, ASHRAE Applications Handbook (SI), ASHRAE, Atlanta, Ga, USA, 1999.
- L. T. Wong and W. K. Chow, “Solar radiation model,” Applied Energy, vol. 69, no. 3, pp. 191–224, 2001.
- J. F. Orgill and K. G. T. Hollands, “Correlation equation for hourly diffuse radiation on a horizontal surface,” Solar Energy, vol. 19, no. 4, pp. 357–359, 1977.
- D. G. Erbs, S. A. Klein, and J. A. Duffie, “Estimation of the diffuse radiation fraction for hourly, daily and monthly-average global radiation,” Solar Energy, vol. 28, no. 4, pp. 293–302, 1982.
- D. T. Reindl, W. A. Beckman, and J. A. Duffie, “Diffuse fraction correlations,” Solar Energy, vol. 45, no. 1, pp. 1–7, 1990.
- B. Y. H. Liu and R. C. Jordan, “The inter-relationship and characteristic distribution of direct, diffuse and total solar radiation,” Solar Energy, vol. 4, no. 3, pp. 1–19, 1960.
- C. K. Pandey and A. K. Katiyar, “A note on diffuse solar radiation on a tilted surface,” Energy, vol. 34, no. 11, pp. 1764–1769, 2009.
- C. K. Pandey and A. K. Katiyar, “A comparative study to estimate daily diffuse solar radiation over India,” Energy, vol. 34, no. 11, pp. 1792–1796, 2009.
- O. P. Singh, S. K. Srivastava, and A. Gaur, “Empirical relationship to estimate global radiation from hours of sunshine,” Energy Conversion and Management, vol. 37, no. 4, pp. 501–504, 1996.
- A. Sözen, E. Arcaklioglu, and M. Özalp, “Estimation of solar potential in Turkey by artificial neural networks using meteorological and geographical data,” Energy Conversion and Management, vol. 45, no. 18-19, pp. 3033–3052, 2004.
- J. Soares, A. P. Oliveira, M. Z. Božnar, P. Mlakar, J. F. Escobedo, and A. J. Machado, “Modeling hourly diffuse solar-radiation in the city of São Paulo using a neural-network technique,” Applied Energy, vol. 79, no. 2, pp. 201–214, 2004.
- J. A. Otkin, M. C. Anderson, J. R. Mecikalski, and G. R. Diak, “Validation of GOES-based insolation estimates using data from the U.S. Climate Reference Network,” Journal of Hydrometeorology, vol. 6, no. 4, pp. 460–475, 2005.
- H. Deneke, A. Feijt, A. van Lammeren, and C. Simmer, “Validation of a physical retrieval scheme of solar surface irradiances from narrowband satellite radiances,” Journal of Applied Meteorology, vol. 44, no. 9, pp. 1453–1466, 2005.
- S. Kimothi, B. K. Bhattacharya, P. D. Semalty, V. K. Pandey, and V. K. Dadhwal, “Estimation of ground insolation using METEOSAT data over India,” Current Science, vol. 86, no. 9, pp. 1308–1312, 2004.
- P. W. Suckling, “Extrapolation of solar radiation measurements: mesoscale analyses from Arizona and Tennessee Valley Authority regions,” Journal of Climate & Applied Meteorology, vol. 22, no. 3, pp. 488–494, 1983.
- S. Younes and T. Muneer, “Improvements in solar radiation models based on cloud data,” Building Services Engineering Research and Technology, vol. 27, no. 1, pp. 41–54, 2006.
- E. Aguado, “Local-scale variability of daily solar radiation—San Diego County, California,” Journal of Climate & Applied Meteorology, vol. 25, no. 5, pp. 672–678, 1986.
- T. Muneer, S. Younes, and S. Munawwar, “Discourses on solar radiation modeling,” Renewable and Sustainable Energy Reviews, vol. 11, no. 4, pp. 551–602, 2007.
- M. Donatelli, G. Bellocchi, and F. Fontana, “RadEst3.00: software to estimate daily radiation data from commonly available meteorological variables,” European Journal of Agronomy, vol. 18, no. 3-4, pp. 363–367, 2003.
- S. Safi, A. Zeroual, and M. Hassani, “Prediction of global daily solar radiation using higher order statistics,” Renewable Energy, vol. 27, no. 4, pp. 647–666, 2002.
- A. Ångström, “Solar and terrestrial radiation,” Quarterly Journal of the Royal Meteorological Society, vol. 50, no. 210, pp. 121–125, 1924.
- J. K. Page, “The estimation of monthly mean values of daily total short wave radiation on vertical and inclined surfaces from sun shine records for latitudes 40°N-40°S,” Proceedings of the United Nations Conference on New Sources of Energy, vol. 98, no. 4, p. 378, 1961.
- J. A. Prescott, “Evaporation from water surface in relation to solar radiation,” Transactions of The Royal Society of South Australia, vol. 64, pp. 114–118, 1940.
- K. K. Gopinathan, “Empirical correlations for diffuse solar irradiation,” Solar Energy, vol. 40, no. 4, pp. 369–370, 1988.
- M. Collares-Pereira and A. Rabl, “The average distribution of solar radiation-correlations between diffuse and hemispherical and between daily and hourly insolation values,” Solar Energy, vol. 22, no. 2, pp. 155–164, 1979.
- J. Glover and J. S. G. Mc Culloch, “The empirical relation between solar radiation and hours of sunshine,” Quarterly Journal of the Royal Meteorological Society, vol. 84, pp. 172–175, 1958.
- V. Bahel, H. Bakhsh, and R. Srinivasan, “A correlation for estimation of global solar radiation,” Energy, vol. 12, no. 2, pp. 131–135, 1987.
- N. A. Elagib and M. G. Mansell, “New approaches for estimating global solar radiation across Sudan,” Energy Conversion and Management, vol. 41, no. 5, pp. 419–434, 2000.
- I. T. Togrul, H. Togrul, and D. Evin, “Estimation of global solar radiation under clear sky radiation in Turkey,” Renewable Energy, vol. 21, no. 2, pp. 271–287, 2000.
- A. K. Katiyar, A. Kumar, C. K. Pandey, V. K. Katiyar, and S. H. Abdi, “Correlations for the estimation of monthly mean hourly diffuse solar radiation: a time dependent approach,” The International Journal of Energy and Environment, vol. 1, no. 5, pp. 833–840, 2010.
- A. K. Katiyar, A. Kumar, Akhilesh, C. K. Pandey, and B. Das, “A comparative study of monthly mean daily clear sky radiation over India,” The International Journal of Energy and Environment, vol. 1, no. 1, pp. 177–182, 2010.
- M. Iqbal, “Correlation of average diffuse and beam radiation with hours of bright sunshine,” Solar Energy, vol. 23, no. 2, pp. 169–173, 1979.
- D. Y. Goswami, S. Vijayaraghavan, S. Lu, and G. Tamm, “New and emerging developments in solar energy,” Solar Energy, vol. 76, no. 1–3, pp. 33–43, 2004.
- A. Madhlopa, “Solar radiation climate in Malawi,” Solar Energy, vol. 80, no. 8, pp. 1055–1057, 2006.
- S. Tarhan and A. Sari, “Model selection for global and diffuse radiation over the Central Black Sea (CBS) region of Turkey,” Energy Conversion and Management, vol. 46, no. 4, pp. 605–613, 2005.
- E. O. Falayi, J. O. Adepitan, and A. B. Rabiu, “Empirical models for the correlation of global solar radiation with meteorological data for Iseyin, Nigeria,” International Journal of Physical Sciences, vol. 3, no. 9, pp. 210–216, 2008.
- K. Skeiker, “Correlation of global solar radiation with common geographical and meteorological parameters for Damascus province, Syria,” Energy Conversion and Management, vol. 47, no. 4, pp. 331–345, 2006.
- M. M. Kvalevåg and G. Myhre, “Human impact on direct and diffuse solar radiation during the industrial era,” Journal of Climate, vol. 20, no. 19, pp. 4874–4883, 2007.
- E. O. Ogolo, “Evaluating the performance of some predictive models for estimating global solar radiation across varying climatic conditions in Nigeria,” Indian Journal of Radio and Space Physics, vol. 39, pp. 121–131, 2010.
- C. K. Pandey and A. K. Katiyar, “Temperature base correlation for the estimation of global solar radiation on horizontal surface,” The International Journal of Energy and Environment, vol. 1, no. 4, pp. 737–744, 2010.
- H. K. Elminir, “Experimental and theoretical investigation of diffuse solar radiation: data and models quality tested for Egyptian sites,” Energy, vol. 32, no. 1, pp. 73–82, 2007.
- K. Bakirci, “Correlations for estimation of daily global solar radiation with hours of bright sunshine in Turkey,” Energy, vol. 34, no. 4, pp. 485–501, 2009.
- A. M. Al-Salihi, M. M. Kadum, and A. J. Mohammed, “Estimation of global solar radiation on horizontal surface using routine meteorological measurements for different cities in Iraq,” Asian Journal of Scientific Research, vol. 3, pp. 240–248, 2010.
- Y. Jiang, “Estimation of monthly mean daily diffuse radiation in China,” Applied Energy, vol. 86, no. 9, pp. 1458–1464, 2009.
- R. F. Mechlouch and A. B. Brahim, “A global solar radiation model for the design of solar energy systems,” Asian Journal of Scientific Research, vol. 1, pp. 231–238, 2008.
- M. J. Ahmad and G. N. Tiwari, “Evaluation and comparison of hourly solar radiation models,” International Journal of Energy Research, vol. 33, no. 5, pp. 538–552, 2009.
- A. K. Katiyar, C. K. Pandey, and V. K. Katiyar, “Correlation model of hourly diffuse solar radiation based on ASHRAE model: a study case in India,” International Journal of Renewable Energy Technology, vol. 3, no. 4, pp. 341–355, 2012.
- C. Gueymard, “Prediction and performance assessment of mean hourly global radiation,” Solar Energy, vol. 68, no. 3, pp. 285–303, 2000.
- C. P. Jacovides, F. S. Tymvios, V. D. Assimakopoulos, and N. A. Kaltsounides, “Comparative study of various correlations in estimating hourly diffuse fraction of global solar radiation,” Renewable Energy, vol. 31, no. 15, pp. 2492–2504, 2006.
- R. Chen, E. Kang, X. Ji, J. Yang, and J. Wang, “An hourly solar radiation model under actual weather and terrain conditions: a case study in Heihe river basin,” Energy, vol. 32, no. 7, pp. 1148–1157, 2007.
- A. Mefti, M. Y. Bouroubi, and A. Adane, “Generation of hourly solar radiation for inclined surfaces using monthly mean sunshine duration in Algeria,” Energy Conversion and Management, vol. 44, no. 19, pp. 3125–3141, 2003.
- P. G. Loutzenhiser, H. Manz, C. Felsmann, P. A. Strachan, T. Frank, and G. M. Maxwell, “Empirical validation of models to compute solar irradiance on inclined surfaces for building energy simulation,” Solar Energy, vol. 81, no. 2, pp. 254–267, 2007.
- C. K. Pandey and A. K. Katiyar, “A comparative study of solar irradiation models on various inclined surfaces for India,” Applied Energy, vol. 88, no. 4, pp. 1455–1459, 2011.
- N. L. Forero, L. M. Caicedo, and G. Gordillo, “Correlation of global solar radiation values estimated and measured on an inclined surface for clear days in Bogotá,” Renewable Energy, vol. 32, no. 15, pp. 2590–2602, 2007.
- G. A. Kamali, I. Moradi, and A. Khalili, “Estimating solar radiation on tilted surfaces with various orientations: a study case in Karaj (Iran),” Theoretical and Applied Climatology, vol. 84, no. 4, pp. 235–241, 2006.
- A. De Miguel, J. Bilbao, and M. Diez, “Solar radiation incident on tilted surfaces in Burgos, Spain: isotropic models,” Energy Conversion and Management, vol. 36, no. 10, pp. 945–951, 1995.
- A. Skartveit and J. A. Olseth, “Modelling slope irradiance at high latitudes,” Solar Energy, vol. 36, no. 4, pp. 333–344, 1986.
- D. Yeboah-Amankwah and K. Agyeman, “Differential Ångstrom model for predicting insolation from hours of sunshine,” Solar Energy, vol. 45, no. 6, pp. 371–377, 1990.
- A. D. Şahin and Z. Şen, “Statistical analysis of the Angstrom formula coefficients and application for Turkey,” Solar Energy, vol. 62, no. 1, pp. 29–38, 1998.
- R. E. Bird, “A simple, solar spectral model for direct-normal and diffuse horizontal irradiance,” Solar Energy, vol. 32, no. 4, pp. 461–471, 1984.
- B. Leckner, “The spectral distribution of solar radiation at the earth's surface-elements of a model,” Solar Energy, vol. 20, no. 2, pp. 143–150, 1978.
- K. Yang, G. W. Huang, and N. Tamai, “Hybrid model for estimating global solar radiation,” Solar energy, vol. 70, no. 1, pp. 13–22, 2001.
- K. Yang and T. Koike, “Estimating surface solar radiation from upper-air humidity,” Solar Energy, vol. 72, no. 2, pp. 177–186, 2002.
- C. Lingamgunta and T. N. Veziroglu, “A universal relationship for estimating clear sky insolation,” Energy Conversion and Management, vol. 45, no. 1, pp. 27–52, 2004.
- H. Suehrcke, “On the relationship between duration of sunshine and solar radiation on the earth's surface: Ångstrom's equation revisited,” Solar Energy, vol. 68, no. 5, pp. 417–425, 2000.
- A. Driesse and D. Thevenard, “A test of Suehrcke's sunshine-radiation relationship using a global data set,” Solar Energy, vol. 72, no. 2, pp. 167–175, 2002.
- C. Rigollier, M. Lefèvre, and L. Wald, “The method Heliosat-2 for deriving shortwave solar radiation from satellite images,” Solar Energy, vol. 77, no. 2, pp. 159–169, 2004.
- R. Perez, P. Ineichen, K. Moore et al., “A new operational model for satellite-derived irradiances: description and validation,” Solar Energy, vol. 73, no. 5, pp. 307–317, 2002.
- S. Janjai, T. Jantarach, and J. Laksanaboonsong, “A model for calculating global illuminance from satellite data,” Renewable Energy, vol. 28, no. 15, pp. 2355–2365, 2003.
- L. Ramirez, L. Mora-López, and M. Sidrach-de-Cardona, “A multivariate qualitative model for the prediction of daily global radiation from three hourly global radiation values,” Energy, vol. 26, no. 2, pp. 205–215, 2001.
- C. P. Jacovides, M. D. Steven, and D. N. Asimakopoulos, “Spectral solar irradiance and some optical properties for various polluted atmospheres,” Solar Energy, vol. 69, no. 3, pp. 215–227, 2000.
- A. S. Rapti, “Atmospheric transparency, atmospheric turbidity and climatic parameters,” Solar Energy, vol. 69, no. 2, pp. 99–111, 2000.
- Z. Jin, W. Yezheng, and Y. Gang, “Estimation of daily diffuse solar radiation in China,” Renewable Energy, vol. 29, no. 9, pp. 1537–1548, 2004.
- C. A. Roulet, “Solar energy and global heat balance of a city,” Solar Energy, vol. 70, no. 3, pp. 255–261, 2001.
- K. S. Reddy and M. Ranjan, “Solar resource estimation using artificial neural networks and comparison with other correlation models,” Energy Conversion and Management, vol. 44, no. 15, pp. 2519–2530, 2003.
- A. S. S. Dorvlo, J. A. Jervase, and A. Al-Lawati, “Solar radiation estimation using aritificial neural networks,” Applied Energy, vol. 71, no. 4, pp. 307–319, 2002.