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.     

Estimation of global solar irradiation on horizontal and inclined surfaces based on the horizontal measurements

Solar radiation data are essential in the design of solar energy conversion devices. In this regard, empirical models were selected to estimate the global solar radiation on horizontal and inclined surfaces. The hourly solar radiation data measured at the study area during the period of 2004-2007, were used to calculate solar radiations using selected models. The selected models were compared on the basis of statistical methods. Based on the results, a new model, H/H_o = 0.19490 + 0.4771(n/N) + 0.02994 exp(n/N) has been developed, based on Kadir Bakirci linear exponential model. This is highly recommended to estimate monthly mean daily global solar irradiation, on a horizontal surface. Further, a model to convert horizontal solar global radiation to that of radiation on a tilted surface is also presented. It is based upon a relatively simple model proposed by Olmo et al. which requires only measurements of horizontal solar radiation. The developed model appears to give excellent results and has the advantage of being relatively simple for applications. The present work will help to improve the state of knowledge of global solar radiation to the point where it has applications in the estimation of global solar radiation, both on horizontal and inclined surfaces.     

An assessment of the solar radiation climate of the Cyprus environment

The solar radiation climate of Athalassa, Cyprus, is reported upon in detail. The database utilized in this analysis consisted of daily global and diffuse radiation on a horizontal surface, and global radiation on tilted surfaces, together with the calculated daily values of horizontal beam radiation. In addition, the data reported here include maximum and minimum temperature, relative humidity and percentage of possible sunshine. Monthly average hourly global and diffuse radiation for the time interval 5 a.m.–7 p.m. are reported and analyzed. The annual means of the daily global, diffuse and beam solar radiation on a horizontal surface are about 17.26, 5.75 and 12.35 MJ m⁻², respectively. The average monthly fraction of daily horizontal global radiation that is beam radiation varies from 0.61 in February to 0.77 in September. The average monthly clearness index varies from 0.636 in July to 0.491 in December, whereas the ratio of diffuse to global radiation varies from 0.494 in February to 0.257 in July. The solar radiation climate of the Cyprus environs has also been compared to those reported for two neighbouring countries. We conclude, based upon the above analysis, that Athalassa and its environs are characterized on average, by relatively high daily irradiation rates, both global and beam, and a relatively high percentage of clear days.     

Measurements and predictions of solar radiation incident on horizontal surfaces at Santa Fe, Argentina (31° 39′S, 60° 43′W)

Measurements and predictions of solar radiation during a period of 10 years on horizontal surfaces at Santa Fe (31° 39′ S, 60° 43′ W), Argentina, reported as average daily global radiation for each month, are presented. Data are compared to those obtained with a previously published and verified model for computing solar radiation on horizontal planes at the earth's surface for cloudless sky days. Measurements show an important reduction of global radiation with respect to the cloudless sky model predictions for all months of the year. Conversely, averaged daily diffuse solar radiation calculated with Page's formula shows a small increment with respect to the predicted diffuse solar radiation for cloudless sky conditions. When direct solar radiation data, calculated from global and diffuse solar radiation values, are compared to theoretical prediction, a significant decrease is observed. This trend is similar to that obtained for global solar radiation.     

Empirical correlations as a means for estimating monthly average daily global radiation: A critical overview

In regions where solar energy is abundant, solar energy can play a vital role in attaining energy sustainability. Sizing solar energy systems requires the availability of solar radiation data on horizontal surface which can then be used to calculate solar radiation intensity on any tilted surface using appropriate conversion factors or formula. In many parts of the world, especially in developing countries, such data is not readily available. Many researchers have found that monthly average daily value of global solar radiation on horizontal surface can be estimated when meteorological parameters such as duration of sunshine, number of rainy days, relative humidity, etc. are available. Many empirical correlations have been developed based on this approach. The development of such a correlation has been made possible through the availability of solar and other meteorological data required for their validation. This paper presents a review on the existing empirical correlations and critically looks at the practicality of such correlations. This raises the question on the appropriateness of the past and present approaches adopted by researchers in this field. The paper also discusses various related aspects and proposes new directions for future research.     

Solar radiation on tilted south oriented surfaces: validation of transfer-models

Three transfer-models in use for estimating solar radiation on tilted surfaces are tested. A 12 year series of hourly global, diffuse, and reflected solar irradiation measured with horizontal pyranometers as well as hourly global solar irradiation measured with tilted south oriented pyranometers is available. One model uses daily irradiation, the other two use hourly irradiation. The models converting hourly solar irradiation on a horizontal surface to a tilted surface yield better results than that using daily irradiation. The best results are gained if pairs of hourly global and diffuse solar irradiation are available. The root mean square errors exceed 10% only if the sky is covered by more than 85% with clouds or if the solar elevation angle is less than 10°.     

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.     

Simulation and modeling of solar radiation in Saudi Arabia

A mathematical model is used to generate the hourly data for the total solar radiation on a horizontal surface. The generated data are based on the hourly recorded visibility data for 20 years (1970–1989). The model year technique was then applied to model the 20 years of hourly data of solar radiation into one statistically representative year. A model year of hourly data was then generated for the beam and diffuse components of solar radiation on a horizontal surface. Similarly, a model year of hourly data was also generated for the total solar radiation on tilted surfaces with different orientations with its beam, diffuse and reflected components. A simple methodology is proposed for calculating the solar radiation on vertical surfaces, based on a solar impact factor (SIF). Monthly means and daily totals of hourly sums for each month of the year are discussed. The hourly data of solar radiation for a typical day for each month of the year are presented. The data were generated for the four climatic zones of Saudi Arabia, the hot-dry (Riyadh), the warm-humid (Jeddah), the maritime inland desert climate (Dhahran) and the upland climate zone (Taif). The accuracy of the results is discussed and found to be above 90% representative.     

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.     

Calculation of monthly average insolation on a shaded surface at any tilt and azimuth

Estimation of the monthly average solar radiation on surfaces of arbitrary orientation is necessary for many solar performance prediction programs and is useful for other applications. For passive solar applications, especially, overhangs are often used to seasonally modulate the amount of radiation striking the surface.

Liu and Jordan[1] have developed a method for estimation of monthly average radiation on unshaded tilted surfaces based on horizontal surface data. This method has been extended to unshaded surfaces of arbitrary tilt and azimuth by Klein[2]. Utzinger and Klein[3] have presented a graphical method for estimating monthly average radiation on shaded vertical surfaces, while Jones [4]has offered an analytical method for the same configuration. This paper presents an analytical solution to the calculation of monthly average insolation on shaded surfaces at any tilt and azimuth. Results are comparable among the three methods when shaded vertical surfaces are analyzed.

This analytical method offers an alternative to slower and less accurate numerical integration and to less general regression of numerical integration results for use in solar performance prediction programs.     

Generation of typical solar radiation data for İstanbul,Turkey

Typical solar radiation data are very important as input in modelling, designing and performance evaluation of solar energy applications. In this study, typical solar radiation data were obtained for ?stanbul, Turkey both from measured data and synthetic generation. Firstly, a test reference year for daily global solar radiation on a horizontal surface was generated using 19 years measured data. The daily global solar radiation as typical data for ?stanbul was presented throughout a year in a tabular form. Secondly, the daily global solar radiation for ?stanbul was expressed with a trigonometric equation using long‐term measured data. It is expected that the typical data and the equation derived will be useful to the designers of solar energy systems as well as those who need to have fairly good estimates of daily global solar radiation for ?stanbul. Copyright © 2003 John Wiley & Sons, Ltd.     

Computational derivation of irradiance on building surfaces: An empirically-based model comparison

Performance simulation applications require reliable information regarding the intensity of solar irradiance on arbitrarily oriented building surfaces in order to properly predict buildings' energy use or to configure building-integrated solar energy systems. Since measured irradiance databases typically include only horizontal irradiance values, solar radiation intensity on inclined surfaces must be computationally derived. In this context, the present paper compares six options to derive, from horizontal irradiance data, solar radiation intensity levels on inclined surfaces. To evaluate these options, simulated downward vertical irradiance on four orientations were compared with measurements obtained in Austria. Two options that use both global and diffuse horizontal irradiance values for sky radiance generation delivered slightly better results than the others, which require only global horizontal irradiance. However, the range of errors was rather high for all options. Even for the best-ranked option, no more than 64% of the results had a relative error of less than ±20%.     

垂直面太阳散射辐射计算方法研究

建筑设计必须考虑太阳辐射在建筑立面上的热作用,但气象台站仅观测水平面辐射数据,垂直面上的太阳辐射资料稀缺。为提出一种依据水平面辐射观测数据来计算垂直面散射辐射的方法,该文研究并建立辐射观测站,并进行长期辐射观测,积累了一定量的辐射数据。通过对垂直面上散射辐射主要影响因素的分析,提出基于晴空指数Kt和直射辐射与垂直面法线方向夹角φ的垂直面散射辐射计算方法。利用观测数据确定公式中的计算系数,并将该文研究提出的计算方法与国内外的5种太阳散射辐射计算模型进行比较分析。结果表明:1)该文提出的计算方法所需计算参数仅依据国内常规辐射观测数据即可。2)该方法能够实现对不同朝向垂直面散射辐射的计算。3)与国内外常用计算模型相比,该方法在不同天空晴朗度、不同朝向上整体精度更高。研究认为该文方法与国内气象部门的辐射观测数据相匹配,所需计算参数少、精度高、简单易用,可为建筑能耗计算和热环境分析提供新的垂直面散射辐射计算方法。     

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

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

Statistical comparison of solar radiation correlations Monthly average global and diffuse radiation on horizontal surfaces

For most solar energy applications, it is necessary to predict the amount of global and diffuse radiation arriving on a horizontal surface at any specified location. Scientists have developed methods to achieve this using different input parameters. The purpose of this study is to compare statistically correlations for estimating the monthly average daily global/diffuse radiation incident on a horizontal surface and to recommend one in each catagory that best fits measured data from a number of locations chosen and is the simplest to use. The effects of using the new solar constant of 1367 W⁻² in these correlations are also investigated. As a result, Rietveld's and Page's correlations are recommended for estimating monthly average daily global and diffuse radiation incident on a horizontal surface, respectively. In addition, these correlations seem to be just as accurate with the new solar constant.     

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.     

Solar collector surfaces with wavelength selective radiation characteristics

The use of porous materials through which a coolant is forced for the protection of surfaces exposed to high temperature gas streams has been discussed in a number of recent papers. The knowledge of the radiation properties of these materials is required if the designer is to be able to predict the porous wall temperatures to determine whether metallurgical limitations have been exceeded. With this application in mind, measurements were previously reported for the absorptivity for solar radiation of a number of porous surfaces.¹ Since that time total normal emissivity data have been obtained for the same surfaces. In viewing these results, it was discovered that these surfaces combined high absorptivity for solar radiation with a low emissivity value, and consequently their use as solar collectors is suggested. It is the purpose of this paper to describe the experimental apparatus used to obtain the radiation data and to compare the recent emissivity measurements with the solar absorptivity data for the same surfaces. For specified conditions, an efficiency is defined which allows a quantitative comparison of these with other surfaces as solar collectors.     

A general formula for computing the coefficients of the correlation connecting global solar radiation to sunshine duration

Correlations are developed to estimate the regression coefficients a and b of Ångström type correlations for predicting monthly mean daily global solar radiation on a horizontal surface. The suggested equations express the regression coefficients in terms of the latitude, elevation, and percent of possible sunshine and are applicable to any location around the world to compute global solar radiation on horizontal surfaces.     

A comparative study of solar irradiation models on various inclined surfaces for India

This paper presents a statistical approach for the estimation of the diffuse/global irradiation on various inclined surfaces from the measured data of horizontal surface. In fact diffuse solar radiation on an inclined plane consists of two components: sky diffuse radiation and reflected radiation from the ground. For analyzing estimation of the daily tilted sky diffuse component from the daily horizontal diffuse irradiance, we have considered six models Badescu, Circumsolar, Skartveit and Olseth, Hay, Klucher and Liu and Jordan (Isotropic). All these models except Badescu adopted the same methodology for estimating the ground-reflected radiation component, therefore, only sky diffuse component was analyzed at Lucknow (latitude 26.75°, longitude 80.50°), India location. Statistical analysis showed that the Skartveit and Olseth model gives good prediction for the low inclination angle however; Klucher model gave better performance for highly inclined south-facing surfaces. The Root Mean Square Errors (% RMSE) value varies from 3.45% to 24.15% except for Badescu and Circumsolar model which predict worse results. In general, Klucher’s model provides close agreement with the measurements.     

Modelling of diffuse solar fraction with multiple predictors

For some locations both global and diffuse solar radiation are measured. However, for many locations, only global radiation 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 direct on some other plane using trigonometry, we need to have diffuse radiation on the horizontal plane available. There are regression relationships for estimating the diffuse on a tilted surface from diffuse on the horizontal. Models for estimating the diffuse on the horizontal from horizontal global that have been developed in Europe or North America have proved to be inadequate for Australia [13]. Boland et al. [2] developed a validated model for Australian conditions. Boland et al. [3] detailed our recent advances in developing the theoretical framework for the use of the logistic function instead of piecewise linear or simple nonlinear functions and was the first step in identifying the means for developing a generic model for estimating diffuse from global and other predictors. We have developed a multiple predictor model, which is much simpler than previous models, and uses hourly clearness index, daily clearness index, solar altitude, apparent solar time and a measure of persistence of global radiation level as predictors. This model performs marginally better than currently used models for locations in the Northern Hemisphere and substantially better for Southern Hemisphere locations. We suggest it can be used as a universal model.