Techniques for the precise estimation of hourly values of global, diffuse and direct solar radiation

The method usually used to compute solar radiation, when no measured data are available, is the well-known regression technique relating mean daily totals of global and diffuse solar radiation with the mean duration of sunshine. Using this method and taking into account the first order multiple reflections between the ground and the atmosphere, regression parameters were obtained from the monthly mean values of daily totals of global solar radiation and sunshine at a network of 16 stations in India. Daily values of global and diffuse solar radiation were then computed for 121 stations, where sunshine data are available for periods of 6–28 yr, using interpolated values of the regression parameters. Where no sunshine data were available, global and diffuse solar radiation were computed from cloud observations, using the inverse relationship between sunshine and cloudiness. Further, using the empirical relationship between daily totals and the corresponding hourly values of global and diffuse solar radiation, two sets of curves were prepared valid for the whole country, using which mean hourly values of global and diffuse radiation could be deduced from the corresponding daily totals, with a high degree of accuracy. The paper discusses the validity of the techniques used for computing daily and hourly values of global and diffuse solar radiation from sunshine and cloud amounts at an extended network of 145 stations in India and stresses the fact that such techniques are successful, only if accurate data on both radiation and sunshine are available at a widely distributed network of stations for a minimum period from at least 5 to 6 yr, using carefully calibrated and well-maintained instruments of the required quality. Theoretical models have also been used to compute clear sky noon values of global, diffuse and direct solar radiation from the solar constant, allowing for attenuation by atmospheric constituents such as ozone, water vapour, dust and aerosols. Using a simple model, calculations of global and diffuse solar radiation on clear days were made for 145 stations from values of the solar constant and measured values of ozone, water vapour and atmospheric turbidity. A method of extending the technique to overcast skies and partly clouded skies is discussed. The values of the mean annual transmission factor for global solar radiation under cloud-free conditions using the two methods show excellent agreement and establishes the soundness of the regression technique on one hand and the reliability of the theoretical model used for computing clear sky radiation, on the other.     

The estimation of global and sky radiation in Austria

For obtaining the radiation values necessary for utilization of solar energy at as much possible locations in Austria, the monthly sums of global radiation at the horizontal surface are estimated after Angström from the relative duration of sunshine using the extraterrestrial radiations as maximum values. The thereby needed constants, which were evaluated for 19 stations in Austria with synchronous measurements of global radiation and duration of sunshine, are stated for the seasons as functions of altitude above sea level. The sky radiation is estimated by means of relationships after Liu-Yordan. These relationships were evaluated from the longterm measurements of global- and sky radiation at three stations in Austria for the mean monthly sums and for the mean hourly sums.     

CLEAR SKY SOLAR INSOLATION DATA FOR ISLAMABAD

Monthly mean values of both integrated and instantaneous clear sky solar radiation components for Islamabad territory are presented and discussed. The components include global normal, direct normal, global horizontal, direct and diffuse horizontal radiations, sunshine duration, number of clear days and ambient temperature for solar energy applications. Direct normal irradiance values are used to get clear sky sunshine duration by ab-initio. The need for replacing the conventional sunshine recorder is discussed.     

A MULTIPLE LINEAR CORRELATION FOR DIFFUSE RADIATION FROM GLOBAL AND SUNSHINE DATA

Several years of measured data of global and diffuse radiation together with sunshine duration, for five locations in Spain are used to establish empirical relationships to connect monthly mean daily diffuse irradiation with clearness index and relative sunshine duration. A correlation connecting sky radiation with both clearness index and percent possible sunshine together is found to be most accurate for locations in Spain and Portugal. When clearness index and relative sunshine duration are combined together, it is observed that the accuracy of the estimated diffuse radiation data is better than when they are used separately.     

A method for estimating monthly global solar radiation

In this paper a method is followed for estimating monthly totals of global solar radiation from a combination of calculations of monthly cloudless global solar radiation, surface meteorological observations, and empirical formulae relating sunshine duration to global solar radiation. The percent deviation of calculated from observed values is not negligible, but is much less than errors obtained by using extraterrestrial solar radiation totals. In case of values of monthly global solar radiation which are estimated for other regions, the resulted possible errors should be determined again. Some techniques leading to adaptation of the regression equations for other areas are argued.     

The relationship between global solar radiation and sunshine duration in Vietnam

Two approaches of the well-known modified Angstrom formula were developed from long term records of measured monthly mean daily global solar radiation and sunshine hour values obtained from 12 meteorological stations across Vietnam. These formulae were then used to estimate solar radiation for stations where only sunshine records were available. Three other commonly used correlations between solar irradiation and sunshine duration were also used and their results compared with those of two developed models. The procedure of measurement in Vietnamese weather stations was also indicated.     

Can the model proposed by barbaro et al. be used to compute global solar radiation on the romanian territory?

The accuracy of the model proposed by Barbaro et al. [Solar Energy 22, 225–228 (1979)] was verified during (1) monthly average days, (2) days with clear sky, (3) days with overcast sky. The monthly average values were considered of both daily and hourly irradiation. Model verification was performed using measurement data from six Romanian actinometric stations. Precision is acceptable during average and clear days. During days with overcast sky the accuracy of results is low. The model performances are relatively the same on the whole Romanian territory and they are better during warm season.     

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.     

Generation of operational maps of global solar irradiation on horizontal plan and of direct normal irradiation from Meteosat imagery by using SOLARMET

The physical model SOLARMET, elaborated in ENEA (Italian National Agency for New Technologies, Energy and Environment), provides hourly average global solar irradiance on a horizontal surface (GHi) and hourly average direct normal solar irradiance (DNi) for Italy based on primary satellite images in the visible band.

In the present study, the hourly estimates of surface radiation generated by SOLARMET have been summed up to produce monthly average daily irradiation maps. Hourly and monthly maps were done for the years 1996 and 2002. The parameters of this model were obtained by comparing the Meteosat satellite data with ground data gathered in 2002. Differences, relative to 1996, between SOLARMET estimates and observations obtained over two radiation networks of Italian ground sites are presented: the Meteorological Service of the Italian Air Force and National Agro-Meteorological Network; In total 51 ground stations. The comparison between SOLARMET and the previous Italian method carried out in ENEA shows an improvement due to SOLARMET. Such comparison between the values derived using SOLARMET and previous ENEA methodologies and with data from ground-based stations was possible only for monthly averages of daily global radiation due to an almost total lack of direct radiation ground data in Italy.

The operational monthly solar radiation maps, showing solar energy potentials, permit the selection of construction sites to solar energy project developers. In Italy, these data are necessary for installing solar thermal concentration power plants in support of the R&S program recently funded to demonstrate the possibility of these technologies.     

Computation of solar radiation from observations of cloud cover

Techniques of computation of global and diffuse solar radiation from the daily duration of bright sunshine and cloud cover are well-known. However, since radiation computations from cloud cover data provide rather imprecise results, this method is resorted to only when sunshine data are not available. To obtain a better idea of the inverse relationship between the long-term averages of sunshine duration and total cloud cover, an analysis of the monthly mean values of the fraction of the sky C, covered by clouds of all types and the duration of bright sunshine, n, was carried out. The relationship between C and (1−n/N′), where N′ is the maximum possible hours of sunshine, was found to be non-linear. The shape of the regression line connecting the two parameters also shows that ground observations of cloud cover always tend to be overestimates. The differences between such estimates and cloud cover values derived from sunshine duration tend to become zero when skies are either clear or overcast and are a maximum for cloud cover values in the range 0.4–0.7. A cubic regression equation was derived relating C and (1−n/N′) and using this relationship, it has been possible to compute sunshine duration from cloud cover data to an accuracy of about 4–7 per cent and from the cloud derived sunshine data, to compute monthly mean values of global solar radiation to an accuracy of about 6–10 per cent and diffuse solar radiation within an accuracy of about 10–15 per cent.     

Ranking the overall performance of eight sunshine-based global solar radiation models with a nonparametric statistical procedure

By using a nonparametric statistical procedure, the ranking of the overall performance of eight sunshine-based global radiation models is conducted in this paper with measured data of global solar radiation and bright sunshine hours at seven meteorological stations in Yunnan Province, China. It is found that, in this region, the Page model performs best, followed by the monthly independent Rietveld model, monthly specific Dogniaux–Lemoine model, monthly specific Rietveld model, Bahel et al. model, monthly independent Dogniaux–Lemoine model, Glover–McCulloch model and the Gopinathan model.     

A Method of Estimating Monthly Global Radiation for Singapore

The design of solar systems and the determination of cooling and heating load of buildings require information on global radiation in addition to other meteorological data. In this study, equations have been developed for the clearness index K_T , which is the ratio of monthly average daily values of global radiation to that of extraterrestrial radiation on a horizontal surface, as a function of the ratio of monthly average daily values of sunshine hours and day length. The extraterrestrial radiation and the day length can be calculated from Eqs. (5) and (3) respectively. The sunshine hours can be obtained from the meteorological station of Singapore. A reasonable estimate of monthly average daily global radiation can be obtained from these equations.     

Attenuation of solar radiation in the atmosphere

This paper presents the results of measurements of the solar radiant energy absorbed and scattered in the atmosphere. Since much of the information on solar irradiance at the ground is obtained by computation from extraterrestrial radiation data, it is important to know precisely the actual energy that is absorbed and scattered in its passage through the atmosphere for the accurate estimation of the radiant energy received at the ground. Various models exist for the estimation of daily totals of global solar radiation under clear sky and cloudy conditions, taking these effects into consideration and assuming average values for the ozone and water vapour content and the turbidity of the atmosphere. In the present investigation atmospheric attenuation of solar radiation has been calculated from measured values of ozone and water vapour content and turbidity in the atmosphere, at two stations Bangalore (950 metres above sea level) and Nandi Hills (1479 masl). Direct measurements of direct solar radiation for the whole spectrum and various spectral regions were made at Bangalore and Nandi using Ångström pyrheliometers fitted with broad-band pass filters during the clear months January–May 1979. Global solar radiation and sunshine duration measurements were also made at both stations. Using direct measurements of the total ozone and water vapour content and atmospheric turbidity, direct, diffuse and global solar radiation values at the ground were computed from extraterrestrial values of radiation for clear sky conditions. The results are compared with actual measurements and earlier observations of direct solar radiation at other high-level stations. The importance of atmospheric turbidity measurements in the computation of solar radiation is discussed.     

Uses of sunshine duration to estimate the global solar radiation over eight meteorological stations in Egypt

The climatological Ångstrom regression coefficients have been determined by three methods and used to predict the global solar radiation over eight meteorological stations. Each of the three methods depends on the correlation between two ratios. The first ratio is between the long period of monthly average sunshine duration and the corresponding maximum of daily sunshine duration (day length) N, and the second ratio is between the measured monthly average daily global solar radiation and the corresponding monthly mean daily extraterrestrial solar radiation on the horizontal surface ₀. A comparison between the measured data and the estimated values has been done. The t-statistics is used as a statistical indicator to choose the coefficients of the best method that gives a percentage of error less than 10%.     

Solar radiation for Shiraz, Iran: a comparative study for two periods

Instantaneous solar radiation data read from the chart of global solar radiation on a horizontal surface as well as sunshine hours in Shiraz during two periods (1980–1983 and 1988–1990) are analysed and compared with solar conditions in the early 1970s. It is apparent from the recorded data and subsequent analysis that while this area still possesses a relatively high abundance of sunshine, there has been a gradual decay in clearness index. Frequency of clear sky days, the average daily irradiation and the mean cumulative annual irradiation for the two periods under study are presented and a decrease in solar radiation received on a horizontal surface due to down grading of Shiraz from the clear sky conditions enjoyed in the 1960s and 1970s is demonstrated.     

Estimation of monthly mean hourly global radiation for latitudes in the 1°N–81°N range

A way to estimate monthly mean hourly global radiation ( ) from monthly mean daily global radiation ( ) has been to use fits which give as a function of , the monthly mean daily maximum possible number of sunshine hours. In the present work it is shown that these plots are by no means of universal validity, but are clearly dependent on latitude for high latitudes. A new type of correlation is proposed, which gives as a function of , the solar elevation at mid-hour. The values of coefficients for the versus correlations are given for each month of the year, for the hours centered at 0.5 h, 1.5 h, 2.5 h, etc. from the true solar noon, and stations with latitudes in the 1°N–81°N range. The given coefficients are most likely valid for any latitude, north or south.     

Optimum slope of a north-south aligned absorber plate from the north to the south poles

The analytical method developed by Nijegorodov et al. [Renewable Energy, 4, 529–543 (1994)] in order to find the optimum slope of an absorber plate, variously oriented at any latitude, is applied to study the variation of daily optimum slope with latitude from the north to the south poles. For a clear, cloudless condition the daily optimum slopes are found to have symmetry features which reflect the symmetry of the motion of the sun and the north-south symmetry about the equator. Such symmetry features of the optimum slope are discussed. However, the actual optimum slope also depends on the local meteorological and sunshine conditions, due to which the symmetry features of optimum slope are not always exploitable. The effects of meteorological parameters such as temperature, pressure, relative humidity, visibility and cloud cover on the optimum slope are assessed. The method is applied to obtain the mean monthly optimum slopes for the locations of 12 synoptic stations in Botswana from which the climatic and sunshine data are available, and preliminary maps of mean monthly optimum slopes for Botswana for the months of June and December are presented.     

Sky conditions at Ibadan during 1975–1980

The sky conditions at Ibadan, characterized by the clearness index, relative sunshine, diffuse ratio and diffuse coefficient, are presented for the six years 1975 to 1980. It is shown that based on the monthly average of the daily clearness index , the annual sky conditions have six patterns, namely, the harmattan-haze dry season pattern (November, December, and January) with , the dustfree dry season pattern (February, March, and April) with , and four rainy season patterns of August ( ), July and September ( ), June and October ( ) and May ( ). The variations of the diffuse ratio and relative sunshine are also in tune with these six patterns while the diffuse coefficient has an almost constant value of about 0.24 for all seasons. Following the work of Liu and Jordan, statistical “monthly K_τ curves” are established for Ibadan along the lines of the six patterns of sky conditions. These monthly K_τ curves can be utilized to determine the approximate statistical distribution of the daily total radiation for other cities which are in the same weather zone as Ibadan when the monthly average daily total radiation is known for such cities.     

Brazilian Solar Resource Atlas CD-ROM

The Brazilian Solar Resource Atlas CD-ROM is intended to be a tool for solar system design, delivering information that relies on a large interactive database, including, also, a modern device for calculating the solar radiation collected by planes inclined at different tilt angles or tracking the sun around one or two axes. The spatial distribution of the daily solar radiation, monthly and yearly averaged, that hits Brazil is presented in 13 colored maps, together with the methodological procedures used for harmonizing the information and designing the maps. A map containing the location of pyranometric and actinographic terrestrial stations, the information which was used for designing the maps, is also presented. The period of collected data runs from 1978 to 1990. Similarly, the atlas contains 13 colored maps, including daily insolation, monthly and yearly averaged, in addition to the map containing the location of the heliographic stations. The CD-ROM stores a database that includes over 500 stations located in Brazil and on the borders of its neighboring countries. The information is given either as daily, monthly average global solar radiation, or daily, monthly average insolation. A search device is included in the database, allowing to navigate over the maps or to select a desired location. The information may be printed as a report. The CD-ROM also includes a software to perform the following calculations: solar radiation estimates on a fixed plane at any inclination on North-South orientation; estimates of solar radiation collected by a plane tracking the sun about one or two axes; generation of synthetic series based on Markov’s Transition Matrixes.     

Maps for average bright sunshine hours in Turkey

This paper provides the isopleth maps for the monthly average daily bright sunshine hours in Turkey. The data from 50 stations are elaborated. The maps are generated by the aid of a developed computer program.