Solar radiation over Sudan—Comparison of measured and predicted data

Measurements of global solar irradiance on a horizontal surface at 14 meteorological stations in Sudan are compared with predictions made by two independent methods. The first method is based on Angstrom formula which correlates relative global solar irradiance to corresponding relative duration of bright sunshine . Regional regression coefficients are obtained and used for prediction of global solar irradiance. The agreement with measurements is better than 7.5 per cent. In the second method an empirical relation due to Barbaro et al. which uses sunshine duration and minimum air mass as inputs is employed. An appropriate regional parameter is determined and used to predict solar irradiance at all stations with an accuracy better than 8 per cent. A comparison of the two methods is presented. Estimation of diffuse solar irradiance by Page's as well as Liu and Jordan's correlations is also performed and the results are examined.     

Estimation of solar radiation over Jordan—predicted tables

As measured solar radiation data for all parts of Jordan are not available, they have to be estimated using correlation relations and models. This paper presents, for the first time, values of solar radiation over Jordan as estimated from these relations. Measurements of global solar irradiance on a horizontal surface and sunshine duration at nine meteorological stations in Jordan are correlated and used for prediction of the regression coefficients of an Angstrom type correlation relation at these stations and others which only have records of sunshine duration. Regional regression coefficients are obtained and used for prediction of global solar irradiance. The agreement with measurements is better than 5% and 1% on monthly and yearly basis respectively. Estimation of diffuse solar irradiance by Page's and also Liu and Jordan's correlations, as well as the direct beam component are also performed and the results are examined and presented. The abundance of solar energy in Jordan is evident from the daily average global solar irradiance which ranges between 5 and 7 kWh/m². A correlation of Angstrom type of the form: H/Ho = 0.448+0.203 S/So is found suitable for Jordan with correlation coefficient r = 0.93.     

Estimation of global solar radiation in Benin

Following Frère and Rietveld's model, correlation constants a and b were determined for many stations in Benin using:

• - a graphical relationship between the average annual relative sunshine SS/SS′o and the constants (Frère's model).

• - a linear relationship between constant a and the appropriate value of sunshine duration and a hyperbolic relationship between constant b and the relative average annual sunshine (Rietveld's model).

Knowledge of constant for a location can be used to predict global solar radiation for other locations using the Angström-Page approach using a statistical relationship between global solar radiation and sunshine duration.The estimated values were compared with measured values.     

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%.     

The solar radiation climate of Thailand

Geographical, seasonal, and diurnal variations of global solar radiation in Thailand are surveyed. Seasonal effects are shown by separate studies for eight 1.5 month periods of the year defined by standard solar declination values. Detailed maps are given of the geographical distribution of solar radiation prepared from data on cloudiness at 44 stations, duration of sunshine at 18 stations, and linear regressions relating radiation to sunshine at Chiang Mai and Bangkok. The highest mean values are above 19.5 MJ m⁻² d⁻¹ and are widespread in spring. The lowest values are below 15.0 MJ m⁻² d⁻¹ in restricted localities with heavy rainfall in autumn.Rough estimates of diffuse solar radiation and atmospheric turbidity are made from the radiation-sunshine regression parameters. Diffuse radiation averages 8.4 MJ m⁻² d⁻¹. Turbidity at Chiang Mai is high in spring and low in summer and autumn; at Bangkok it is high throughout the year.The diurnal variation of global solar radiation determined from hourly measurements at Chiang Mai and Bangkok is analysed. The mean midday radiation fluxes range from 0.80 kW m⁻² in spring to 0.60 kW m⁻² in autumn. On the average the radiation received in the afternoon is slightly less than that received in the morning.     

Estimation and prediction of global solar radiation over Greece

A regression analysis of the relative monthly values of global solar radiation ( ) the corresponding values of sunshine (n/N), for the period 1961-75, was performed to determine the constants a and b of the Ångström formula, for Athens. The constants a and b were also determined by a graphical relationship between the average annual relative sunshine (n/N) and these constants, for the same station. The latter method was then used to determine the constants a and b for 33 other stations widely distributed throughout Greece, after making a relative correction to these constants. In this way, monthly and annual values of global solar radiation were estimated for 34 stations over Greece from sunshine measurements. The geographical distribution of the annual totals of global solar radiation over Greece was mapped and some types and sub-types were identified.Further, a stepwise multiple regression analysis of the annual total amounts of global solar radiation and the three factors (latitude, longitude and altitude) was carried out; the validity of the assumption of the linear relationship between the annual totals of global solar radiation and the three factors was examined.     

Global and diffuse solar irradiance in Yemen (Y.A.R.)

Measurements of global and diffuse solar irradiance on a horizontal surface were made at Sana'a University during 1980/81 and the results are presented. Use is made of these results and other meteorological data to examine some of the methods of prediction of global solar irradiance and of diffuse solar irradiance . The regression coefficients of the Angstrom correlation relation and the zone parameter of an empirical relation due to Barbaro et al. are determined for Sana'a. The results are extended to compute at five other stations and comparison is made with the available data. The computed and measured values of are in good agreement. The monthly variation of and the effects of latitude and altitude on the regression coefficients and on the clearliness index are discussed.The abundance of solar energy in Yemen is evident from the annual total global solar irradiance which ranges between 7500 and 7910 MJm⁻² in the six towns.Correlations between the diffuse fraction and the clearliness index and between the diffuse fraction and the relative duration of sunshine are determined for Sana'a and compared with the Page and Liu and Jordan correlations. Agreement is found only with Page's correlation during the months March to September.The relation between and is used to compute at the other towns making use of the available sunshine data.The effect of altitude is found to be more distinct on the fraction than on other parameters.     

Assessment of solar and wind energy resources in Ethiopia. I. Solar energy

This paper describes how data from a variety of sources are merged to present new countrywide maps of the solar energy distribution over Ethiopia. The spatial coverage of stations with radiation data was found to be unsatisfactory for the purpose of a countrywide solar energy assessment exercise. Therefore, radiation had to be predicted from sunshine hours by employing empirical models. Using data from seven stations in Ethiopia, linear and quadratic correlation relationships between monthly mean daily solar radiation and sunshine hours per day have been developed. These regional models show a distinct improvement over previously employed countrywide models. To produce a national solar-energy distribution profile, a spatial extension of the radiation/sunshine relationships had to be carried out. To do this, the intercepts (a) and slopes (b) of each of the seven linear regression equations and another six from previous studies, completed in neighbouring Sudan, Kenya and Yemen, were used to interpolate the corresponding values to areas between them. Subsequent to these procedures, 142 stations providing only sunshine data were assigned their “appropriate” a and b values to estimate the amount of solar radiation received, which was then used to produce annual and monthly solar radiation distribution maps for Ethiopia. The results show that in all regions solar energy is an abundant resource.     

Global solar radiation in Northeastern Saudi Arabia

This paper presents the actual global solar radiation on a horizontal surface along with the prevailing meteorological conditions encountered during the measurement period from 1 January–31 December, for one complete year, in the Arabian Gulf Coast near the city of Dhahran. High resolution, real time solar radiation and meteorological data were collected, and processed. Hourly, daily, and monthly statistics of solar radiation was made from the one-minute averaged recorded values. The highest measured daily, and monthly mean solar radiation were found to be 351 and 328 W/m⁻², respectively. The highest one-minute averaged solar radiation values up to 1183 W/m⁻² were observed in the summer season, from May–September. The highest hourly solar radiation value was recorded as 1053 W/m⁻² in the middle of June. Beside the global solar radiation measurements, the main observed meteorological parameters were temperature, pressure, wind speed, precipitation, and relative humidity. On the other hand, the estimation of daily and monthly mean global solar radiation was performed based upon two empirical formulas which relate the solar radiation to the sunshine duration, relative humidity, maximum temperature, the latitude of the monitoring location, sunset hour and declination angles. The agreement between the measured and estimated solar radiation values was found to be satisfactory. Nevertheless, the empirical formula under-estimates the solar radiation values during summer, and over-estimates during winter.     

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.     

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.     

Multilayer Perceptron approach for estimating 5-min and hourly horizontal global irradiation from exogenous meteorological data in locations without solar measurements

Only one thousand stations around the world measures solar radiation sometimes with a poor quality. The objective of this paper is to show if solar irradiations at short time scale, hourly and 5-min, (very under-studied time-step) can be estimated from more available and cheaper data using Artificial Neural Networks. 7 meteorological and 3 calculated parameters are used as inputs; 1023 inputs combinations are possible for each time-step; the best inputs combinations are pursued. A variable selection method based on Pearson's coefficient is firstly used between inputs and between output and inputs; some inputs are redundant (particularly calculated ones) and/or with a weak link with solar radiation (as wind speed and direction), sunshine duration is strongly correlated with solar irradiation. The models have a good adequacy mainly with sunshine duration in the input set. For hourly data, the performances of the 6 and 10 inputs model are nRMSE = 13.90% (nMAE = 13.28%, R² = 0.979) and nRMSE = 13.33% (nMAE = 12.72%, R² = 0.9812); without sunshine duration, the model nRMSE (with 5 inputs) falls to 28.27%. For 5-min data, the 6 and 10 inputs models have a nRMSE equal to 19.35% and 18.65% which is very good for such a time-step. A comparison with literature highlighted the quality of these models.     

Global solar radiation estimation from relative sunshine hours in Yemen

The existing measurements of global solar radiation and sunshine duration for Yemen are examined. The errors of estimating solar radiation from sunshine hour measurements using Angstrom's relation are evaluated. As a simple predictor for global radiation, an average Ansgtrom relations in the form

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for all stations is evaluated. Other Angstrom correlation relations are also proposed by classifying the stations under into four groups. The estimated results are compared and seem to be satisfactory in the latter case.     

Evaluation of the Heliosat-II method using daily irradiation data for four stations in Iran

Efficient use of solar radiation needs detailed knowledge of its spatial and temporal variations. Such information can be achieved using interpolating measured irradiance by ground stations. But more reliable results can be obtained by processing geostationary satellite images. Heliosat is an algorithm which has been developed to estimate global horizontal irradiance at ground level from images taken in the visible band by the Meteosat satellites.The aim of this study was to evaluate the Heliosat-II model by using daily global solar irradiation data measured at the four radiometric stations in Iran as well as Meteosat-5 images which are recorded by a spacecraft over 63°E. Mean RMSD% and MBD% for all stations were 11.7% and 1.9%, respectively. The mean values of intercept, slope and correlation coefficient were 0.82 (kWh m⁻²), 1.05 and 0.93, respectively. Seasonally, the maximum RMSD occurs in autumn (22.1%) and the minimum is experienced in spring (8.4%). This accuracy is a great achievement for producing a high quality solar radiation atlas in a country such as Iran with very sparse radiometric network and frequently unreliable measured irradiation data.     

Quality control and estimation of global solar radiation in China

Measurements of surface radiation in China are too sparse to meet demand for scientific research and engineering applications. Moreover, the radiation data often include erroneous and questionable values though preliminary quality-check has been done before the data release. Therefore, quality control of radiation data is often a prerequisite for using these data. In this study, a set of quality-check procedures were implemented to control the quality of the solar radiation measurements at 97 stations in China. A hybrid model for estimating global solar radiation was then evaluated against the controlled data. The results show that the model can estimate the global radiation with accuracy of MBE less than 1.5 MJ m⁻² and RMSE less than 2.8 MJ m⁻² for daily radiation and RMSE less than 2.0 MJ m⁻² for monthly-mean daily radiation at individual stations over most of China except at a few stations where unsatisfactory estimates were possibly caused by severe air pollution or too dense clouds. The MBE averaged over all stations are about 0.7 MJ m⁻² and RMSE about 2.0 MJ m⁻² for daily radiation and RMSE about 1.3 MJ m⁻² for monthly-mean daily radiation. Finally, this model was used to fill data gaps and to expand solar radiation data set using routine meteorological station data in China. This data set would substantially contribute to some radiation-related scientific studies and engineering applications in China.     

Estimated monthly average global radiation for Turkey and its comparison with observations

Global solar radiation data obtained from actinographs of the Turkish State Meterological Service were compared with data obtained from pyrheliometers that were established recently to determine if the actinograph data were usable in practice. It has been found that the observed actinograph data have a rather high error rate with 14.7% annual and 42.1% monthly averages. It has, however, not been possible to smooth these errors as they are absolutely random. Thus, a well known quadratic model was used to produce available radiation data. A quadratic relationship between solar insolation and duration of solar radiation data has been investigated in order to estimate monthly average global irradiance for Ankara, Antalya, Samsun, Konya, Urfa and zmir. The data from August 1993 to July 1995 have been used in the quadratic model. But, observations of zmir differ from other stations covered for about four years. Solar insolation data used in the quadratic model were obtained from the pyrheliometer with model CR10. Duration of bright sunshine data were obtained from a Siap, Frans or Müller sunshine recorder with 60° global lens. A general quadratic formula was found that represents the whole of Turkey. The estimated monthly average global solar radiation data, then, were produced from this quadratic formula. Comparison of the estimated and measured values showed that the quadratic model was able to estimate global radiation with about a 4% annual relative error and the estimated data seemed to be more reliable than the data measured by actinograph.     

An analysis of thermal and solar zone radiation models using an Angstrom–Prescott equation and artificial neural networks

The correlation between the clearness index and sunshine duration is useful in the estimation of the solar radiation for areas where measured solar radiation data are unavailable. Regression techniques and artificial neural networks were used to investigate the correlations between daily global solar radiation (GSR) and sunshine duration for different climates in China. Measurements made during the 30-year period (1971–2000) from 41 measuring stations covering 9 thermal and 7 solar climate zones and sub-zones across China were gathered and analysed. The performance of the regression and the ANN models in the thermal and solar zones was analysed and compared. The coefficient of determination (R²), Nash–Sutcliffe efficiency coefficient (NSEC), mean bias error (MBE) and root-mean-square error (RMSE) were determined. It was found that the regression models in both the thermal and the solar climate zones showed a strong correlation between the clearness index and sunshine duration (R²=0.79–88). There appeared to be an increasing trend of larger MBE and RMSE from colder climates in the north to warmer climates in the south. In terms of the thermal and solar climate zone models, there was very little to choose between the two models.     

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.     

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 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.