Statistical analysis of solar measurements in Algeria using beta distributions

A method of smoothing solar data by beta probability distributions is implemented in this paper. In the first step, this method has been used to process daily sunshine duration data recorded at thirty-three meteorological stations in Algeria for eleven year periods or more. In the second step, it has been applied to hourly global solar irradiation flux measured in Algiers during the 1987/89 period. For each location and each month of the year, beta probability density functions fitting the monthly frequency distributions of the daily sunshine duration measurements are obtained. Both the parameters characterising the resulting beta distributions are then mapped, enabling us to build the frequency distributions of sunshine duration for every site in Algeria. In the case of solar radiation for Algiers, the recorded data have been processed following two different ways. The first one consists in sorting the hourly global solar irradiation data into eight typical classes of the daily clearness index. The second one is based on the repartition of these data per month. The results of the first classification show that for each class of daily clearness index, the hourly data under consideration are modelled by only one beta distribution. When using the second classification, linear combinations of two beta distributions are found to fit the monthly frequency distributions of the hourly solar radiation data.     

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.     

Diffuse solar irradiation model evaluation in the North Mediterranean Belt area

The performance of daily and hourly diffuse horizontal solar irradiation models and correlations is examined using an assembled data set of multivariate meteorological time series from countries in the North Mediterranean Belt area. The correlations reviewed use only daily global, hourly global or daily diffuse irradiation as input, for the daily or hourly time scale. The best overall performance was presented by the Frutos correlation for the estimation of the daily diffuse radiation by an adapted version of the Liu and Jordan correlation for the mean daily diffuse radiation profile, and by the Hollands and Crha model for estimation of hourly diffuse values from the corresponding global values. The results show that the best correlation for each site varies. Two empirical piecewise correlations were also developed by the authors with the help of the data bank available, yielding models that showed even better fits to the data. The results show some seasonal and location dependence.     

Solar radiation models—A review

Solar radiation models for predicting the average daily and hourly global radiation, beam radiation and diffuse radiation on horizontal surface are reviewed in this article. Estimations of monthly average hourly global radiation from daily summations are discussed. It was observed that Collares‐Pereira and Rabl model as modified by Gueymard (CPRG) yielded the best performance for estimating mean hourly global radiation incident on a horizontal surface for Indian regions. Estimations of monthly average hourly beam and diffuse radiation are discussed. It was observed that Singh‐Tiwari and Jamil‐Tiwari both models generally give better results for climatic conditions of Indian regions. Therefore, their use is recommended for composite climate of Indian regions. Empirical correlations developed to establish a relationship between the hourly diffuse fraction and the hourly clearness index using hourly global and diffuse irradiation measurements on a horizontal surface are discussed. Fifty models using the Angstrom–Prescott equation to predict the average daily global radiation with hours of sunshine are considered. It was reported that Ertekin and Yaldiz model showed the best performance against measured data of Konya, Turkey. Copyright © 2010 John Wiley & Sons, Ltd.     

Two estimation methods for monthly mean hourly total irradiation on tilted surfaces from monthly mean daily horizontal irradiation from solar radiation data of Ajaccio, Corsica

The sizing of a photovoltaic or a thermal solar system is generally based on monthly mean values of daily solar radiation on tilted surfaces. Many authors have demonstrated that it will be better to use monthly mean values of hourly radiation, particularly taking into account the Sun's position and to predict long-term performances of solar systems. (Liu and Jordan, 1963; Clark et al., 1984). Moreover, for most of the sites around the world, only monthly mean values of daily horizontal total irradiation are available for use in such calculations. We propose, by using well-known correlations in the literature, to estimate these monthly mean values of hourly total irradiation on tilted planes from monthly mean values of daily total horizontal irradiation, using three steps:

• — determination of monthly mean value of hourly total horizontal irradiation;

• — determination of monthly mean value of hourly diffuse horizontal irradiation;

• — determination of monthly mean value of hourly total irradiation on tilted planes.

In the first step, using the Collares Pereira and Rabl correlation, the root mean square error (RMSE) between correlated and experimental calculated data is 8%. In the second step, we used two methods: the first one utilizes the Erbs correlation and the second one is based on a local correlation which has been developed in our centre. Both of them gave identical results with an RMSE lower than 9%. We calculated monthly mean values of hourly total irradiation on three tilted planes (30°, 45° and 60°) and we compared these results with the experimental ones, obtaining a RMSE respectively of less than 10%. The method is then validated by these results.     

A procedure to obtain global radiation maps from sunshine durations at isolated stations in a region with complex orography

In this paper the procedure followed to obtain preliminary maps of monthly average daily global radiation is discussed. The information on which these maps are based is monthly average daily percent sunshine durations at stations covering the considered territory with very irregular density. The possibility of correlations between monthly average percent sunshine and meteorological parameters, other than cloudiness, is examined but found to be absent. A local fit procedure (octant-search), followed by smoothing, is used to construct percent sunshine maps, over the entire territory, coherent with the values relative to the single stations. Finally we have considered the possibility of important variations in the elevation and the influence of this parameter on the global radiation. Hence, among the various relationships relating monthly average daily global radiation to average percent sunshine duration, we have chosen one in which the daily clear sky global radiation (which depends on elevation above sea level) appears instead of the daily extra-terrestrial radiation. The clear sky global radiation has been calculated with a model deduced from Hottel's transmission model which includes elevation dependence. When more data become available, an analogous procedure could be used to obtain definitive maps, employing more reliable values for parameters relating global radiation to percent sunshine tested with experimental data. This method has been applied to the territory of Ethiopia, in order to obtain preliminary maps of global radiation.     

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.     

A simple model for estimating monthly mean daily sums of solar irradiation and its local distribution

This paper deals with linear correlations between solar irradiation sums and sunshine duration for mapping global, diffuse and direct irradiation. All values represent long-term averages of monthly mean daily sums. The first part of this paper describes a set of fourteen correlation equations based on an earlier study. The constants of all correlations depend on a common numerical triple that describes the climatic conditions. The constants, correlation coefficients and the triple are determined and discussed with reference to the example of two stations in the Federal Republic of Germany. In the second part, a general method for generating solar irradiation maps is proposed and applied for the state of North-Rhine Westphalia (FRG). The distribution of global and diffuse irradiation in terms of yearly averages is shown and discussed. © 1997 John Wiley & Sons, Ltd.     

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

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

Correlations for estimating solar radiation using sunshine hours and temperature measurement in Osogbo,Osun State,Nigeria

In this study, the global solar radiation on horizontal surface in Osogbo, Osun state, Nigeria was analyzed using 11-year data (1997–2007). Correlations using linear and quadratic expressions were developed to relate the global solar radiation on horizontal surface based on relative sunshine hours and temperature measurements for evaluating the monthly average daily global solar radiation. The calculated monthly clearness index values indicate that the prevailing weather condition in Osogbo is heavily overcast. All the developed quadratic correlations gave better correlation coefficients (0.834, 0.872 and 0.823 respectively) than the linear models. However, the Hargreaves and Samani related based quadratic model gave the best among the three developed quadratic expressions and is therefore suggested for estimating the monthly global radiation in this site and its surroundings.     

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.     

A method for estimating direct normal solar irradiation from satellite data for a tropical environment

In order to investigate a potential use of concentrating solar power technologies and select an optimum site for these technologies, it is necessary to obtain information on the geographical distribution of direct normal solar irradiation over an area of interest. In this work, we have developed a method for estimating direct normal irradiation from satellite data for a tropical environment. The method starts with the estimation of global irradiation on a horizontal surface from MTSAT-1R satellite data and other ground-based ancillary data. Then a satellite-based diffuse fraction model was developed and used to estimate the diffuse component of the satellite-derived global irradiation. Based on this estimated global and diffuse irradiation and the solar radiation incident angle, the direct normal irradiation was finally calculated. To evaluate its performance, the method was used to estimate the monthly average hourly direct normal irradiation at seven pyrheliometer stations in Thailand. It was found that values of monthly average hourly direct normal irradiation from the measurements and those estimated from the proposed method are in reasonable agreement, with a root mean square difference of 16% and a mean bias of −1.6%, with respect to mean measured values. After the validation, this method was used to estimate the monthly average hourly direct normal irradiation over Thailand by using MTSAT-1R satellite data for the period from June 2005 to December 2008. Results from the calculation were displayed as hourly and yearly irradiation maps. These maps reveal that the direct normal irradiation in Thailand was strongly affected by the tropical monsoons and local topography of the country.     

Study of hourly solar radiation data in Istanbul

This paper presents a study of the solar radiation data measured in Istanbul (41.1°N, 29.0°E) during 1992 and 1993. The monthly and annual average values of total solar radiation and clearness index are analysed. The monthly averages of daily total radiation are 1.23 kW h m⁻² day⁻¹ for January and 6.55 kW h m⁻² day⁻¹ for July. The annual average value of daily total radiation is 3.81 kW h m⁻² day⁻¹. The monthly averages of clearness index for January and July are 0.28 and 0.50, respectively. The annual average value of clearness index is 0.38. In the second part of the study, the seasonal relative frequency of hourly total radiation and clearness index is studied. 46% of the annual data corresponds to a value greater than 300 W m⁻². The annual average frequency of clear hours is 24%. The analysis points to the conclusion that solar radiation will be efficient and useful between April and September for heating purposes. A polynomial relationship is developed between hourly clearness index and hourly fractional sunshine duration. Some statistical tests are used to check this relationship for four different ranges of optical air mass.     

Study of diffuse and global radiation characteristics in India

Recently, the Indian Meteorological Department has made available, for 13 locations in India, pyranometric data for total and diffuse radiation on an hourly and daily basis. The period of observation is from 1957 to 1975. This data is analysed to reexamine the correlations between monthly-average daily values of diffuse and total insolation and between hourly and daily insolation. The relationship between monthly diffuse/total and total/extraterrestrial ratios is found to be linear. The present correlation implies that the diffuse component is significantly larger than that predicted by other correlations. No noticeable effect of location or seasonal variation was found. Comparison of the present data with earlier studies for India indicates a trend of increasing diffuse radiation with the lapse of time. The ratio of hourly to daily insolation agrees with the Liu and Jordan correlation for total insolation but differs significantly for diffuse radiation. The need for refinement of the Liu and Jordan correlation between hourly and daily diffuse radiation is pointed out.     

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%.     

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.     

Experimental and theoretical investigation of global and diffuse solar radiation in the United Arab Emirates

In the present study, the global, direct and diffuse components of solar radiation as well as temperature, relative humidity and wind speed have been continuously monitored and analysed on an hourly, daily and monthly basis. The monthly average daily total solar radiation varies from 2700 W h/m² in December to 8000 W h/m² in June with an average clearness index of 0.65. Experimental data are compared to the predictions of different theoretical models as functions of declination and hour angles. Correlations are obtained describing the variation of hourly, daily and monthly averages of total and diffuse solar radiation using polynomial expressions. Empirical correlations describing the dependence of the daily average diffuse to total radiation ratio on the clearness index are also obtained. Data for the daily diffuse to total radiation ratio are compared to correlations obtained by other investigators. The comparison shows a reasonable agreement with some scatter due to the seasonal dependence of the correlation. Comparison of calculations with experimental measurements under clear sky conditions show excellent agreement with a maximum error of 8%.     

Analysis of solar radiation data for Port Harcourt, Nigeria

The data on global irradiation incident on a horizontal surface in Port Harcourt during the 13-year period 1977–1989 are analyzed and shown to vary with the climatic changes of the year. The range of variation is found to be greatest in August. Based on the calculated average monthly clearness index values only five seasonal patterns are identified for Port Harcourt. The percentage of days with duration of sunshine less than 1.5 h is 28.3% while that greater than 9 h is 4.3%. The Angstrom type of regression model relating total global irradiation to sunshine duration has been found to be reasonably adequate only if long-term average monthly values are used.     

Technical note a multiple linear correlation for diffuse radiation from global solar radiation and sunshine data over Egypt

Measurements of global solar radiation, diffuse radiation and sunshine duration data during the period from 1982 to 1988 at different locations over Egypt were used to establish empirical relationships that would connect the daily monthly average diffuse irradiation with both relative sunshine duration and clearness index separately and in combination. The selected locations were chosen to represent the different weather conditions of North, Middle and South Egypt. Our correlation equations were tested using measured data for the year 1992 at the same locations. The correlation connecting diffuse radiation with both clearness index and percentage possible sunshine is found to be applicable over Egypt.     

A comparison of estimated and measured values of solar radiation in Elazi , Turkey

In this study, variation of global solar radiation reaching the Elazi region at hourly and monthly average daily periods was examined measuring daily global solar radiation between April 1994 and March 1995 by a Kipp–Zonen pyranometer. Taking the measured values as reference, the statistical performance of the three equations used in estimating the monthly average global solar radiation was investigated. Secondly, it was shown that ‘bright sunshine hours/daylength’ and its standard derivation could be used to estimate the monthly daily ‘solar radiation/extraterrestrial radiation’ by applying the maximum likelihood quadratic fit method to the data taken from the state Meteorological Office in Elazi between 1983–1994.