Correlations for direct normal and global horizontal irradiation on a French Mediterranean site

The purpose of this study is to establish some correlations on direct normal and global horizontal irradiation for a mediterranean site. The correlations have been developed for monthly mean values, daily and hourly values of irradiation data. We have used linear or polynomial regressions between energetical ratio and sunshine duration. For the monthly means and the daily values, the ratio fits very well the sunshine duration while, for hourly values, we express as a function of . In all cases, these correlations are, for this mediterranean site, in good accordance with experimental data. Nevertheless, a study for other locations has to be developed.     

Diffuse solar radiation estimates from sunshine hours and clearness index for Karachi, Pakistan

Correlations for the estimation of monthly average daily diffuse solar radiation as a function of the sunshine hours and clearness index have been obtained from Karachi. Generally, two types of correlations are used: (a) diffuse radiation as a function of relative sunshine hours and extraterrestrial radiation, and (b) diffuse radiation as a function of global and extraterrestrial radiation. These correlations are mostly first- and second-order polynomials in the sunshine hours and clearness index, indicating the presence of the diffuse solar radiation component. The diffuse solar radiation shows a peak value during the monsoon months of July–August. The diffuse to global ratio is found to be 0.32 from the analysis, and the diffuse to extraterrestrial radiation ratio is nearly 0.19 throughout the year. Among the established relations, Iqbal and Stanhill overestimate the radiation value, while Liu and Jordan underestimate it.     

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.     

Theoretical prediction and validation of global horizontal solar irradiance for a tropical climate in India

This paper aims to propose monthly models responsible for the theoretical evaluation of the global horizontal irradiance of a tropical region in India which is Sivagangai situated in Tamilnadu. The actual measured global horizontal irradiance hails from a 5 MW solar power plant station located at Sivagangai in Tamilnadu. The data were monitored from May 2011 to April 2013. The theoretical assessment was conducted differently by employing a programming platform called Microsoft Visual Basic 2010 Express. A graphical user interface was created using Visual Basic 2010 Express, which provided the evaluation of empirical parameters for model formulation such as daily sunshine duration (S), maximum possible sunshine hour duration (S₀), extra terrestrial horizontal global irradiance (H₀) and extra terrestrial direct normal irradiance (G₀). The proposed regression models were validated by the significance of statistical indicators such as mean bias error, root mean square error and mean percentage error from the predicted and the actual values for the region considered. Comparison was made between the proposed monthly models and the existing normalized models for global horizontal irradiance evaluation.     

Monthly average solar radiation in panama—Daily and hourly relations between direct and global insolation

Regressions are developed to estimate daily global and direct radiation and the hourly distribution of direct radiation for Barro Colorado Island, Panama from monthly mean values observed 35 km away at Chiva-Chiva. The ratio model of Liu and Jordan and the logarithmic model of Anderson for estimating direct from global radiation are compared. Both gave satisfactory results after accounting for “seasonal” variation, but the ratio model was preferred in this case for the smaller number of separate regressions required. The ratio model fitted for diffuse radiation at Chiva-Chiva agreed closely with regressions for stations at similar latitude. For a given value of the clearness index, the direct component of solar radiation was relatively (but not absolutely) reduced during the dry season compared with the wet season. A likely explanation for this unexpected result is increased marine and terrestrial aerosol during the dry season when offshore winds are stronger and burning of crop and wasteland occurs. The models of Whillier and of Garnier and Ohmura, which assume constant atmospheric transmittance throughout the day, gave unsatisfactory fits to the hourly distribution of direct radiation. They were also unable to mimic an observed morning/afternoon asymmetry that was strongest in the wet season. Hourly direct radiation was accurately estimated from hourly global radiation by quadratic polynomials fitted separately to the morning and afternoon data. The resulting regressions will enable estimation of radiation in forest understory from measurements of insolation in the open by computerized image analysis of hemispherical canopy photos.     

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%.     

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 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.     

Estimation of monthly mean daily diffuse radiation in China

In this study, several equations are employed to estimate monthly mean daily diffuse solar radiation for eight typical meteorological stations in China. Estimated values are compared with measured values in terms of statistical error tests such as mean percentage error (MPE), mean bias error (MBE), root mean square error (RMSE). All the models fit the data adequately and can be used to estimate monthly mean daily diffuse solar radiation from global solar radiation and sunshine hours. This study finds that the quadratic model performed better than the other models:     

The fluctuation of solar irradiance in Hong Kong

Measurements of the total global solar irradiance on a horizontal surface in Hong Kong during the 10-yr period 1969-78 are analysed. Mean annual, monthly and daily totals and their frequency distributions are computed and examined. The seasonal and climatic effects on the fluctuation of solar irradiance in Hong Kong are discussed. The effect is particularly large during the spring months when the transition from cold to warm weather occurs.The diurnal variation of total global solar irradiance in Hong Kong is also examined and the measured hourly data are observed to be in good agreement with Liu and Jordan's procedure of estimation from daily totals.Results of regression analysis relating total solar irradiance with duration of bright sunshine hours based on data for Hong Kong are summarized. The yearly regression coefficients are found to be varying in an unsystematic manner.Estimation of the Hong Kong monthly average diffuse solar irradiance based on the correlation with the cloudiness index is also performed and the results are found to vary between 7.39 MJ m^?2 d^?1 in the summer and 4.44 MJ m^?2 d^?1 in the winter.     

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.     

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.     

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.     

Evaluation and establishment of diffuse solar radiation models for Bursa,Turkey

The main objective of the present study is to evaluate the applicability of the diffuse solar radiation models from previous studies and establish new models for Bursa. Therefore, 35 regression models from previous studies in the literature are used and categorized as follows: (1) cloudness index is the function of clearness index; (2) cloudness index is the function of relative sunshine duration; (3) the diffuse coefficient is the function of the clearness index; and (4) the diffuse coefficient is the function of the relative sunshine duration. Also, new four diffuse solar radiation models were developed using 1968–2015 long-term global solar radiation and sunshine duration data. The new models are then compared with 35 empirical equations available in previous studies in terms of different statistical tests. Consequently, Models 6 and 8 are found as the most accurate and high-performance empirical models for estimation of the monthly mean diffuse solar radiation on a horizontal surface for Bursa, Turkey.     

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.     

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.     

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.     

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.     

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.