Correlation of global solar radiation with meteorological parameters over Egypt

Global solar radiation measurements on a horizontal surface (G_m), mean daily maximum temperature (T), mean daily relative humidity (RH), mean daily sea level pressure (MSL), mean daily vapor pressure (V) and hours of bright sunshine (S) are presented, analyzed, arranged in tables and graphs and discussed for five selected locations over Egypt. The locations chosen represent the different weather conditions of Egypt. Matrough and Al Arish are in the north, Cairo in the middle and Kharga and Aswan in the south of Egypt. A correlation between the measurements of global solar radiation and the meteorological parameters were given for the considered locations. The common relationship for all Egypt was also estimated. The correlation and the regression coefficients and the standard errors of estimate are listed in Table 1. The values of correlation coefficients vary from 89% to 99% and the errors of estimation are between 0.01 and 0.04.

Table 1. Geographic location of the selected stations and correlation, regression coefficients and standard errors of estimate for the model ((5), (6), (7), (8) and (9))

Full-size table (<1K)

     

Quality control of global solar radiation using sunshine duration hours

The aim of this study was to develop a new and automatic method for controlling the quality of daily global solar radiation, G_d, using sunshine duration hours. The new method has three levels of tests: first, G_d is compared against daily extraterrestrial radiation that is received on a horizontal surface (0.03×G_od?G_d<G_od); second, G_d should only exceed by a small amount of the daily clear sky irradiation that is observed under highly transparent clear skies (G_d<1.1G_cd); and third, the method uses a series of persistence checks that utilize the relation between daily global solar radiation and relative sunshine duration hours. The method is capable of identifying systematic and non-systematic errors and its ability has been shown in three different climates including semi-arid, coastal humid and very arid climates.     

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.     

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.     

Estimation of monthly global solar radiation from sunshine duration measurement in Elazi

In this study, the relation between a and b terms and / was investigated to estimate the global solar radiation in Elazi by using different regression analyses. Equations which contain the whole year and two different periods, winter and summer, were developed. Eqs. (5)–(7) which represent second, third and fourth degree equations respectively, gave the best results in all of the equations having an error less than 1%. Contrary to expectations, the equations developed for summer and winter periods had higher errors than the others.     

Prediction of global solar radiation from bright sunshine hours and other meteorological data

Three existing empirical relations which predict global radiation from bright sunshine hours and meteorological parameters, were tried for 14 Indian stations where all relevant data was available. A large amount of error (±50%) was found. So a new empirical relation was established between global radiation and meteorological parameters. The new relation predicted the insolation within a ±10% error limit in most cases. Global radiation dependence on ambient temperature and relative humidity was introduced through atmosperic water content per unit volume. The relation is WAT = RH(4.7923+0.3647×T+0.0055×T²+0.0003×T³)G = G_ext(0.414+0.400×SS-0.0055×WAT)$\text{SS}\text{= S}\text{Z}\text{?}$     

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.     

Global solar radiation estimation using sunshine duration in Spain

Several equations were employed to estimate global solar radiation from sunshine hours for 16 meteorological stations in Spain, using only the relative duration of sunshine. These equations included the original Angström–Prescott linear regression and modified functions (quadratic, third degree, logarithmic and exponential functions). Estimated values were compared with measured values in terms of the coefficient of determination, standard error of the estimate and mean absolute error. All the models fitted the data adequately and can be used to estimate global solar radiation from sunshine hours. This study finds that the third degree models performed better than the other models, but the linear model is preferred due to its greater simplicity and wider application. It is also found that seasonal partitioning does not significantly improve the estimation of global radiation.     

Estimation of daily and monthly direct, diffuse and global solar radiation from sunshine duration measurements

An accurate 200 W/m² threshold pyreheliometer instrument for measuring the duration of bright sunshine has been used to derive daily and monthly regressions for direct, diffuse, and global solar radiation component vs sunshine duration. Daily regression for diffuse/global are linear in sunshine duration, while quadratic regression forms are employed for direct normal, direct horizontal, and global/extraterrestrial components. Only the daily direct normal component had regression values which depend on season while all of the monthly regressions depend on season. Linear regression relations for monthly direct normal, diffuse/global and global/extraterrestrial are employed, with a quadratic form being used for direct horizontal. Effects of rainfall, especially in overcast conditions, and of atmospheric turbidity and precipitable water, especially under clear-sky conditions, are observed and documented.     

Global solar radiation estimation with sunshine duration in Tibet,China

Eight models using only the sunshine duration for estimating the global solar radiation on a horizontal surface are evaluated at Changdu, Geer, Lasa and Naqu stations in Tibet, China against the measured meteorological data during 1994–2008. Based on statistical error tests, results show that the simple linear Ångström–Prescott model is reasonably accurate in practice, and the modifications with complex expression are not necessary in Tibet. Then, two general Ångström–Prescott models for estimating the daily and monthly average daily global solar radiation respectively in Tibet are proposed.     

Technical note: Techniques to obtain improved predictions of global radiation from sunshine duration

Data for 42 stations in different parts of the world in the northern hemisphere have been employed to partition monthly averaged daily global radiation and sunshine duration in a bid to obtain improved fits to Angstroms correlation. It has been found that regression fits to the correlation using data for biannual groups of months from March–August (months 3–8) and September–February (months 9–2), or March–September (months 3–9) and October–February (months 10–2), give an improvement in the rms error over the year, which is 25% or higher than the errors for annual fits for half of the cases. In no case is there an increase in rms error from the partitioning.It is found that biannual regression parameters for a pyranometer station may be used to predict with good accuracy global radiation for locations hundreds of kilometers away from the station if the climate, altitude and latitude are similar.A use of the seasonal partitioning of data leads to the following relations with station independent coefficients for     

Evaluation of sunshine duration from cloud data in Egypt

In this study, three empirical formulae have been deduced to estimate relative sunshine duration, n/N, using readily available observed data of cloud amount, C, in Egypt. The monthly mean values of n/N and C recorded at 34 stations during the period (1990–2005) have been used in the present study. The three deduced formulae have been verified for any locality in Egypt which lies above (zone 1) and below latitude 30° (zone 2) and for the whole country of Egypt. The agreement between measured and estimated values of the three deduced formulae were remarkable. It was found that the maximum possible error of estimated values, e (%), of the three deduced empirical formulae have not exceeded ±7.27% with mean percentage error (MPE) values range from −0.62% to +0.81%; meanwhile the values of statistical tests of main bias error (MBE) and root mean square error (RMSE) are very close to zero. It has been concluded that Egypt's deduced formula gives precise estimations for n/N and was recommended for use at any location in Egypt. The sunshine distribution and its percentage frequency over Egypt were also studied. The results revealed that latitudinal dependent of n/N. Egypt has minimum value of n/N (0.48) during January at the northern part of the country and maximum value (0.92) during June at the southern part.     

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.     

Empirical correlation of estimating global solar radiation using meteorological parameters

An empirical model for the estimation of solar energy on the basis of Angstrom's model is proposed in this work. Seven regression equations are developed by using different meteorological parameters such as mean sunshine duration per hour, temperature, relative humidity, wind speed, and rainfall. The performance of the model is determined on the basis of statistical indicators like correlation coefficient(r), coefficient of determination (R²), root mean square error (RMSE), mean percentage error (MPE), and mean bias error (MBE). The results show that the equation with the highest value of r, R² and the least value of RMSE, MPE, and MBE provides better results.     

Parameterization of a simple model to estimate monthly global solar radiation based on meteorological variables, and evaluation of existing solar radiation models for Tabouk, Saudi Arabia

Using 9 years of solar radiation data, we established a simple model to calculate the monthly mean global solar radiation on a horizontal surface in Tabouk (28.38° N, 36.6° E, Saudi Arabia). The model correlates the global solar radiation with five meteorological parameters. These parameters are the perceptible water vapor, air temperature, relative humidity, atmospheric pressure, and the mean monthly daily fraction of possible sunshine hours. The estimated global radiation from the model was compared with the measured values using the mean bias error (MBE), coefficient of correlation (R), root mean square error (RMSE), and mean percentage error (MPE). The t statistics were also applied as another indication of suitability. The model has a high coefficient of correlation (R = 0.99), MBE = −14 × 10⁻⁴ kW h/m², RMSE = 0.10 kW h/m², and MPE = −0.03%. It is believed that the model developed in this work is applicable for estimating, with great accuracy. The monthly mean daily global radiation at any site having similar conditions to those found in Tabouk.Furthermore, 29 regression models available in the literature were used to estimate the global solar radiation data for Tabouk. The selected models were different in terms of the variables they use and in the number of the variables they contained. The models were compared on the basis of the statistical errors considered above. Apart from Abdall’s model, which showed a reasonable estimate (MPE = −2.04%, MBE = −0.22 kW h/m², and RMSE = 0.59 kW h/m²), all the models under or overestimate the measured solar radiation values. Comparisons between these models and the produced model, from this study, were also considered. According to the statistical results, the model of Abdall showed the prediction closest to those estimated using the developed model.     

A comparative study to estimate daily diffuse solar radiation over India

A detailed study of monthly average daily diffuse solar radiation for selected Indian locations have been performed using five years (2001–2005) measured data. The data of four prominent locations (Jodhpur, Calcutta, Bombay and Pune), representing varying weather conditions of the entire country, have been taken for the present study. The correlations between the diffuse fraction (H_d/H) and the sunshine fraction (S/S₀) have been developed using regression analysis method for each selected location as well as for all Indian locations, we call it All India Correlation (AIC). The results obtained from present AIC are well compared with the measured data along with the estimates of Liu and Jordan, Gopinathan and Iqbal for different locations. The comparisons between various data conclude that AIC can be used to estimate diffuse fraction for any location in India. For further validation and to show the accuracy of present correlations, statistical tests of root mean square error (RMSE), mean bias error (MBE) and mean percentage error (MPE) are also performed.     

A review of sunshine-based models used to estimate monthly average global solar radiation

This paper is a review and evaluation of the methods of estimating monthly average global solar radiation using bright sunshine hours. It presents model validation and comparison techniques and summarizes comparisons of some of the models using the data of various locations. It tabulates data for about 100 locations, with different climates, which have appeared in the literature and gives the values of the Ångstrom coefficients for 100 locations together with their geographical parameters. It also compares some recent models to obtain information about their global applicability.