Analysis of the solar radiation data for Beer Sheva, Israel, and its environs

The solar radiation climate of Beer Sheva, Israel, is reported upon in detail. The database utilized in this analysis consisted of global radiation on a horizontal surface, normal incidence beam radiation, and global radiation on a south-facing surface tilted at 40°. Monthly-average hourly and daily values are reported for each of these three types of measured radiations, together with the calculated monthly-average daily values for the components of the global radiation, viz. the horizontal beam and diffuse radiations. The monthly-average hourly and daily clearness index values have also been calculated and analyzed. Monthly-average daily frequency distributions of the clearness index values are reported for each month. The solar radiation climate of Beer Sheva has also been compared to those reported for a number of countries in this region. The annual-average daily global radiation incident on a horizontal surface is 18.91 MJ/m² and that for normal incidence beam radiation is 21.17 MJ/m². The annual-average daily fraction of the horizontal global radiation that is beam is 0.72. The annual-average daily value for the clearness index is 0.587 and the average frequency of clear days annually is 58.6%. We conclude, based upon the above analysis, that Beer Sheva and its environs are characterized by relatively high, average-daily irradiation rates, both global and beam, and a relatively high frequency of clear days.     

A method for characterization and inter-comparison of sites with regard to solar energy utilization by statistical analysis of their solar radiation data as performed for three sites in the Israel Negev region

A method for the characterization and inter-comparison of sites with regard to their suitability for utilization of solar energy based upon the statistical analysis of their solar radiation intensities is presented. In this method each monthly data set of the daily global, horizontal beam and diffuse radiation intensities was analyzed and the following parameters were determined: monthly average daily radiation intensity, coefficient of variation, skewness and kurtosis. The values of the skewness and kurtosis have been applied, using generally accepted rules, to describe the distribution curves for each of the radiation intensity data sets. In addition, the same type of statistical analysis was applied to the monthly average daily ratios of the horizontal beam to global radiation, diffuse to global and the clearness index for the three sites. In this investigation, this statistical analysis method has been applied to the global and beam radiation measured at three sites located in the southern, Negev region of Israel, viz., Beer Sheva, Sde Boker and Eilat. The southern region of Israel is characterized by relatively high average daily irradiation intensities for both global and normal incidence radiation. They have been characterized with regard to the distribution of their intensity levels and a site inter-comparison has also been performed. An inter-comparison of the results of these analyses for the three sites has been performed on a monthly basis. The results of this analysis are used both to characterize and compare the composition of the solar radiation at the three sites under investigation. The results of this study will be presented in detail.     

The assessment of different models to predict the global solar radiation on a surface tilted to the south

Global and diffuse solar radiation intensities are, in general, measured on horizontal surfaces, whereas stationary solar conversion systems (both flat plate solar collector and PV) are tilted towards the sun in order to maximize the amount of solar radiation incident on the collector surface. Consequently, the solar radiation incident on a tilted surface must be determined by converting the solar radiation intensities measured on a horizontal surface to that incident on the tilted surface of interest. There exist a large number of models designed to perform such a conversion. 11 such models have been tested utilizing data measured in Beer Sheva, Israel. The data consist of hourly global and diffuse solar radiation on a horizontal surface, normal incidence beam and global radiation on a south-oriented surface tilted at 40°. The horizontal diffuse radiation measured using a shadow ring was corrected using four different correction models. This resulted in 44 model permutations. The individual model performance is assessed by an inter-comparison between the calculated and measured solar global radiation on the south-oriented surface tilted at 40° using both graphical and statistical methods. The relative performance of the different models under different sky conditions has been studied. Different grading systems have been applied in an attempt to score the relative performance of the models.     

Analysis of diffuse radiation data for Beer Sheva: Measured (shadow ring) versus calculated (global-horizontal beam) values

We have utilized concurrently measured global, normal incidence beam, and diffuse radiation data, the latter measured by means of a shadow ring pyranometer to study the relative magnitude of the anisotropic contribution (circumsolar region and nonuniform sky conditions) to the diffuse radiation. In the case of Beer Sheva, the monthly average hourly anisotropic correction factor varies from 2.9 to 20.9%, whereas the “standard” geometric correction factor varies from 5.6 to 14.0%. The monthly average hourly overall correction factor (combined anisotropic and geometric factors) varies from 8.9 to 37.7%. The data have also been analyzed using a simple model of sky radiance developed by Steven in 1984. His anisotropic correction factor is a function of the relative strength and angular width of the circumsolar radiation region. The results of this analysis are in agreement with those previously reported for Quidron on the Dead Sea, viz, the anisotropy and relative strength of the circumsolar radiation are significantly greater than at any of the sites analyzed by Steven. In addition, the data have been utilized to validate a model developed by LeBaron et al. in 1990 for correcting shadow ring diffuse radiation data. The monthly average deviation between the corrected and true diffuse radiation values varies from 4.55 to 7.92%.     

Analysis of erythemal UVB and UVA irradiance at Beer Sheva,Israel from 1994 through 2012

The erythemal UVB and UVA irradiance monitored at Beer Sheva, Israel from June 1994 through March 2012 has been analyzed. A statistical analysis was applied to the daily values for each month and average, median, standard deviation, coefficient of variation (%), maximum and minimum values are reported. The maximum and minimum monthly average daily values for both erythemal UVB and UVA occur in June and December, respectively. They are 1.658 Wm⁻²(ER) and 0.346 Wm⁻²(ER) for the case of erythemal UVB and the corresponding values for UVA are 300.78 Wm⁻² and 135.52 Wm⁻². A similar statistical analysis was performed on the monthly average daily values throughout the time interval of this study. In addition, the monthly average daily values were analyzed to determine if there existed any trends for the individual months. A linear regression analysis was applied to the monthly average daily erythemal UVB and UVA irradiance as a function of year. No statistically significant trends were observed, based upon the corresponding p-values; a possible exception being the UVA irradiance during February, which may have a slight negative trend. Typical erythemal UVB and UVA irradiance meteorological years were developed for Beer Sheva and its environs.     

Analysis of solar radiation measurements at Al-Arish area, North Sinai, Egypt

This paper presents basic data for a five year period from 1986 to 1990 for global and diffuse solar radiation data at Al-Arish (31°04′N, 33°49′E). These data have been processed, analysed, presented, arranged in tables and graphs and discussed. Mean annual monthly and daily total, the diurnal variation and the frequency of daily totals of global solar radiation are computed and discussed. A correlation between the hourly values of the clearness and diffuse index were obtained and the recommended correlation equations were also given. The isopleths of hourly global radiation were also designed and discussed. The frequency distribution and the frequency of extended periods of low radiation income have been studied which are of particular interest in the field performance of solar energy systems.     

A novel approach for calculating the monthly average daily fraction of diffuse solar radiation

A novel approach for calculating the monthly average daily fraction of diffuse radiation has been developed. It is based upon the use of concurrent total solar radiation measurements for both a tilted surface and a horizontal surface. It divides the data into two categories, clear and cloudy day, on an hourly basis. The clear day data is analyzed by means of both Liu and Jordan's and Page's empirical equations. The cloudy day data is analyzed by Liu and Jordan's equation for determining the insolation ratio on a tilted to a horizontal surface. A monthly average value for the diffuse fraction is then determined by calculating a weighted average of the clear and cloudy day values.The monthly average values, for twelve months of Beer Sheva data, for the fraction of diffuse radiation have been calculated and compared to the empirical relationships derived by Liu and Jordan and Page. The agreement between the calculated values and empiriical relationship is somewhat better in the latter case.     

Monthly mean hourly global solar radiation estimation

In this paper, selected empirical models were used to estimate the monthly mean hourly global solar radiation from the daily global radiation at three sites in the east coast of Malaysia. The purpose is to determine the most accurate model to be used for estimating the monthly mean hourly global solar radiation in these sites. The hourly global solar radiation data used for the validation of selected models were obtained from the Malaysian Meteorology Department and University Malaysia Terengganu Renewable Energy Station. In order to indicate the performance of the models, the statistical test methods of the normalized mean bias error, normalized root mean square error, correlation coefficient and t-statistical test were used. The monthly mean hourly global solar radiation values were calculated by using six models and the results were compared with corresponding measured data. All the models fit the data adequately and can be used to estimate the monthly mean hourly global solar radiation. This study finds that the Collares-Pereira and Rabl model performed better than the other models. Therefore the Collares-Pereira and Rabl model is recommended to estimate the monthly mean hourly global radiations for the east coast of Malaysia with humid tropical climate and in elsewhere with similar climatic conditions.     

Statistical properties of hourly global radiation

A model is described which generates synthetic daily sequences of hourly radiation values, on the horizontal plane, for any location, with the daily clearness index K_t as input. The model assumes that for each K_t and solar hour the probability density of the hourly clearness index k_t is (simply) a truncated Gaussian function. A first-order autoregressive model is fitted for the k_t variable, normalised using parametrisations for the time-dependent average and standard deviation values. Values generated by this ARMA (1,0) model can then be transformed backwards to generate synthetic sequances of k_t values. Using a diffuse fraction correlation and a tilted radiation model, the horizontal global data can be transformed to any desired plane, thus providing solar system designers with the necessary hourly data for the accurate sizing of every type of solar system, including stand-alone, high solar fraction and passive ones.     

Modeling hourly and daily fractions of UV,PAR and NIR to global solar radiation under various sky conditions at Botucatu,Brazil

In this analysis, using available hourly and daily radiometric data performed at Botucatu, Brazil, several empirical models relating ultraviolet (UV), photosynthetically active (PAR) and near infrared (NIR) solar global components with solar global radiation (G) are established. These models are developed and discussed through clearness index _KT$K_{\text{T}}$ (ratio of the global-to-extraterrestrial solar radiation). Results obtained reveal that the proposed empirical models predict hourly and daily values accurately. Finally, the overall analysis carried out demonstrates that the sky conditions are more important in developing correlation models between the UV component and the global solar radiation. The linear regression models derived to estimate PAR and NIR components may be obtained without sky condition considerations within a maximum variation of 8%. In the case of UV, not taking into consideration the sky condition may cause a discrepancy of up to 18% for hourly values and 15% for daily values.     

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.     

A multivariate qualitative model for the prediction of daily global radiation from three hourly global radiation values

A new model for the prediction of daily global radiation using three hourly radiation values is proposed. This model is obtained by multivariate regression analysis. The hourly clearness index and various qualitative variables are used as independent variables. The hourly values are obtained from net ground measures of hourly global radiation corresponding to the hours in which Meteosat secondary images are available over Europe. The qualitative variables allow us to include additional non-numerical information, specifically, the season of the year. The proposed model is the same for all the locations analysed. This model can be used for the prediction of daily global radiation based on hourly global radiation data obtained from satellite images.     

A model for the diffuse fraction of hourly global radiation

Hourly values of diffuse and beam irradiance are often required in cases where, at best, only global irradiance is available. For use in the evaluation of the climatological potential for solar energy utilization in Norway, an analytical model is proposed expressing the hourly diffuse fraction of global irradiance in terms of hourly solar elevation and clearness index. This model, developed for average snow-free close to sea level conditions in Norway, fairly well fits the average picture of an extensive independent data base.     

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.     

Comparative study of various correlations in estimating hourly diffuse fraction of global solar radiation

Proper design and performance predictions of solar energy systems require accurate information on the availability of solar radiation. The diffuse-to-global solar radiation correlation, originally developed by Liu and Jordan, has been extensively used as the technique providing accurate results, although it is latitude dependent. Thus, in the present study, empirical correlations of this type were developed to establish a relationship between the hourly diffuse fraction (k_d) and the hourly clearness index (k_t) using hourly global and diffuse irradiation measurements on a horizontal surface performed at Athalassa, Cyprus. The proposed correlations were compared against 10 models available in the literature in terms of the widely used statistical indicators, rmse, mbe and t test. From this analysis, it can be concluded that the proposed yearly correlation predicts diffuse values accurately, whereas all candidate models examined appear to be location-independent for diffuse irradiation predictions.     

基于GA-BP神经网络的逐时总辐射分组模型研究

通过分析影响太阳辐射的主要因素,提出以太阳高度角、季节和天气（晴空指数）作为数据划分依据的分组模型建立方法。以拉萨和西安地区的逐时气象数据和辐射数据为例,基于遗传算法（genetic algorithm,GA）优化的BP神经网络,建立太阳高度角、季节和天气类型的逐时总辐射分组模型。该研究揭示分组模型误差变化的规律,并将其估算误差与AllData模型比较。结果显示,相较于AllData模型,分组模型的估算误差均有降低。其中,天气分组模型误差最小,且西安的天气分组模型结果优于拉萨。西安天气分组模型平均绝对百分比误差（MAPE）和相对均方根误差（rRMSE）相较AllData模型结果分别下降3.96%和4.18%。研究结果表明分组模型能够降低逐时总辐射估算误差,可为估算逐时总辐射提供方法借鉴。     

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%.     

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.     

Dependence on cloudiness and solar altitude of global solar radiation received at 315 and 545 nm on horizontal surfaces

The study of monthly mean half hourly values of global radiation received at 315 (u.v.) and 545 nm (green) on a horizontal surface at Uccle (Belgium) in 1980 for clear (half hourly sunshine fraction σ = 1) and overcast (σ = 0) skies shows that for any solar altitude, global radiation received at 315 nm is less absorbed by clouds than radiation received at 545 nm. An explanation is given of the dependence on solar altitude for clear skies of the ratio between monthly mean half hourly values of global radiation received at both wavelengths, based on considerations concerning the direct and diffuse components.     

Estimating surface solar radiation from upper-air humidity

A numerical model is developed to estimate global solar irradiance from upper-air humidity. In this model, solar radiation under clear skies is calculated through a simple model with radiation-damping processes under consideration. A sky clearness indicator is parameterized from relative humidity profiles within three atmospheric sublayers, and the indicator is used to connect global solar radiation under clear skies and that under cloudy skies. Model inter-comparisons at 18 sites in Japan suggest (1) global solar radiation strongly depends on the sky clearness indicator, (2) the new model generally gives better estimation to hourly-mean solar irradiance than the other three methods used in numerical weather predictions, and (3) the new model may be applied to estimate long-term solar radiation. In addition, a study at one site in the Tibetan Plateau shows vigorous convective activities in the region may cause some uncertainties to radiation estimations due to the small-scale and short life of convective systems.