Estimation of global solar radiation in arid and semi-arid climates of East and West Iran

In Iran, most of the models used so far, have provided solar estimation for a few specific locations based on the short-term solar observations. Using different radiation models, (e.g. Sabbagh, Paltridge–Proctor, Daneshyar) and various input parameters (e.g. cloud cover, sunshine duration, relative humidity, temperature, and altitude) we developed a general height-depended formula for the prediction of the direct and diffuse monthly average daily solar radiation for 64 mountainous arid and semi-arid locations in West and East Iran. The models mentioned are modified and new coefficients are defined for the diffuse component based on the long-term observed diffuse data. Model results are validated against up to 13-year daily solar observations at 10 solar radiation sites. In comparison with the previous studies, the newly developed method performs more accurate estimation (less than 3% MPE error) in the arid and semi-arid regions. Comparison of the model results indicates that calibration of the coefficients made to the diffuse formula against the longer period experimental data can improve the estimations of global solar radiation.     

A simplified model for generating sequences of global solar radiation data for isolated sites: Using artificial neural network and a library of Markov transition matrices approach

The purpose of this work is to develop a hybrid model which will be used to predict the daily global solar radiation data by combining between an artificial neural network (ANN) and a library of Markov transition matrices (MTM) approach. Developed model can generate a sequence of global solar radiation data using a minimum of input data (latitude, longitude and altitude), especially in isolated sites. A data base of daily global solar radiation data has been collected from 60 meteorological stations in Algeria during 1991–2000. Also a typical meteorological year (TMY) has been built from this database. Firstly, a neural network block has been trained based on 60 known monthly solar radiation data from the TMY. In this way, the network was trained to accept and even handle a number of unusual cases. The neural network can generate the monthly solar radiation data. Secondly, these data have been divided by corresponding extraterrestrial value in order to obtain the monthly clearness index values. Based on these monthly clearness indexes and using a library of MTM block we can generate the sequences of daily clearness indexes. Known data were subsequently used to investigate the accuracy of the prediction. Furthermore, the unknown validation data set produced very accurate prediction; with an RMSE error not exceeding 8% between the measured and predicted data. A correlation coefficient ranging from 90% and 92% have been obtained; also this model has been compared to the traditional models AR, ARMA, Markov chain, MTM and measured data. Results obtained indicate that the proposed model can successfully be used for the estimation of the daily solar radiation data for any locations in Algeria by using as input the altitude, the longitude, and the latitude. Also, the model can be generalized for any location in the world. An application of sizing PV systems in isolated sites has been applied in order to confirm the validity of this model.     

Estimating direct, diffuse, and global solar radiation for various cities in Iran by two methods and their comparison with the measured data

Two computational methods for calculating hourly, daily, and monthly average values of direct, diffuse, and global solar radiation on horizontal collectors have been presented in this article for location with different latitude, altitude, and atmospheric conditions in Iran. These methods were developed using two different independent sets of measured data from the Iranian Meteorological Organization (IMO) for two cities in Iran (Tehran and Isfahan) during 14 years of measurement for Tehran and 4 years of measurement for Isfahan. Comparison of calculated monthly average global solar radiation, using the two models for Tehran and Isfahan with measured data from the IMO, has indicated a good agreement between them. Then these developed methods were extended to another location (city of Bandar-Abbas), where measured data are not available. But the work of Daneshyar [1] predicts its monthly global radiation. The maximum discrepancy of 7% between the developed models and the work of Daneshyar [1] was observed.     

Empirical model development and comparison with existing correlations

This study utilized monthly mean daily values of global solar-radiation and sunshine duration at 41 locations in Saudi Arabia and developed an empirical correlation for the estimation of global solar radiation at locations where it is not measured. The paper also presents the comparison between the present correlation and other models developed under different geographical and varied meteorological conditions. The comparisons are made using standard statistical tests, namely mean bias error (MBE), root mean square error (RMSE), mean percentage error (MPE), and mean absolute bias error (MABE) tests. The errors are calculated using monthly mean daily measured and estimated values of global solar radiation at all 41 locations. The study found that the present correlation produced the best estimates of global solar radiation.     

Monthly average daily global solar radiation in P.D.R. Yemen

In this paper a study has been made to estimate average global radiation using hours of bright sunshine and measured solar radiation data available for six locations in P.D.R. Yemen. For Aden, data were obtained from Aden Airport. For other locations in P.D.R. Yemen data were obtained from Agricultural Research Center's meteorological sections. Linear regression analysis of the monthly average global radiation and the sunshine duration data of six locations has been performed using the least squares technique. All the above mentioned data have been used in Ångström's correlation to find the monthly average daily global solar radiation. Results obtained are useful for any solar energy system application in P.D.R. Yemen.     

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.     

Statistical comparison of solar radiation correlations Monthly average global and diffuse radiation on horizontal surfaces

For most solar energy applications, it is necessary to predict the amount of global and diffuse radiation arriving on a horizontal surface at any specified location. Scientists have developed methods to achieve this using different input parameters. The purpose of this study is to compare statistically correlations for estimating the monthly average daily global/diffuse radiation incident on a horizontal surface and to recommend one in each catagory that best fits measured data from a number of locations chosen and is the simplest to use. The effects of using the new solar constant of 1367 W⁻² in these correlations are also investigated. As a result, Rietveld's and Page's correlations are recommended for estimating monthly average daily global and diffuse radiation incident on a horizontal surface, respectively. In addition, these correlations seem to be just as accurate with the new solar constant.     

Assessment of diffuse solar energy under general sky condition using artificial neural network

In this paper, artificial neural network (ANN) models are developed for estimating monthly mean hourly and daily diffuse solar radiation. Solar radiation data from 10 Indian stations, having different climatic conditions, all over India have been used for training and testing the ANN model. The coefficient of determination (R²) for all the stations are higher than 0.85, indicating strong correlation between diffuse solar radiation and selected input parameters. The feedforward back-propagation algorithm is used in this analysis. Results of ANN models have been compared with the measured data on the basis of percentage root-mean-square error (RMSE) and mean bias error (MBE). It is found that maximum value of RMSE in ANN model is 8.8% (Vishakhapatnam, September) in the prediction of hourly diffuse solar radiation. However, for other stations same error is less than 5.1%. The computation of monthly mean daily diffuse solar radiation is also carried out and the results so obtained have been compared with those of other empirical models. The ANN model shows the maximum RMSE of 4.5% for daily diffuse radiation, while for other empirical models the same error is 37.4%. This shows that ANN model is more accurate and versatile as compared to other models to predict hourly and daily diffuse solar radiation.     

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%.     

Generation of operational maps of global solar irradiation on horizontal plan and of direct normal irradiation from Meteosat imagery by using SOLARMET

The physical model SOLARMET, elaborated in ENEA (Italian National Agency for New Technologies, Energy and Environment), provides hourly average global solar irradiance on a horizontal surface (GHi) and hourly average direct normal solar irradiance (DNi) for Italy based on primary satellite images in the visible band.

In the present study, the hourly estimates of surface radiation generated by SOLARMET have been summed up to produce monthly average daily irradiation maps. Hourly and monthly maps were done for the years 1996 and 2002. The parameters of this model were obtained by comparing the Meteosat satellite data with ground data gathered in 2002. Differences, relative to 1996, between SOLARMET estimates and observations obtained over two radiation networks of Italian ground sites are presented: the Meteorological Service of the Italian Air Force and National Agro-Meteorological Network; In total 51 ground stations. The comparison between SOLARMET and the previous Italian method carried out in ENEA shows an improvement due to SOLARMET. Such comparison between the values derived using SOLARMET and previous ENEA methodologies and with data from ground-based stations was possible only for monthly averages of daily global radiation due to an almost total lack of direct radiation ground data in Italy.

The operational monthly solar radiation maps, showing solar energy potentials, permit the selection of construction sites to solar energy project developers. In Italy, these data are necessary for installing solar thermal concentration power plants in support of the R&S program recently funded to demonstrate the possibility of these technologies.     

Methodology for generating daily clearness index index values Kt starting from the monthly average daily value . Determining the daily sequence using stochastic models

The facility to generate weather data from limited inputs and independently of specific locations would allow simulations of energetic systems to be run at locations for which detailed weather records do not exist. This article presents a methodology to calculate synthetic daily solar radiation values and describes how sequences of daily global radiation can be generated using as input the monthly average radiation. A stochastic model, ARIMA(1,1,1) is presented, as well.     

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.     

Characteristics of the monthly averaged hourly diffuse irradiance at Lagos and Zaria, Nigeria

An extensive study of characteristics of the monthly averaged hourly diffuse radiation has been carried out for the southern and coastal city of Lagos, latitude 6.58°N, and at Zaria, latitude 11.10°N, a northern city situated in the savannah belt. Correlations have been established for the prediction of the monthly averaged hourly diffuse fraction of the total irradiance reaching these locations. The inclusion of the solar elevation as an explanatory variable in the usual K-K_t correlation improved the correlation for Zaria using the root mean square error as a measure by 31.6%, while the correlation for Lagos was not improved by the inclusion of the solar elevation as a predictor. Comparison with five models from higher latitudes indicate that their use for the prediction of the diffuse solar irradiance at Nigerian locations will not give correct results. © 1999 Elsevier Science Ltd. All rights reserved.     

Climatological study of the adrano site of the eurelios solar mirror power plant

This article concerns the climatological characterization of the Adrano site, where is operating the EURELIOS solar mirror power plant. Meteorological characteristics such as climatic trend of air temperature, wind roses, average monthly values of global radiation, and insolation are presented. In particular, the percentage of solar radiation received at the site has been evaluated with respect to the extraterrestrial radiation and the average daily insolation at Adrano has been compared with that of a nearby station (Catania) for which statistical, long-term estimates exist.     

Empirical relations for the determination of solar radiation in Ibadan, Nigeria

Variations in the average monthly, seasonal and daily patterns of total radiation, relative humidity, temperature and sunshine duration in Ibadan have been presented. Various empirical models relating solar radiation to the basic climatological parameters such as relative humidity, sunshine hours, temperature as well as geographical declination, latitude and altitude factors were investigated from the viewpoint of obtaining appropriate empirical formulae to determine solar radiation from such common parameters. The average monthly total radiation is shown to be predicted with reasonable accuracy by a couple of empirical formulae with the best result obtained from a newly proposed formula. The new formula is shown to give also good agreement when applied to the analysis of annual daily insolation data on a seasonal basis. Finally, the proposed formula predicts a linear relationship between the daily diffuse radiation and the daily total radiation in line with the Liu and Jordan model but with the fiffuse component generally higher in qualitative agreement with observations in the tropics.     

Solar ponds—Corrections

Variations in the average monthly, seasonal and daily patterns of total radiation, relative humidity, temperature and sunshine duration in Ibadan have been presented. Various empirical models relating solar radiation to the basic climatological parameters such as relative humidity, sunshine hours, temperature as well as geographical declination, latitude and altitude factors were investigated from the viewpoint of obtaining appropriate empirical formulae to determine solar radiation from such common parameters. The average monthly total radiation is shown to be predicted with reasonable accuracy by a couple of empirical formulae with the best result obtained from a newly proposed formula. The new formula is shown to give also good agreement when applied to the analysis of annual daily insolation data on a seasonal basis. Finally, the proposed formula predicts a linear relationship between the daily diffuse radiation and the daily total radiation in line with the Liu and Jordan model but with the fiffuse component generally higher in qualitative agreement with observations in the tropics.     

Calculation of monthly average insolation on a shaded surface at any tilt and azimuth

Estimation of the monthly average solar radiation on surfaces of arbitrary orientation is necessary for many solar performance prediction programs and is useful for other applications. For passive solar applications, especially, overhangs are often used to seasonally modulate the amount of radiation striking the surface.

Liu and Jordan[1] have developed a method for estimation of monthly average radiation on unshaded tilted surfaces based on horizontal surface data. This method has been extended to unshaded surfaces of arbitrary tilt and azimuth by Klein[2]. Utzinger and Klein[3] have presented a graphical method for estimating monthly average radiation on shaded vertical surfaces, while Jones [4]has offered an analytical method for the same configuration. This paper presents an analytical solution to the calculation of monthly average insolation on shaded surfaces at any tilt and azimuth. Results are comparable among the three methods when shaded vertical surfaces are analyzed.

This analytical method offers an alternative to slower and less accurate numerical integration and to less general regression of numerical integration results for use in solar performance prediction programs.     

Modeling global solar radiation using Particle Swarm Optimization (PSO)

The quantity of solar radiation received by the earth’s surface is very important to numerous renewable energy applications. However, direct measurement of solar data is not widely available, especially in developing countries. This paper uses Particle Swarm Optimization (PSO) to train an artificial neural network (PSO–ANN) using data from available measurement stations to estimate monthly mean daily Global Solar Radiation (GSR) at locations where no measurement stations are available. The inputs to the networks are: month of the year, latitude, longitude, altitude, and sunshine duration, and the output is the monthly mean daily GSR at the specified location. Using training data from 31 stations and testing data from 10 locations, the PSO–ANN outperforms a neural network trained using the standard backpropagation (BP) algorithm (BP–ANN) with an average Mean Absolute Percentage Error (MAPE) of 8.85% for the PSO–ANN and 12.61% for the BP–ANN. The performance is improved significantly, when we use the leave-one-out method, where data from 40 locations is used for training and data from the 41st station is used for assessing the performance. In this case the average of MAPE on data from the 10 testing stations is about 7%. We used the same method to assess the performance of the PSO–ANN on testing data from each of the 41 stations with an overall average MAPE of about 10.3%. Comparison with BP–ANN and an empirical model showed the superiority of the PSO–ANN.     

Effect of sunshine and solar declination on the computation of monthly mean daily diffuse solar radiation

Several years of measured data for 17 European locations have been used to develop models for estimating monthly mean daily values of diffuse radiation (Hd) from combinations of the following: clearness index, sunshine fraction, and solar declination. Two models giving the highest correlation coefficients and the lowest standard errors of estimation are tested with data for 10 European locations not used in their development. From consideration of the MBE and RMSE values, a model which estimates Hd values from clearness index, relative sunshine duration and solar declination is found to be the most accurate. Comparison with Hd values predicted with the European Community solar radiation model (ECM) confirms this conclusion.     

Calculation of monthly average insolation on tilted surfaces

Several simplified design procedures for solar energy systems require monthly average meteorological data. Monthly average daily totals of the solar radiation incident on a horizontal surface are available. However, radiation data on tilted surfaces, required by the design procedures, are generally not available. A simple method of estimating the average daily radiation for each calendar month on surfaces facing directly towards the equator has been presented by Liu and Jordan [1]. This method is verified with experimental measurements and extended to allow calculation of monthly average radiation on surfaces of a wide range of orientations.