Survey of the incident solar radiation in Brazil by use of meteosat satellite data

Meteosat-2 satellite data in the visible band were used to calculate monthly averages from daily mean incident solar radiation over Brazil, using the IGMK physical model for the period 1985–1986. Satellite estimates are compared with ground data from 22 national stations. The global root mean square error between model and ground results for all data points was 13%, and the mean bias error was 1.23 MJ m⁻². About 68% of the individual errors were below 10% and clustered around 8%. Global radiation estimated by the model ranged from 9.0 to 27 MJ m⁻² with the diffuse to global ratio falling into the 0.2–0.5 interval. Enhanced inverted zonal trends were found for both satellite predictions and the ground station results.     

Solar radiation on tilted south oriented surfaces: validation of transfer-models

Three transfer-models in use for estimating solar radiation on tilted surfaces are tested. A 12 year series of hourly global, diffuse, and reflected solar irradiation measured with horizontal pyranometers as well as hourly global solar irradiation measured with tilted south oriented pyranometers is available. One model uses daily irradiation, the other two use hourly irradiation. The models converting hourly solar irradiation on a horizontal surface to a tilted surface yield better results than that using daily irradiation. The best results are gained if pairs of hourly global and diffuse solar irradiation are available. The root mean square errors exceed 10% only if the sky is covered by more than 85% with clouds or if the solar elevation angle is less than 10°.     

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.     

Estimation of hourly solar radiation for India

The ASHRAE constants predict high values of the hourly beam radiation and very low values of the hourly diffuse radiation when used to predict radiation at Indian locations. Hence a procedure has been developed for the estimation of direct, diffuse and global hourly solar radiation on a horizontal surface for any location in India. To calculate hourly solar radiation, an exponential curve, similar to the one used by ASHRAE, was fitted to the measured solar radiation data of six cities from different regions of India. The statistical analysis was carried out for the data computed using ASHRAE constants and the set of constants obtained for India using the measured data of four different Indian cities selected randomly. Three statistical indicators were used to compare the accuracy of the developed procedure. The results show that ASHRAE constants are not suitable to estimate hourly solar radiation in India. Hourly solar radiation estimated by constants obtained for India are fairly comparable with measured data. The mean percentage error with Indian constants for these four Indian cities was found as low as 2.27, −6.29 and −6.09% for hourly beam, diffuse and global radiation, respectively.     

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.     

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.     

Global solar radiation in Northeastern Saudi Arabia

This paper presents the actual global solar radiation on a horizontal surface along with the prevailing meteorological conditions encountered during the measurement period from 1 January–31 December, for one complete year, in the Arabian Gulf Coast near the city of Dhahran. High resolution, real time solar radiation and meteorological data were collected, and processed. Hourly, daily, and monthly statistics of solar radiation was made from the one-minute averaged recorded values. The highest measured daily, and monthly mean solar radiation were found to be 351 and 328 W/m⁻², respectively. The highest one-minute averaged solar radiation values up to 1183 W/m⁻² were observed in the summer season, from May–September. The highest hourly solar radiation value was recorded as 1053 W/m⁻² in the middle of June. Beside the global solar radiation measurements, the main observed meteorological parameters were temperature, pressure, wind speed, precipitation, and relative humidity. On the other hand, the estimation of daily and monthly mean global solar radiation was performed based upon two empirical formulas which relate the solar radiation to the sunshine duration, relative humidity, maximum temperature, the latitude of the monitoring location, sunset hour and declination angles. The agreement between the measured and estimated solar radiation values was found to be satisfactory. Nevertheless, the empirical formula under-estimates the solar radiation values during summer, and over-estimates during winter.     

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.     

Solar radiation data for Quebec

Calculated values of solar radiation are presented for five Quebec sites in the form of tables giving for each month the average and extreme values of total radiation on a horizontal surface. These results are a summary of hourly values calculated from cloud observations for periods of 3–5 yr. Comparisons with measured values at Montreal show good agreement for hourly, daily and monthly radiation.     

Models of diffuse solar radiation

For some locations both global and diffuse solar radiation are measured. However, for many locations, only global is measured, or inferred from satellite data. For modelling solar energy applications, the amount of radiation on a tilted surface is needed. Since only the direct component on a tilted surface can be calculated from trigonometry, we need to have diffuse on the horizontal available. There are regression relationships for estimating the diffuse on a tilted surface from diffuse on the horizontal. Models for estimating the diffuse radiation on the horizontal from horizontal global that have been developed in Europe or North America have proved to be inadequate for Australia [Spencer JW. A comparison of methods for estimating hourly diffuse solar radiation from global solar radiation. Sol Energy 1982; 29(1): 19–32]. Boland et al. [Modelling the diffuse fraction of global solar radiation on a horizontal surface. Environmetrics 2001; 12: 103–16] developed a validated model for Australian conditions. We detail our recent advances in developing the theoretical framework for the approach reported therein, particularly the use of the logistic function instead of piecewise linear or simple nonlinear functions.Additionally, we have also constructed a method, using quadratic programming, for identifying values that are likely to be erroneous. This allows us to eliminate outliers in diffuse radiation values, the data most prone to errors in measurement.     

Solar radiation over Saudi Arabia and comparisons with empirical models

We present a comparison between models developed by the present authors and 16 other models for different geographical and varied meteorological conditions. The comparisons are made using the mean bias error (MBE), root mean square error (RMSE), mean percentage error (MPE), and mean absolute bias error (MABE). These errors are calculated using monthly-mean, measured daily and estimated values of total solar radiation for 41 locations in Saudi Arabia. We find that our latitude, longitude, altitude, and sunshine-duration-dependent model given in Eq. (1)produced the best estimates for global solar radiation. The second- and third-best estimates were obtained from our linear model and other models given in Eq. (2)and Eq. (11), respectively.     

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.     

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。     

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 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.     

Simulation and modeling of solar radiation in Saudi Arabia

A mathematical model is used to generate the hourly data for the total solar radiation on a horizontal surface. The generated data are based on the hourly recorded visibility data for 20 years (1970–1989). The model year technique was then applied to model the 20 years of hourly data of solar radiation into one statistically representative year. A model year of hourly data was then generated for the beam and diffuse components of solar radiation on a horizontal surface. Similarly, a model year of hourly data was also generated for the total solar radiation on tilted surfaces with different orientations with its beam, diffuse and reflected components. A simple methodology is proposed for calculating the solar radiation on vertical surfaces, based on a solar impact factor (SIF). Monthly means and daily totals of hourly sums for each month of the year are discussed. The hourly data of solar radiation for a typical day for each month of the year are presented. The data were generated for the four climatic zones of Saudi Arabia, the hot-dry (Riyadh), the warm-humid (Jeddah), the maritime inland desert climate (Dhahran) and the upland climate zone (Taif). The accuracy of the results is discussed and found to be above 90% representative.     

Correlations for estimation of daily global solar radiation with hours of bright sunshine in Turkey

In this study, seven different empirical equations are employed to estimate the monthly average daily global solar radiation on a horizontal surface for provinces in the different regions of Turkey, using only the relative duration of sunshine. Daily global solar radiation and sunshine measurement data collected for the provinces of Turkey are obtained from the Turkish State Meteorological Service. The regression constants of the new models developed in this study are found for the provinces of Turkey, as well as that of some models given in the literature. In order to indicate the performance of the models, the statistical test methods of the mean bias error (MBE), mean absolute bias error (MABE), mean relative error (MRE), root mean square error (RMSE) and correlation coefficient (r) are used.     

Estimation of global solar radiation on horizontal surfaces in Jeddah, Saudi Arabia

The measured data of global solar radiation on a horizontal surface, as well as the number of sunshine hours, mean daily ambient temperature, maximum and minimum ambient temperatures, relative humidity and amount of cloud cover, for Jeddah (latitude 21° 42′37″N, longitude 39° 11′12″E), Saudi Arabia for the period 1996–2006 are analyzed. The data are divided into two sets. The sub-data set 1 (1996–2004) are employed to develop empirical correlations between the monthly average of daily global solar radiation fraction (H/H₀) and various meteorological parameters. The nonlinear Angström type model developed by Sen and the trigonometric function model proposed by Bulut and Büyükalaca are also evaluated. New empirical constants for these two models have been obtained for Jeddah. The sub-data set 2 (2005, 2006) are then used to evaluate the derived correlations. Comparisons between measured and calculated values of H have been performed. It is indicated that, the Sen and Bulut and Büyükalaca models satisfactorily describe the horizontal global solar radiation for Jeddah. All the proposed correlations are found to be able to predict the annual average of daily global solar radiation with excellent accuracy. Therefore, the long term performance of solar energy devices can be estimated.     

Solar radiation for Shiraz, Iran: a comparative study for two periods

Instantaneous solar radiation data read from the chart of global solar radiation on a horizontal surface as well as sunshine hours in Shiraz during two periods (1980–1983 and 1988–1990) are analysed and compared with solar conditions in the early 1970s. It is apparent from the recorded data and subsequent analysis that while this area still possesses a relatively high abundance of sunshine, there has been a gradual decay in clearness index. Frequency of clear sky days, the average daily irradiation and the mean cumulative annual irradiation for the two periods under study are presented and a decrease in solar radiation received on a horizontal surface due to down grading of Shiraz from the clear sky conditions enjoyed in the 1960s and 1970s is demonstrated.     

Prediction of direct and global solar irradiance using broadband models: Validation of REST model

In the present paper, three parametric models Yang, CPCR2 and REST (without considering transmittance due to nitrogen dioxide) have been analyzed for four Indian stations, namely New Delhi, Mumbai, Pune and Jaipur over the period of 1995–2002, under cloudless conditions. These stations have different climatic conditions. The beam radiation at normal incidence as well as global solar radiation at horizontal surface was computed for these locations during all seasons except monsoon (June to September). The computed values of beam and global irradiance was compared with reference values in case of beam and measured values in case of global solar radiation on the basis of percentage root mean square error (RMSE) and mean bias error (MBE). The maximum RMSE is 6.5% in REST model, as compare to 15% in Yang and 11% in CPCR2 model for predicting direct normal irradiance. The predicted global radiation at horizontal is showing maximum RMSE 7% in REST model, 13.4% in Yang and 25.9% in CPCR2 model. This shows that REST model has good agreement with measured data for these Indian stations as compare to other two models.