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.     

The solar radiation climate of Thailand

Geographical, seasonal, and diurnal variations of global solar radiation in Thailand are surveyed. Seasonal effects are shown by separate studies for eight 1.5 month periods of the year defined by standard solar declination values. Detailed maps are given of the geographical distribution of solar radiation prepared from data on cloudiness at 44 stations, duration of sunshine at 18 stations, and linear regressions relating radiation to sunshine at Chiang Mai and Bangkok. The highest mean values are above 19.5 MJ m⁻² d⁻¹ and are widespread in spring. The lowest values are below 15.0 MJ m⁻² d⁻¹ in restricted localities with heavy rainfall in autumn.Rough estimates of diffuse solar radiation and atmospheric turbidity are made from the radiation-sunshine regression parameters. Diffuse radiation averages 8.4 MJ m⁻² d⁻¹. Turbidity at Chiang Mai is high in spring and low in summer and autumn; at Bangkok it is high throughout the year.The diurnal variation of global solar radiation determined from hourly measurements at Chiang Mai and Bangkok is analysed. The mean midday radiation fluxes range from 0.80 kW m⁻² in spring to 0.60 kW m⁻² in autumn. On the average the radiation received in the afternoon is slightly less than that received in the morning.     

Estimation of monthly Angström–Prescott equation coefficients from measured daily data in Toledo, Spain

In this study, daily global radiation for Toledo (39°53′05″N, 4°02′58″W, Spain) were utilized to determine monthly-specific equations for estimating global solar radiation from sunshine hours and to obtain improved fits to monthly Angström–Prescott's coefficients.Models were compared using the root mean square error (RMSE), the mean bias error (MBE) and the t-statistic. According to our results, all the models fitted the data adequately and can be used to estimate the specific monthly global solar radiation.Average RMSE and MBE for comparison between observed and estimated global radiation were 1.260 and −0.002 MJ m⁻² day⁻¹, respectively. The t-statistic was used as the best indicator, this indicator depends on both, and is more effective for determining the model performance. The agreement between the estimated and the measured data were remarkable and the method was recommended for use in Toledo (Spain).     

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.     

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.     

Investigation of solar radiation in Botswana and some anomalous phenomena observed

Daily global insolation on a horizontal surface in Botswana is recorded continuously at several synoptic stations and at the University of Botswana's Physics Department. Over a number of years, daily total insolation on a tilted surface (β = −30°) was recorded at the Botswana Technology Centre. Hourly, and instantaneous direct normal, global, diffuse and UV-components are continuously recorded at the University of Botswana. All these measurements are done with standard EPLAB equipment.It is found out that the instantaneous direct normal radiation at Solar noon can be as high as 1150 W·m⁻²; and that at 30 min before sunset it can be above 600 W·m⁻²; and it can also be as high as 100 W·m⁻² at sunset or sunrise moments (i.e. with half of the solar disk under the horizon).Daily direct normal solar radiation can exceed 45 MJ·m⁻². Mean daily global radiation varies from 31 MJ·m⁻² in December to 16 MJ·m⁻² in June. Such big values of daily direct normal and global radiation are explained by low humidity and low turbidity.Cases of an anomalous phenomenon which lead to an abnormally big phase shift when direct normal radiation is increasing greatly after Solar noon are observed, and discussed. It is also found that when humidity is low and visibility is high, hourly I_g values recorded with a pyranometer can be less than I_bn (cosθ_z) + I_d-values. This discrepancy could be quite common for regions where humidity and turbidity are low. The trend in the behaviour of the UV-component during the last five years is also analyzed and discussed. The conclusion is made that the ozone layer over Botswana is continuously being depleted.     

Some aspects of solar radiation climatology of Iraq

Study of the climatology of global solar radiation is considered very useful for assessing the potential efficiency of systems designed for solar energy utilization. This paper explores some aspects of solar radiation climatology in Iraq. Analysis of the monthly averages global solar radiation and the general atmospheric transparency for the period 1971–1985 for three different climatological zones (Mosul, Baghdad, Nasiriyah) are discussed. The frequency distribution of daily clearness index for each station is determined using histograms of frequencies. The percentage number of days with solar radiation and sunshine duration values below a certain value is analyzed and discussed. The period of successive days having radiation less than 5 MJ/m² · day⁻¹ and 10 MJ/m² · day⁻¹ is examined and presented graphically.     

Contribution to the study of solar radiation in Burgos, Spain

A series of daily measurements of global solar radiation on horizontal surface realized during the period 1978–1982, in Burgos, Spain, is analysed. The mean decadic values show fluctuations, in the spring and at the beginning of the summer especially. The absolute maximums generally appear in July with values that oscillate between 23 and 26 MJ m⁻², and the minimums in January or December with values between 4 and 5 MJ m⁻². Averaging the analogous months we obtain the maximums in July with a value of 23 MJ m⁻². We have studied the elemental statistic characteristics and we remark that the interquartile range is small in the winter months and increases in the spring and summer. The number of the days in which the radiation has remained inferior to a given value, has been calculated in the frequency analysis, remarking that in the days corresponding to the period of the winter appear radiation values inferior to 10 MJ m⁻² and only 3% of July days are below this value. We have defined and determined the potential radiation and have calculated the extraterrestrial radiation in order to know the attenuation of global radiation in its passage through the atmosphere. We remark that the energy percentage transmitted by the atmosphere increases from winter to summer, a maximum value of 59% is obtained in July and a minimum of 30% in December. The atmospheric transparency without clouds oscillates between 71% in the spring and 62% in the winter.     

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.     

Effects of grain boundaries in polycrystalline silicon thin-film solar cells based on the two-dimensional model

The two-dimensional calculation for polycrystalline Si thin-film solar cells was performed. Two models, “stripe structure” and “columnar structure”, were applied for the solar cells composed of grains. For the stripe structure of 20 μm active layer, to keep the efficiency distribution within 5% for individual unit cells, the stripe width requires more than 500 μm for a minority-carrier lifetime of 1×10⁻⁵ s and recombination velocity at the grain boundary of 1×10⁴ cm/s. For the columnar structure of 10 μm active layer, to keep the efficiency independent of grain size, the recombination velocity should be kept less than 1×10³ cm/s. If imperfect passivation of a grain boundary is given, the way of decreasing carrier concentration to 10¹⁴ cm⁻³ in an active layer may realize insusceptible output. An appropriate device modeling is needed in the two-dimensional calculation for polycrystalline Si thin films with an electron diffusion length close to or more than grain size and with a poorly passivated grain boundary. The calculated efficiency using bad model will include an error of about 1% as overestimation.     

Preliminary results of a V-groove back-pass solar collector

The study conducted by the Solar Energy Research Group, Universiti Kebangsaan Malaysia shows that solar energy has a great potential to be used in drying processes. A prototype solar drying system was designed and tested in the campus (Othman et. al, 1994). The study shows that the system can be upgraded by improving the solar collector. This paper presents the preliminary result on the performance of the V-groove back-pass solar collector modified from V-groove double flow solar collector designed earlier (Othman et. al, 1992). The results shows that the collector maintained the output temperature eventhough there are changes of solar radiation intensity. At 0.65 ms⁻¹ air flow rate, the output temperature of the collector can manage to maintain 40°C in the range of solar intensity of 800 Wm⁻² to 300 Wm⁻² within 15 minutes time interval, and at 0.45 ms⁻¹, the output temperature is 43°C in the range of solar intensity of 800 Wm⁻² to 600 Wm⁻². The min daily efficiency of 20% is recorded at 450 Wm⁻² of min daily solar radiation at 0.65 ms⁻¹ flow rate. At 0.45 ms⁻¹ flow rate with the equal amount of daily min solar radiation the min daily efficiency is 13%. The result is expected to be better if the study is conducted in May - June when the weather is better.     

Estimating monthly mean valuesof daily total solar radiation for Australia

Monthly mean values of daily total solar radiation were obtained for the widest possible network acrossAustralia. Bureau of Meteorology sources yielded 11 stations with long term records of both measured daily total solar radiation and sunshine hour values. Monthly modified Angstrom equations were developed from these data and used to estimate radiation values for a further 90 stations in the Bureau of Meteorology network that had sunshine hour data. Measured daily total solar radiation data were obtained from a variety of sources mostly outside the Bureau of Meteorology network for an additional 33 stations. Finally, estimates of solar radiation from detailed cloud cover data were used for a further 12 stations, selected because they filled in significant gaps in coverage. These various sources yielded a total of 146 sets of monthly mean values of daily total solar radiation. For each month optimal surfaces, which were functions of position only, were fitted to this network of values using Laplacian smoothing splines with generalized cross validation. Residuals from the fitted surfaces at the data points were acceptably low. Fitted surfaces which included, in addition to position variables, a cloudiness index based on a transform of mean monthly precipitation further reduced these residuals. The latter fitted surfaces permit estimation of monthly mean values of total daily solar radiation at any point on the continent with a root mean square predictive error of no more than 1.25 MJ m⁻² day⁻¹ (5.2 per cent of the network mean) in summer and 0.74 MJ m⁻² day⁻¹ (5.5 per cent of the network mean) in winter.     

First solar radiation atlas for the Arab world

In the year 1998, the Arab League Educational, Cultural and Scientific Organization (ALESCO), Directorate of Science and Scientific Research, Tunis, had launched the “Solar Radiation Atlas for the Arab World”. This atlas contains three sets of maps (using Mercator projection) for monthly means, where each stands for one month. These are sunshine duration, global solar radiation and diffuse solar radiation. The atlas contains data for nearly 280 stations from 19 Arab states which cover latitudes from 0° (tropic) to 37°N and longitudes 19°E to nearly 60°E with different elevations from the sea level. It also contains useful tables of the monthly recorded means of the direct, diffuse and global solar radiation as well as the sunshine duration for 16 Arab states including 207 cities.The maximum recorded annual mean (10 years) of the global solar radiation in the Arab world was 6.7 kW h/m²/day in Nouakchott (latitude 20°56′N, longitude 17°02′E), Mauritania, and 6.6 kW h/m²/day in Tamenraset (latitude 36°11′N and longitude 5°31′E), Algeria, while the lowest recorded annual mean global solar radiation was 4.1 kW h/m²/day in Mosul (latitude 43°N and longitude 36°E), Iraq. Furthermore, the maximum recorded annual mean sunshine duration in the Arab world was 10.7 h in Aswan (latitude 23°58′N, longitude 32°47′E), Egypt, and the lowest was 7.5 h in Tunis (latitude 36°50′N, longitude 10°14′E), Tunisia.     

A comparison between one year of daily global irradiation from ground-based measurements versus METEOSAT images from seven locations in Tunisia

Three numerical images from METEOSAT B2 per day have been processed over a period of 12 months, from October 1985 to September 1986, to estimate the daily values of available solar radiation in Tunisia. The methodology used, GISTEL, on the images of the “visible” channel of METEOSAT, is described. Results are compared with measured radiation values from seven stations of the “Institut de la Météorologie de Tunisie.” Among more than 2200 measured-estimated daily pairs, a high percentage, 89%, show a relative error of + or −10%. Many figures concerning Sidi-Bou-Saïd, Kairouan, Thala, and Gafsa are presented to show the capability of GISTEL to map the daily available solar radiation with a sufficient spatial resolution in countries where radiation measurements are too scarce.     

Solar energy outside the Earth's atmosphere

Extensive measurements have been made in different countries and by many research groups to determine the solar constant and the spectral distribution of solar energy. Earlier determinations were made from ground-based observations. The extrapolation to zero air mass under the highly variable conditions of the atmosphere led to large uncertainties in the proposed values.In recent years renewed interest in this topic has arisen due to the direct effect of solar radiation on thermal balance of spacecraft, electrical output of solar panels, and other satellite-related problems. Measurements of the solar constant have been made by total irradiance detectors from high altitude research aircraft, balloons, and space probes. Their data have produced converging evidence that the value of the solar constant commonly accepted in earlier years, 2·00 cal cm⁻² min⁻¹, was too high.Spectral irradiance measurements at high altitude were made using a variety of monochromators and filter radiometers. The results of all recent high altitude measurements have been critically examined by an ad hoc committee on “Solar Electromagnetic Radiation.” The committee has proposed standard values for engineering use for the solar constant and the solar spectrum. These values will be presented and also the reasons for recommending their acceptance. Detailed comparisons have been made between the revised spectral irradiance values and those which had been widely accepted in earlier years. New values have been computed for frequently-cited astrophysical quantities which are derived from the solar constant and the solar spectrum. The spectrum has been extended to 10A in the X-ray range and to 10 m in the microwave range. The revised value of the solar constant is 1·94 cal cm⁻² min⁻¹. The proposed standard solar spectrum shows significant differences from other curves throughout the spectral range.     

Global solar radiation measurements in Maceió, Brazil

This work focuses on the variability of the global solar radiation over the area of Maceió (9°40′S, 35°42′W, 127 m), located in Northeastern State of Alagoas, Brazil, during the1997–1999 period. Solar radiation variability was evaluated on 5 min, hourly, daily, monthly and seasonal scales. The results showed that the maximum values of the hourly global solar irradiation, , in the dry (September–February) and rainy (March–August) seasons were 3.18 and 2.50 MJ m⁻², respectively. The peaks of the hourly average, , for both periods were 2.79 MJ m⁻² and the daily average of the global solar irradiation, , was 19.89 MJ m⁻². The daily clearness index, , was found to be 0.53 (rainy period) and 0.59 (dry period). In clear, partially cloudy (the most frequent) and overcast days, the daily averages of global solar irradiation were 25.20, 19.00 and 8.00 MJ m⁻², respectively. On an annual scale the global solar irradiation changed from 15.00 MJ m⁻² by August to 24.04 MJ m⁻² by November.     

Performance analysis of non-isothermal solar reactors for methanol decomposition

A procedure for analyzing the performance of non-isothermal solar reactors for methanol decomposition was developed, based on a model of thermal loss from direct steam generation collector and a comprehensive kinetic model of methanol decomposition employing BASF K3-110 catalyst. It was found that catalytic bed temperature tends towards a certain value, which depends on the chemical reaction type, radiation intensity and collector structure mainly. For a beam incidence angle of 0°, system efficiency increases from 56% at a radiation intensity of 400 W m⁻² to almost 58% at a radiation intensity of 1000 W m⁻². For a radiation intensity of 400 W m⁻², beam incidence angle of 20°, absorber length of 10 m, feed temperature of 373 K and ratio of reaction section of 0.9, the mole flow rate of feed in the range of 0.21–0.23 mol s⁻¹ results in a maximum quantity of reacted methanol of 0.146 mol s⁻¹, while a mole flow rate of feed of 0.15 mol s⁻¹ leads to a maximum system efficiency of 54.2%. The research indicates that the pre-heating section should be as short as possible for effective use of solar energy.     

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.     

Luminous efficacy models and their application for calculation of photosynthetically active radiation

From a spectral radiative transfer model, an algorithm is developed for the conversion of illuminance to different measures of Photosynthetically Active Radiation (PAR) (in W m⁻² or in μEm⁻²s⁻¹). This illuminance to PAR conversion may even be used in combination with a luminous efficacy model and, thus, form a photosynthetic efficacy model. In this work, two luminous efficacy models are chosen, one empirical and one derived from the above radiative transfer model. Observed PAR energy flux and PAR photon flux from seven Nordic stations (56–70°N) and illuminance from one U.S. station (43°N) are, together with observed all-wave solar irradiance from all stations, used for verification.Observed and modelled luminous efficacies agree on the average within 1% at high solar elevation under cloudless sky, while it is indicated that the illuminance, PAR energy flux, and PAR photon flux radiometers are mutually inconsistent by some 6–16%. Even differences in cosine response between radiometer types are apparent at low solar elevation under cloudless sky. In the present climates, the global radiation efficacy is 10–12% higher under an average cloudless atmosphere than it is outside the atmosphere. By introducing an average cloud deck in this cloudless atmosphere, a further efficacy increase, slightly exceeding these 10–12%, is observed. However, observations indicate that the cloud transmittance algorithm used in the radiative transfer model significantly overestimates the global radiation efficacy increase caused by horizontally inhomogeneous cloud decks.     

A study of solar ultraviolet radiation at Makkah solar station

Analysis of solar ultraviolet radiation (295–385 nm) and total global radiation (290–3000 nm), continuously recorded at a station in Makkah (21.5°N, 39.8°E) for 17 months in 1987–1988, has shown that the monthly average daily UV was 200 Wh m⁻². The ratio of UV to total global radiation varied from a maximum of 0.043 to a minimum of 0.028. A drop of 25% below the average 0.036, detected in the summer months, is attributed to scattering and absorption by dust and low tropospheric ozone. Comparison with Dhahran and Kuwait has shown that the effect was localised. A study of diurnal variation and clear, midday hourly radiation and the ratio of UV to global radiation, , also revealed an overall depletion in the summer months, despite the relative decrease in attenuation of Iv during cloudy days and at low solar altitudes. Multiple regressions of Hv and Iv on relevant variables with coefficients of determination exceeding 90% have been performed. Frequency distribution of daily UV is briefly discussed.