Solar irradiance on non-horizontal surfaces at the East-Mediterranean coastal plain of Israel

A large volume of global, diffuse and direct solar radiation observed at the National Radiation Center in Bet-Dagan (the East-Mediterranean coastal plain of Israel) has been analysed to evaluate the solar irradiance climatology on non-horizontal surfaces of various slope aspects and tilt angles. The isotropic approximation was used with respect to the diffuse sky radiation, as well as with regard to the reflected radiation from the ground. The feasibility of applying this approximation for the assessment of the insolation climate on non-horizontal surfaces is discussed. The monthly curves of daily total insolation on inclined surfaces were drawn, and their characteristic patterns for the various slope aspects and seasons are examined.     

Solar-desalination prospects for the sultanate of Oman

Climatic data (for the three years 1988–1990) have been surveyed for various locations in Oman and hence the prospects there for the solar desalination of water have been assessed. In particular, the behaviour of a solar still on Masirah Island (located at 20·67° N) has been predicted. The use of average monthly insolation data, measured for 3 years from 1988 to 1990, enabled the calculation of how much of this radiation is incident on the still's inclined transparent cover. Assuming (pessimistically) that only 50% of this transmitted radiation stimulates the evaporation process, the rate of distillate is predicted to be approximately 2 litres day⁻¹ m⁻² of the inclined cover.

A peculiar feature of the Masirah climatic conditions is the drop, in July, of the amount of insolation received at ground level per day. This phenomenon is associated with the monsoon season experienced in the south-eastern part of Oman: the monsoon results in a large amount of dust suspended in the atmosphere, which reduces the amount of direct solar radiation transmitted to the ground. Drizzle and mist are the causes of the analogous drop in the amount of solar radiation received per day at ground level at Salalah and surrounding mountains in the Dhofar region of Oman.

Because of the shortage of potable water in a country with an abundance of solar energy, it is probable that solar desalination is likely to play a vital role in the ultimate energy and environmental strategy for achieving a sustainable and prosperous Oman.     

Unveiling the solar resource potential for photovoltaic applications in Mauritius

Mauritius is considered to have high solar resource potential but it has not yet been fully quantified and exploited due to the lack of valid solar energy data. This paper unveils the solar potential of Mauritius. Ground-based measurements were performed at intervals of 30 s in order to obtain accurate global horizontal irradiance data which can depict all changes in solar power. The latter is used to evaluate average monthly global horizontal irradiance, maximum irradiance, monthly average insolation and monthly sky clearness index. A solar geometry model was used to define the average monthly, seasonal and yearly maximum elevations and extraterrestrial radiation. Measurement data were compared to Meteonorm and NASA SSE 3-hourly averaged solar data. Comparison shows that average irradiance values are in good agreement, whereas insolation and sky clearness values obtained from external sources are inferior to high quality measurement data. The results, presented in this paper, complement solar data of Meteonorm and NASA SSE and secondly, provides PV and solar engineers as well as scientists with highly valuable information on the solar resource of Mauritius that can be used during planning and design of PV systems as well as for conducting further research in Mauritius and surrounding regions.     

Estimated monthly average global radiation for Turkey and its comparison with observations

Global solar radiation data obtained from actinographs of the Turkish State Meterological Service were compared with data obtained from pyrheliometers that were established recently to determine if the actinograph data were usable in practice. It has been found that the observed actinograph data have a rather high error rate with 14.7% annual and 42.1% monthly averages. It has, however, not been possible to smooth these errors as they are absolutely random. Thus, a well known quadratic model was used to produce available radiation data. A quadratic relationship between solar insolation and duration of solar radiation data has been investigated in order to estimate monthly average global irradiance for Ankara, Antalya, Samsun, Konya, Urfa and zmir. The data from August 1993 to July 1995 have been used in the quadratic model. But, observations of zmir differ from other stations covered for about four years. Solar insolation data used in the quadratic model were obtained from the pyrheliometer with model CR10. Duration of bright sunshine data were obtained from a Siap, Frans or Müller sunshine recorder with 60° global lens. A general quadratic formula was found that represents the whole of Turkey. The estimated monthly average global solar radiation data, then, were produced from this quadratic formula. Comparison of the estimated and measured values showed that the quadratic model was able to estimate global radiation with about a 4% annual relative error and the estimated data seemed to be more reliable than the data measured by actinograph.     

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.     

The determination of hourly insolation on an inclined plane using a diffuse irradiance model based on hourly measured global horizontal insolation

Using only measured hourly values of global insolation on a horizontal surface, a method has been developed for computing the corresponding hourly values of insolation on a surface inclined at any angle and oriented in any direction. The method uses a solar radiation model in which the diffuse component is calculated from global horizontal radiation using three different relationships; the appropriate equation is selected according to the value of the ratio of measured hourly global insolation to hourly global insolation computed for clear sky conditions. The method has been checked using measured hourly values in Melbourne over a 5-yr period of insolation on both a horizontal surface and a plane inclined at 38° to the horizontal facing north. The differences between the computed hourly values and the measured hourly values are found to be approximately normally distributed about zero with a standard deviation of 0.16 MJ m⁻². This method is particularly useful for predicting the heat output of inclined solar flat plate collectors when only measured global horizontal insolation is available, which is often the case. Good agreement was found between the predicted output of a typical collector using measured 38° insolation and the computed hourly values using this method. Since the method has been checked only against Melbourne data it should be applied elsewhere with caution, but it is believed to have general application.     

Estimation of half-hour solar radiation values from hourly values

A statistical Markovian insolation model for predicting the time-sequence of half-hour solar radiation values on a horizontal surface which uses the hourly insolation values is developed. The hourly transition density function, governing the diurnal evolution of the hourly solar radiation values, is used for obtaining the half-hour transition density function. A transition density function is a measure of the probability of the event at the next immediate hour of interest when the event at the present hour is given. The estimation of half-hour transition density function is done through the fundamental decomposition theorem for the density function. This assumes a set of well defined intermediate states. As a first approximation, the half-hour transition density function is assumed to be temporally stationary. Furthermore, it is assumed that the cumulative probability distribution functions of the normalised initial hour solar radiation value and the normalised initial half-hour solar radiation values are not significantly different; the hourly, or half-hourly solar flux values are normalised by the corresponding extraterrestrial solar flux values. The validity of these assumptions is established through the successful time-sequence predictions of the half-hour insolation values. The time-sequence aspect of solar radiation values is proved by comparing the predicted joint cumulative distribution functions for several successive normalised half-hour values, with the corresponding distribution function for the recorded values. In order to prove that the predicted and actual distribution functions are from the same set, the non-parametric statistical test proposed by Kolmogorov and Smirnov has been used.     

On the estimation of global solar insolation

A curve suitable for estimation of global solar energy insolation in equatorial regions has been generated from humidity considerations using an empirical “universal” formula and experimental solar insolation data recorded for over 20 yr at specific locations in Kenya, East Africa. The curve has then been used to estimate global insolation in other locations in Kenya and the neighbouring countries with longstanding experimental data. The agreement between the experimental and theoretical insolation values is found to be satisfactory. This curve, we believe, can serve a useful purpose in estimating global solar insolation in other tropical locations with similar climatic conditions as those in Kenya which lack proper global solar insolation acquisition equipment.     

Measurement of solar energy radiation at Nsukka and the determination of the regression coefficients

Solar radiation for Nsukka, latitude 6.8°N, longitude 7.35°E, located 488 m above sea level, was collected for 11 yr using a Gunn-Bellani instrument, and the data obtained were restandardized using an Eppley precision pyranometer. The sunshine data during this period were also obtained using a Campbell-Stokes sunshine recorder.

It is observed that the insolation level for the month of November during the period of measurement is the highest, with an average of 17.50 MJ/m². The level of insolation during this month varied sinusoidally with an amplitude of 3.84 MJ/m². The clearness index, k_T, is 0.53, and there is an indication that the atmosphere was persistently laden with dust. August has the least insolation level with an average of 11.86 MJ/m² and a k_T of 0.32. The atmosphere during this month was always covered with cloud. This work confirmed the assertion by Awachie and co-workers that dust and haze attenuate insolation less than cloud cover. The Nsukka weather is rated to be heavily overcast, and over 90% of the total solar radiation is diffuse, with an average k_T value of 0.43.

The average regression coefficients a and b for Nsukka are 0.21 and 0.51 respectively. These values do not agree with the general relations and values already quoted by some workers. The predicted insolation values for Nsukka using these coefficients in the Angstrom type of formula agree with the measured data with an error of 0.7%. This level of accuracy compares well with those obtained when the insolation values are predicted for each year using the values of a and b deduced for the respective year. Furthermore, there was an indication that the level of accuracy obtained using average values of a and b might increase if a longer period is considered. Thus, with reliable average values of a and b obtained over a reasonably long period, and knowledge of the bright sunshine hours, the measurement of solar radiation in a location, for design purposes, may not be necessary.     

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.     

Prediction of direct solar radiation for low atmospheric turbidity

Based on a few simplifying assumptions, an equation has been derived for the prediction of direct solar radiation in relation to surface humidity and absolute air mass for clear sky and minimal smoke and dust content of the atmosphere. The constants of the equation were statistically obtained from accurate measurements of insolation at three altitudes under varying humidity conditions. Accuracy of prediction has been found to be ±10 per cent within 95 per cent confidence limits. A nomogram has been presented for quick assessment of insolation which has been checked against data computed from Robinson's[1] diagram.     

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.     

The oblateness effect on the extraterrestrial solar radiation

Calculations of the daily solar radiation incident at the top of the Earth's atmosphere, with and without the effect of the oblateness, are presented in a figure illustrating the seasonal and latitudinal variation of the ratio of both insolations. It is shown that, in summer, the daily insolation of an oblate Earth is slightly increased in two regions symmetric with respect to the summer solstice. In winter, the flattening effect results in a somewhat more extensive polar region, the solar energy input being always reduced (in some cases by more than 2 per cent) when compared to a spherical one. In addition, we also numerically studied the mean daily solar radiation. It is found that the mean summer daily insolation is scarcely increased between the equator and the subsolar point, but decreased poleward of the above mentioned limit. In winter, however, the mean daily insolation is always reduced, the maximum loss of insolation attaining as much as 1 per cent in the 55–85° latitude interval. The partial gain of the mean summertime insolation being much smaller than the reduction during winter season evidently yields a mean annual daily insolation which is decreased, maximally by about 0.3 per cent, at all latitudes.     

Brazilian Solar Resource Atlas CD-ROM

The Brazilian Solar Resource Atlas CD-ROM is intended to be a tool for solar system design, delivering information that relies on a large interactive database, including, also, a modern device for calculating the solar radiation collected by planes inclined at different tilt angles or tracking the sun around one or two axes. The spatial distribution of the daily solar radiation, monthly and yearly averaged, that hits Brazil is presented in 13 colored maps, together with the methodological procedures used for harmonizing the information and designing the maps. A map containing the location of pyranometric and actinographic terrestrial stations, the information which was used for designing the maps, is also presented. The period of collected data runs from 1978 to 1990. Similarly, the atlas contains 13 colored maps, including daily insolation, monthly and yearly averaged, in addition to the map containing the location of the heliographic stations. The CD-ROM stores a database that includes over 500 stations located in Brazil and on the borders of its neighboring countries. The information is given either as daily, monthly average global solar radiation, or daily, monthly average insolation. A search device is included in the database, allowing to navigate over the maps or to select a desired location. The information may be printed as a report. The CD-ROM also includes a software to perform the following calculations: solar radiation estimates on a fixed plane at any inclination on North-South orientation; estimates of solar radiation collected by a plane tracking the sun about one or two axes; generation of synthetic series based on Markov’s Transition Matrixes.     

Evaluation of models for predicting insolation on slopes within the Colorado alpine tundra

This empirical study evaluates insolation predictions for the Colorado tundra from models based upon isotropic and anisotropic distribution approximations for diffuse sky and reflected solar radiation. The data set of hourly insolation values was obtained from 40 locations on an alpine ridge by simultaneous measurement of direct beam irradiance and total insolation to the horizontal ridge crest and two nearby sloping surfaces. Six models are used to predict insolation, two based on the isotropic distribution of diffuse solar radiation and four on anisotropic diffuse distribution fields. Three models (one isotropic and two anisotropic) employ measurements of normal direct beam irradiance while the other 3 models incorporate the correlation between the “clearness index” and the ratio of diffuse sky to total insolation. The precision of insolation estimates from models using the correlation method is only slightly less than from other models. Accounting for the increase of diffuse radiation in the circumsolar sky improves insolation predictions. However, inclusion of additional regions of diffuse radiation anisotropy decreases model accuracy. Errors of insolation estimates for the alpine tundra from all models vary in a systematic manner as a function of relative azimuth and ground slope angles.     

Investigation of cloudless solar radiation with PV module employing Matlab-Simulink

This paper focuses on a novel approach to the prediction of Voltage-Current (V-I) characteristics of a Photovoltaic panel under varying weather conditions and also the modelling of hourly cloudless solar radiation to provide the insolation on a PV module of any orientation, located at any site. The empirical model developed in this study uses standard specifications together with the actual solar radiation and cell temperature. This proposed work develops a Matlab-Simulink model to generate solar radiation at any location and for any time of the year. A new model for V-I characteristics and maximum power operation of a Photovoltaic (PV) module is also presented, which aims to model the effect on V-I and P-V curves of varying climatic conditions. Moreover, this model has been implemented using the Matlab-Simulink and is used to investigate the effect of meteorological conditions on the performance of a PV module generator. Thus the combined model of cloudless solar radiation and the photovoltaic module provides a tool that may be loaded in the library for analysis purpose. It is found that the predicted solar radiation strongly agrees with the experimental data.     

Incident solar radiation on Argentina from the geostationary satellite GOES: Comparison with ground measurements

Daily values of the solar radiant energy incident on earth's surface constitute a quantity of increasing importance, not only in nonconventional energy development but also for agricultural, weather, and climate monitoring and predictions. In Argentina, the solar global radiation has been measured since 1978 through a network of pyranometers distributed all over the country. Simultaneously, in the area limited by 21° and 41°S latitude and 53° and 67°W longitude, insolation determinations have been made using the geostationary satellite GOES from May 1982 to June 1984. Therefore, it was possible to compare the simultaneous hourly and daily values of solar global radiation corresponding to the northern part of the country during 1982 and 1983. In this article, the results of the comparison are presented. It is shown that the standard error of the satellite-derived hourly and daily insolation values when compared against pyranometers is about 25%, and in the range of 15 to 20% of the mean values, respectively. Therefore, operational estimation of surface insolation in the region using GOES data appears normally feasible.     

Solar radiation utilizability

The nonlinear behaviour of many solar energy systems requires consideration of the fluctuating nature of solar radiation. Utilizability curves constructed for this purpose consider the radiation fluctuation on the basis of hourly or daily insolation values. Solar collectors, however, do not see radiation fluctuations in terms of hourly or daily insolation values, but respond to instantaneous radiation fluctuations caused by clouds. The fluctuation of instantaneous and short-time integrated radiation has been shown to differ significantly from that of daily insolation. This paper presents utilizability curves constructed from the cumulative probability distribution of instantaneous terrestrial insolation values. It is shown that hourly and daily utilizability curves give a conservative estimate of long-term performance. Experimental measurements of the collector performance further suggest the use of instantaneous utilizability curves in place of daily curves. The effect of the collector time constant on utilizability is discussed.