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.     

Evaluation of models to predict insolation on tilted surfaces

An empirical study was performed to evaluate the validity of various insolation models which employ either an isotropic or an anisotropic distribution approximation for sky light when predicting insolation on tilted surfaces. Data sets of measured hourly insolation values were obtained over a 6-month period using pyranometers which received diffuse and total solar radiation on a horizontal plane and total radiation on surfaces tilted toward the equator at 37° and 60° angles above the horizon. Data on the horizontal surfaces were used in the insolation models to predict insolation on the tilted surface; comparisons of measured vs calculated insolation on the tilted surface were examined to test the validity of the sky light approximations. It was found that the Liu-Jordan isotropic distribution model provides a good fit to empirical data under overcast skies but underestimates the amount of solar radiation incident on tilted surfaces under clear and partly cloudy conditions. The anisotropic-clear-sky distribution model by Temps and Coulson provides a good prediction for clear skies but overstimates the solar radiation when used for cloudy days. An anisotropic-all-sky model was formulated in this effort which provided excellent agreement between measured and predicted insolation throughout the 6-month period.     

An operational system for mapping insolation from goes satellite data

A system for mapping the mesoscale distribution of insolation from GOES satellite data has become operational at the University of Wisconsin Space Science and Engineering Center. An energy balance model of the earth-atmosphere system is used in conjunction with radiometrically calibrated GOES measurements to estimate surface insolation from satellite images taken at hourly intervals. Integration of these hourly estimates into daily insolation totals has produced results within 9 per cent (standard error of the mean) of pyranometer measurements on a much finer space scale than is available from the surface pyranometer network.The model has been applied, using satellite data display facilities and software designed for large satellite data sets, to produce monthly maps of insolation over large geographical areas at a resolution of approx. 12 × 12 km. Although the density of the surface pyranometer network is inadequate to directly verify the mapping results, the quality of the daily insolation estimates compared with the measurements of single pyranometers suggests that the insolation maps will have a similar accuracy.     

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°.     

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

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

A model for the calculation of solar global insolation

A theoretical model is described that is designed to give the total global insolation falling on the earth's surface and the transmission of the atmosphere. It is compared to a model by Braslau and Dave[1] and found to agree to within a few percent in all cases. Climatogical values of total pricipitable water, turbidity, and surface albedo are required as the model inputs, and the sources of these data are described. The model has been applied to 26 stations in the National Weather Service (NWS) pyranometer network, where measured true solar noon atmospheric transmission values are available, as part of the NOAA program to rehabilitate the old pyranometer observations. For three of these stations where reliable true solar noon irradiance and transmission values are available, the model calculations and observations are compared. At 18 locations the calculated and measured daily mean insolation values are compared for clear days. At one location (Boulder, Colorado) calculated and measured radiation climatologies for all weather conditions are compared. In all comparisons the model and observations differ by no more than 2.7 per cent, which is within the experimental accuracy (±5 per cent) of the pyranometers. Possible sources of errors are discussed.     

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.     

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

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

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.     

Optimum tilt angle for solar collectors used in Cyprus

Flat-plate solar collectors are widely used in Cyprus for water heating purposes. The roofs of nearly all the residential premises on the island are fitted with such collectors. This article examines the theoretical aspects of choosing a tilt angle for the solar flat-plate collectors used in Cyprus and makes recommendations on how the collected energy can be increased by varying the tilt angle. In this paper, the collector surface is assumed to be facing South and the calculations are based upon the measured values of daily global solar radiation on a horizontal surface on the island. The beam and diffuse components of the horizontal global radiation are then estimated and the solar radiation on a tilted surface is calculated as the angle of tilt is varied from 0° to 90°. It is shown that very nearly optimal energy can be collected if the angle of tilt is varied seasonally, four times a year.     

Measurements and predictions of solar radiation incident on horizontal surfaces at Santa Fe, Argentina (31° 39′S, 60° 43′W)

Measurements and predictions of solar radiation during a period of 10 years on horizontal surfaces at Santa Fe (31° 39′ S, 60° 43′ W), Argentina, reported as average daily global radiation for each month, are presented. Data are compared to those obtained with a previously published and verified model for computing solar radiation on horizontal planes at the earth's surface for cloudless sky days. Measurements show an important reduction of global radiation with respect to the cloudless sky model predictions for all months of the year. Conversely, averaged daily diffuse solar radiation calculated with Page's formula shows a small increment with respect to the predicted diffuse solar radiation for cloudless sky conditions. When direct solar radiation data, calculated from global and diffuse solar radiation values, are compared to theoretical prediction, a significant decrease is observed. This trend is similar to that obtained for global solar radiation.     

Total suspended particles and solar radiation over Cairo and Aswan

Measurements were carried out at Cairo (30.05°N, 31.17°E) and Aswan (23.58°N, 32.47°E) in Egypt for three years (1990–1992) by the Egyptian Meteorological Authority. The measurements were done using an Eppley ultraviolet radiometer to measure the global ultraviolet solar radiation (UV), Eppley pyranometers to measure the global solar radiation (G) and the pyrgeometers with silicon dome from Eppley to measure the atmospheric infrared radiation (IR). The clearness index (K_t) and the diffuse fraction (K_d) for both regions have been calculated. Finally the total suspended particles for Cairo and Helwan and their interaction with the solar radiation has been found.     

The dependence on solar elevation of the correlation between monthly average hourly diffuse and global radiation

In the present work, the dependence on of the correlation between and is studied, , , and respectively being the monthly average hourly values of the global, diffuse, and extraterrestrial radiation, all of them on a horizontal surface, and the solar elevation at midhour. The dependence is studied for Uccle for the following sky conditions. Condition A: clear skies (fraction of possible sunshine = 1) and the maximum values of direct radiation measured during the period considered (each of the hours before or after the solar noon for which radiation is received); Condition B: corresponding to all the values of radiation measured when the sunshine fraction is 1 during the period considered; Condition C: corresponding to all the data collected, independently of the state of the sky; Condition D: corresponding to overcast skies ( ).From the available values of and (monthly average hourly direct radiation on a horizontal surface), values of and for 5° ≤ ≤ 45° and Δ = 5° are calculated using Newton's divided difference interpolation formula. The interpolated values occupy three clearly different regions in the plot, one for each of the conditions A,B, and C. For Condition A and each value of best linear fits with high correlation coefficients are obtained for the correlation. The influence of the Linke turbidity factor on the correlation for Condition A is studied for 5° ≤ ≤ 35°, Δ = 5°.     

Comparison of diffuse/global ratios calculated from one-minute, hourly and daily solar radiation data

One-minute values of direct, diffuse and global radiation have been continuously collected at Davis, California (38.5°N, 121.1°W) since 1 January, 1979. These datasets are quality controlled to insure the most accurate and reliable data possible. Analysis of one-minute data has provided an opportunity to evaluate some of the bias that may be inherent in statistical representation of solar radiation data. A simple mean and standard deviation do not adequately describe the variation in the data and we show that a more representative treatment includes the box and whisker analysis. In this the mean, median, first and third quartiles, and the maximum and minimum ranges are presented. It is possible to compute the variability between days more completely with this technique while the means may be very close. This has application to evaluation of solar collectors as a better method of evaluating theire efficiency. This is applied to diffuse/global ratios which show a seasonal dependence although some clear winter days have ratios close to clear summer values; however, the first and third quartile and median distinctly separate these days. Analysis of solar radiation data should be conducted with caution as shown by these results.A simple model is proposed to compute hourly global values from the integrated daily total. Comparisons of calculated with measured hourly values indicated less than a 10 per cent error between 0700 to 1600 with the maximum value being slightly underestimated. This procedure allows one to evaluate solar collectors with only daily values and presents a method for thoroughly evaluating our solar resources.     

Solar radiation on Mars

Detailed information on solar radiation characteristics on Mars are necessary for effective design of future planned solar energy systems operating on the surface of Mars. In this paper we present a procedure and solar radiation related data from which the diurnally, hourly and daily variation of the global, direct beam and diffuse insolation on Mars are calculated. The radiation data are based on measured optical depth of the Martian atmosphere derived from images taken of the sun with a special diode on the Viking cameras; and computation based on multiple wavelength and multiple scattering of the solar radiation.     

Performance evaluation of hybrid (wind/solar/diesel) power systems

Depleting oil and gas reserves, combined with the growing concerns of global warming, have made it inevitable to seek alternative/renewable energy sources. The integration of renewables such as solar and wind energy is becoming increasingly attractive and is being used widely, for substitution of oil-produced energy, and eventually to minimize atmospheric degradation. The literature shows that commercial/residential buildings in Saudi Arabia consume an estimated 10–40% of the total electric energy generated. In the present investigation, hourly wind-speed and solar radiation measurements made at the solar radiation and meteorological monitoring station, Dhahran (26°32′ N, 50°13′ E), Saudi Arabia, have been analyzed to investigate the feasibility of using hybrid (wind+solar+diesel) energy conversion systems at Dhahran to meet the energy needs of twenty 2-bedroom houses. The monthly average wind speeds for Dhahran range from 4.1 to 6.4 m/s. The monthly average daily values of solar radiation for Dhahran range from 3.6 kWh/m² to 7.96 kWh/m². The performance of hybrid systems consisting of different rated power wind farms, photovoltaic (PV) areas, and storage capacities together with a diesel back-up are presented. The monthly average daily energy generated from the above hybrid system configuration has been presented. The deficit energy generated from the back-up diesel generator and the number of operational hours of the diesel system to meet a specific annual electrical energy demand of 702,358 kWh have also been presented.     

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.     

Estimation of monthly mean hourly global radiation for latitudes in the 1°N–81°N range

A way to estimate monthly mean hourly global radiation ( ) from monthly mean daily global radiation ( ) has been to use fits which give as a function of , the monthly mean daily maximum possible number of sunshine hours. In the present work it is shown that these plots are by no means of universal validity, but are clearly dependent on latitude for high latitudes. A new type of correlation is proposed, which gives as a function of , the solar elevation at mid-hour. The values of coefficients for the versus correlations are given for each month of the year, for the hours centered at 0.5 h, 1.5 h, 2.5 h, etc. from the true solar noon, and stations with latitudes in the 1°N–81°N range. The given coefficients are most likely valid for any latitude, north or south.     

A model for determining the spectral quality of daylight on a horizontal surface at any geographical location

Using solar irradiance data gathered over 8 yrs (1968–1976) a very simple model for determining daily and hourly totals of solar irradiance has been derived. The simplified model works extremely well for broad spectral regions, i.e. the total irradiance, the visible (400 nm–700 nm), and the total IR (800 nm–2800 nm). Smaller regions (100 nm bands) are not computed with the same accuracy because of the spectral dependency of such parameters as the albedo, water vapor and ozone. Also, this model does not give good results around sunrise and sunset.The computational accuracy of the model of daily totals and hourly totals on clear days is within ±10% when compared to values obtained from Eppley precision pyranometers. The accuracy for 100 nm bands is considerably less being greater than ±10 per cent on clear days and cloud corrections will increase the errors to ±25 per cent.     

Model evaluation and optimum collector slope for a tropical country

Various models proposed in the literature, viz. the Beam method, proposed by Morse & Czarnecki; two methods proposed by Liu & Jordan, using hourly values and average daily values of solar radiation: and Klucher's method are compared in this paper using measured hourly values of global and diffuse radiation on a horizontal surface and the total radiation on a tilted surface. It was observed that the model proposed by Klucher estimates the radiation more consistently with the experimental observations for clear as well as cloudy sky conditions.

This method was used for predicting the year round radiation availability on (i) a fixed collector inclined at an optimum tilt, (ii) a partially tracking collector in which the slope is fixed but following the sun's azimuth angle, and (iii) a fully tracking collector. In this analysis, measured values of hourly global and diffuse solar radiation on a horizontal plane for four widely separated Indian stations, viz. Delhi (28°38′N), Poona (18°29′N), Calcutta (22°36′N), and Madras (13°8′N) as per India Meteorological Department classification for climatic analysis, have been used.

With the model proposed, the radiation availability on different slopes for all the twelve months of the year for a fixed and partially tracking collector have been evaluated and optimum tilts for various seasons of a year for different solar energy applications for all the four Indian stations have been determined. For a typical winter month at New Delhi in the semi-arid zone of India, a fixed collector, a partially tracking collector and a fully tracking collector receive 60, 80 and 95% more radiation compared to that received on a horizontal plane respectively. Another observation is that the variation of the insolation received on inclined surfaces is not at all sensitive to the angle of tilt in the neighbourhood of the optimum angle of operation.