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 global solar radiation in Benin

Following Frère and Rietveld's model, correlation constants a and b were determined for many stations in Benin using:

• - a graphical relationship between the average annual relative sunshine SS/SS′o and the constants (Frère's model).

• - a linear relationship between constant a and the appropriate value of sunshine duration and a hyperbolic relationship between constant b and the relative average annual sunshine (Rietveld's model).

Knowledge of constant for a location can be used to predict global solar radiation for other locations using the Angström-Page approach using a statistical relationship between global solar radiation and sunshine duration.The estimated values were compared with measured values.     

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.     

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.     

Equations for estimating global solar radiation in data sparse regions

The knowledge of the amount of solar radiation in an area/region is very essential in the field of Solar Energy Physics. In this work two equations are put forward for estimating global solar radiation from common climate variables in data sparse regions. The first is the Hargreaves equation, R_s=0.16R_aT_d^0.5 where R_a is the extraterrestrial solar radiation and T_d is the temperature difference (maximum minus minimum), while the second is the Angstrom equation, R_s=R_a(0.28+0.39n/N) where n and N are the measured sunshine hours and the maximum daylight duration respectively. The global solar radiation estimated by the two equations for three sites, Owerri (5°28′N, 7°2′E), Umudike (5°29′N, 7°33′E) and Ilorin (8°32′N, 4°46′E), located in different climate zones of in Nigeria, West Africa, are in agreement with those of earlier workers and that from Photovoltaic Geographic Information System (PVGIS) project. The implication of this in solar photovoltaic applications has been stressed.     

Correlating beam radiation with sunshine duration

For seven locations in north and central India, monthly averaged data of daily beam irradiation on a horizontal surface, I, have been correlated with bright sunshine duration, s, using the relation (I/I₀) = b₀(s/S′) where I₀ is the monthly mean value of extraterrestrial irradiation over a day, S′ is the corresponding duration over which Campbell-Stokes type sunshine recorders remain sensitive. It is found that b₀ is a constant that is period and region dependent. Monthly estimates of beam radiation using the relation above show that for the seven stations rms errors are within 3–6%. Tests made for other stations in India also gave good estimates. For the computation of I, global radiation is not required unlike most estimation techniques and therefore the method should find a wide application.It may be observed that b₀ values turn out to be roughly equal to exp(-md T ) where m is the relative airmass, d is the Raleigh optical thickness and T is the Linke turbidity factor.     

Estimation and prediction of global solar radiation over Greece

A regression analysis of the relative monthly values of global solar radiation ( ) the corresponding values of sunshine (n/N), for the period 1961-75, was performed to determine the constants a and b of the Ångström formula, for Athens. The constants a and b were also determined by a graphical relationship between the average annual relative sunshine (n/N) and these constants, for the same station. The latter method was then used to determine the constants a and b for 33 other stations widely distributed throughout Greece, after making a relative correction to these constants. In this way, monthly and annual values of global solar radiation were estimated for 34 stations over Greece from sunshine measurements. The geographical distribution of the annual totals of global solar radiation over Greece was mapped and some types and sub-types were identified.Further, a stepwise multiple regression analysis of the annual total amounts of global solar radiation and the three factors (latitude, longitude and altitude) was carried out; the validity of the assumption of the linear relationship between the annual totals of global solar radiation and the three factors was examined.     

Compilation and evaluation of solar and wind energy resources in Sudan

A number of years worth of data concerning the solar radiation on a horizontal surface, sunshine duration and wind speed in Sudan have been compiled, evaluated and presented in this article.Measurements of global solar radiation on a horizontal surface at 16 stations for several years are compared with predictions made by several independent methods. In the first method the Angstrom formula was used to correlate relative global solar irradiance to the corresponding relative duration of bright sunshine.Regression coefficients are obtained and used for prediction of global solar irradiance. The predicted values were consistent with measured values (± 8.01% variation).In the second method, by Barbaro et al. [Solar Energy, 1978, 20, 431] sunshine duration and minimum air mass were used to drive an empirical correlation for the global radiation. The predicted values compared well with measured values (± 12% variation).The diffuse solar irradiance is estimated. The results of two formulas have close agreement. A radiation map of Sudan was prepared from the estimated radiation values. The annual daily mean global radiation ranges from 3.05 to 7.62 kW h m⁻² per day.Routine wind data from 70 stations were analyzed. Monthly averaged wind speed and average powers were determined for each station. The derived annual average speeds range from 1.53 to 5.07 m s⁻¹. Maximum extractable average wind powers were found to vary between 1.35 and 49.5 W m⁻². A wind map of Sudan was also prepared.Sudan possessed a relatively high abundance of sunshine and moderate wind speed. It is concluded that Sudan is blessed with abundant solar and wind energy.     

Solar and terrestrial radiation dependent on the amount and type of cloud

Ten-year (1964–1973) continuous records at Hamburg of hourly sums of solar and terrestrial, downward and upward radiation flux densities have been evaluated with regard to simultaneous hourly cloud observations. The irradiance at given solar elevation is plotted vs total cloud amount for each season and for the whole year; in the same way, the ratio of the irradiance under clouded to that under cloudless sky is presented. Additional diagrams show the irradiance under cloudless and under overcast sky as function of solar elevation. The ratio of global radiation at total cloud amount N okta, G(N), to global radiation at cloudless sky, G(0), at the same solar elevation γ turned out to be indepenent of γ and can be parameterized by

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. The influence of cloud type is demonstrated by diagrams showing the irradiance under skies overcast by a specific cloud type as function of solar elevation for each season and for the year; also, the corresponding ratios “overcast” to “cloudless” are presented. In the case of global radiation, the ratios which may be interpreted as the transmittances of the specific cloud types for global radiation, turned out to be independent of solar elevation and have the following mean values: Ci, Cc, Cs 0.61; Ac, As 0.27; Sc, Cu 0.25; St 0.18; Ns 0.16.     

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).     

Solar radiation over Sudan—Comparison of measured and predicted data

Measurements of global solar irradiance on a horizontal surface at 14 meteorological stations in Sudan are compared with predictions made by two independent methods. The first method is based on Angstrom formula which correlates relative global solar irradiance to corresponding relative duration of bright sunshine . Regional regression coefficients are obtained and used for prediction of global solar irradiance. The agreement with measurements is better than 7.5 per cent. In the second method an empirical relation due to Barbaro et al. which uses sunshine duration and minimum air mass as inputs is employed. An appropriate regional parameter is determined and used to predict solar irradiance at all stations with an accuracy better than 8 per cent. A comparison of the two methods is presented. Estimation of diffuse solar irradiance by Page's as well as Liu and Jordan's correlations is also performed and the results are examined.     

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.     

Uses of sunshine duration to estimate the global solar radiation over eight meteorological stations in Egypt

The climatological Ångstrom regression coefficients have been determined by three methods and used to predict the global solar radiation over eight meteorological stations. Each of the three methods depends on the correlation between two ratios. The first ratio is between the long period of monthly average sunshine duration and the corresponding maximum of daily sunshine duration (day length) N, and the second ratio is between the measured monthly average daily global solar radiation and the corresponding monthly mean daily extraterrestrial solar radiation on the horizontal surface ₀. A comparison between the measured data and the estimated values has been done. The t-statistics is used as a statistical indicator to choose the coefficients of the best method that gives a percentage of error less than 10%.     

Bivarate models: relationships between solar irradiation and either sunshine duration or extremum temperatures

The Republic of Botswana is one of the sunniest countries in Southern Africa. It has very little cloud cover, insufficient rainfall, very low humidity, and very low wind speed throughout the year for most parts of the country. The daily extremum temperatures appear to be very much related to solar irradiation which in turn depends on sunshine duration. In Botswana, solar irradiation on a horizontal surface is measured only at Sebele, but sunshine duration and extremum temperatures are measured at several locations throughout the country. This paper presents bivariate models that relate solar irradiation to sunshine duration, and solar irradiation to extremum temperatures for Sebele, Botswana. Autocorrelation analysis revealed that the solar irradiation series is stationary for d=2 and D=0, sunshine duration series is stationary for d=0 and D=0, while the extremum temperatures series are stationary for either d=0 and D=N where N=1, 2, . . . or d=1 and D=1. It is found that there is a lag of three months between the peaks of the differenced series of fractional sunshine duration and fractional solar irradiation. On the other hand it is found that there is at most a lag of one month between the peaks of the differenced series of maximum temperature and solar irradiation, and that there is no lag between the peaks of the differenced series of minimum temperature and solar irradiation. Analysis of the noise component revealed that the bivariate processes under consideration behaved either as a purely seasonal MA processes of order (0,1,1) or as ARIMA processes of order (0, 1, 1)×(0, 1, 1)₁₂ or as a purely nonseasonal, autoregressive process of order 2. We claim that the relationships found for Sebele can be applied to estimate solar irradiation at other locations with climatic conditions similar to Botswana.     

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.     

Statistical comparison of models for estimating the monthly average daily diffuse radiation at a subtropical African site

Nine correlations have been developed in this paper to estimate the monthly average diffuse radiation for Dakar, Senegal. A 16-year period data on the global (H) and diffuse (H_d) radiation, together with data on the bright sunshine hours (N), the fraction of the sky’s cloud cover (Ne/8), the water vapour pressure in the air (e) and the ambient temperature (T) have been used for that purpose. A model inter-comparison based on the MBE, RMSE and t statistical tests has shown that estimates in any of the obtained correlations are not significantly different from their measured counterparts, thus all the nine models are recommended for the aforesaid location. Three of them should be particularly selected for their simplicity, universal applicability and high accuracy. Those are simple linear correlations between and , or . Even presenting adequate performance, the remaining correlations are either simple but less accurate, or multiple or nonlinear regressions needing one or two input variables.     

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.     

On the relationship between duration of sunshine and solar radiation on the earth’s surface: Ångström’s equation revisited

The paper presents a relationship between the relative sunshine duration and solar irradiation on the earth’s surface. Following a review of the literature on Ångström’s equation and the properties of instantaneous solar radiation, the sunshine–radiation relationship is derived from monthly average values of daily beam radiation which are used as a measure for the fraction of clear sky, . The resulting (non-linear) relationship, , unlike the Ångström–Prescott relation, does not contain empirical constants and only requires the monthly average clear sky atmospheric transmittance to account for the climate of a particular location ( is typically between 0.65 to 0.75). The relationship is verified for monthly intervals for Perth and Townsville, Australia and compared to existing Ångström–Prescott equations for a wide range of climates and locations. The excellent agreement of the proposed relationship with the average value of data in the latter comparison suggests that it may be universally valid and that the Ångström–Prescott equation is a local (linear) approximation of the derived relationship. For daily time intervals the sunshine–radiation relationship changes to f_clear=(K/K_clear)³. The paper closes with a discussion on applications of the new relationship including the performance prediction of solar energy systems.     

Evaluation of sunshine duration from cloud data in Egypt

In this study, three empirical formulae have been deduced to estimate relative sunshine duration, n/N, using readily available observed data of cloud amount, C, in Egypt. The monthly mean values of n/N and C recorded at 34 stations during the period (1990–2005) have been used in the present study. The three deduced formulae have been verified for any locality in Egypt which lies above (zone 1) and below latitude 30° (zone 2) and for the whole country of Egypt. The agreement between measured and estimated values of the three deduced formulae were remarkable. It was found that the maximum possible error of estimated values, e (%), of the three deduced empirical formulae have not exceeded ±7.27% with mean percentage error (MPE) values range from −0.62% to +0.81%; meanwhile the values of statistical tests of main bias error (MBE) and root mean square error (RMSE) are very close to zero. It has been concluded that Egypt's deduced formula gives precise estimations for n/N and was recommended for use at any location in Egypt. The sunshine distribution and its percentage frequency over Egypt were also studied. The results revealed that latitudinal dependent of n/N. Egypt has minimum value of n/N (0.48) during January at the northern part of the country and maximum value (0.92) during June at the southern part.     

Forecasting based on neural network approach of solar potential in Turkey

As Turkey lies near the sunny belt between 36 and 42°N latitudes, most of the locations in Turkey receive abundant solar energy. Average annual temperature is 18–20 °C on the south coast, falls down to 14–16 °C on the west coast, and fluctuates 4–18 °C in the central parts. The yearly average solar radiation is 3.6 kW h/m² day, and the total yearly radiation period is 2610 h. The main focus of this study is put forward to solar energy potential in Turkey using artificial neural networks (ANNs). Scaled conjugate gradient (SCG), Pola-Ribiere conjugate gradient (CGP), and Levenberg–Marquardt (LM) learning algorithms and logistic sigmoid transfer function were used in the network. In order to train the neural network, meteorological data for last 4 years (2000–2003) from 12 cities (Çanakkale, Kars, Hakkari, Sakarya, Erzurum, Zonguldak, Balıkesir, Artvin, Çorum, Konya, Siirt, Tekirdağ) spread over Turkey were used as training (nine stations) and testing (three stations) data. Meteorological and geographical data (latitude, longitude, altitude, month, mean sunshine duration, and mean temperature) is used as input to the network. Solar radiation is the output. The maximum mean absolute percentage error was found to be less than 6.78% and R² values to be about 99.7768% for the testing stations. These values were found to be 5.283 and 99.897% for the training stations. The trained and tested ANN models show greater accuracy for evaluating solar resource posibilities in regions where a network of monitoring stations have not been established in Turkey. The predictions from ANN models could enable scientists to locate and design solar energy systems in Turkey and determine the best solar technology.