A comparative study to estimate daily diffuse solar radiation over India

A detailed study of monthly average daily diffuse solar radiation for selected Indian locations have been performed using five years (2001–2005) measured data. The data of four prominent locations (Jodhpur, Calcutta, Bombay and Pune), representing varying weather conditions of the entire country, have been taken for the present study. The correlations between the diffuse fraction (H_d/H) and the sunshine fraction (S/S₀) have been developed using regression analysis method for each selected location as well as for all Indian locations, we call it All India Correlation (AIC). The results obtained from present AIC are well compared with the measured data along with the estimates of Liu and Jordan, Gopinathan and Iqbal for different locations. The comparisons between various data conclude that AIC can be used to estimate diffuse fraction for any location in India. For further validation and to show the accuracy of present correlations, statistical tests of root mean square error (RMSE), mean bias error (MBE) and mean percentage error (MPE) are also performed.     

Contribution to the study of solar radiation in Abu Dhabi

Measurements of global solar radiation for 10 yr in Abu Dhabi are used to examine the suitability of a method of prediction of global solar radiation. It shows a good degree of accuracy. A correlation between the clearness index, H/H₀, and the fraction of maximum possible number of sunshine hours is obtained and found to be H/H₀ = 0.307 + 0.312n/N. The diffuse solar radiation is predicted by two methods which show almost similar results. Correlation between the diffuse solar radiation as a fraction of the global radiation, H_d/H, and the fraction possible number of sunshine hours, n/N, is established using both methods, for comparison sake, since measurements of diffuse solar radiation are not available. The comparison shows a good agreement between the two correlations. The relation between the diffuse solar radiation as a fraction of the global radiation H_d/H, and the clearness index, H/H₀, is established and compared with those obtained elsewhere in order to justify their use, since direct measurements are not available. The relation shows a latitude dependency.     

An analysis of thermal and solar zone radiation models using an Angstrom–Prescott equation and artificial neural networks

The correlation between the clearness index and sunshine duration is useful in the estimation of the solar radiation for areas where measured solar radiation data are unavailable. Regression techniques and artificial neural networks were used to investigate the correlations between daily global solar radiation (GSR) and sunshine duration for different climates in China. Measurements made during the 30-year period (1971–2000) from 41 measuring stations covering 9 thermal and 7 solar climate zones and sub-zones across China were gathered and analysed. The performance of the regression and the ANN models in the thermal and solar zones was analysed and compared. The coefficient of determination (R²), Nash–Sutcliffe efficiency coefficient (NSEC), mean bias error (MBE) and root-mean-square error (RMSE) were determined. It was found that the regression models in both the thermal and the solar climate zones showed a strong correlation between the clearness index and sunshine duration (R²=0.79–88). There appeared to be an increasing trend of larger MBE and RMSE from colder climates in the north to warmer climates in the south. In terms of the thermal and solar climate zone models, there was very little to choose between the two models.     

A model for determining the global solar radiation for Makurdi,Nigeria

An empirical model for determining the monthly average daily global solar radiation on a horizontal surface for Makurdi, Nigeria (Latitude 7°7′N and Longitude 8°6′E) was developed using the Angstrom–Page equation. The solar radiation (W/m²), hours of bright sunshine and cloudiness were measured hourly from 0600 H to 1800 H daily for 18 months. The constants ‘a’ and ‘b’ of the Angstrom linear type equation were determined by plotting the clearness index (H/H_o) against the possible sunshine hours (n_s/N) to obtain the line of best fit. The constant ‘a’ was obtained from the intercept of the line on the y-axis while the constant ‘b’ was obtained from the slope of the line. The developed model for determining the global horizontal solar radiation at the location was H = H_o [0.17 + 0.68(n/N)] with a coefficient of correlation of 0.78. The mean bias error and root mean square error that were used to test the performance of the constants were 0.17% and 1.22% respectively. The measured solar radiation was compared with the solar radiation predicted by the model and no significant difference was found between them using F-LSD at P ≤ 0.05.     

A hybrid model for estimating global solar radiation

In view of the site-dependence of Ångström correlation, this study developed a hybrid model to estimate global radiation H. Unlike Ångström correlation H=(α+βS/S₀)H₀, this model suggested that H=(a+b S/S₀)H_b+(c+d S/S₀)H_d, H_b and H_d are effective beam radiation and effective diffuse radiation, which imply latitude, elevation and seasonal effect on radiation. H_b and H_d are calculated by an arithmetic model derived from spectral model. The hybrid model was designed for estimating monthly mean daily global radiation with hourly-recorded bright sunshine time, and its applicability was verified at observatories in Japan.     

Relationship between “clearness index” and “cloudiness index” at a tropical station (Ilorin, Nigeria)

Total (global) solar radiation, H, and diffuse solar radiation, H_d were measured at Ilorin (8° 30′N 4° 42′E) Nigeria. From these, the daily values of H/H₀ and H_d/H were computed, where H₀ is the extraterrestrial radiation. The relationship between the two ratios and their variation with the prevailing atmospheric conditions were examined.The ratios were found to be opposite in characteristics. H/H₀ has high values in clear atmospheres and low values in cloudy or turbid atmospheres; and vice-versa for H_d/H. The two ratios are negatively linearly related and with this fact, two simple mathematical models were obtained for estimating H_d/H in terms of H/H₀.     

Daily UV radiation modeling with the usage of statistical correlations and artificial neural networks

The information regarding solar UV radiation (UVA + UVB) in Brazil and around the world is scarce with low spatial and temporal coverage. This information scarcity, due to the small number of measuring stations, has directed some researchers towards the creation of computational parametric models or the generation of statistical models for the estimation of the UV radiation from the measurement of the global radiation. Information about UV irradiation is expanded for other places where there is only global radiation data. Thus, two stations were set up, in 2008, one in the city of Pesqueira and the other in Araripina, both in the state of Pernambuco, for simultaneous measurements of daily global solar and UV radiation. Another station is being set up in Recife-PE, completing a group of stations that are located between latitudes 8 and 10° and longitudes 34–38° W, representing the typical climate of the region. The daily values of G global and UV ultraviolet radiation (A + B) striking the horizontal plane in Pesqueira and Araripina during the time period (2008–2010) were measured, analyzed and compared. The collected data enabled the generation of three different statistical models for estimating the daily UV solar radiation from the daily global radiation: a) linear correlation between global and UV radiation (model 1), b) polynomial correction of the average fraction of UV irradiation, 〈F_UV〉 as a function of the transmittance index of global solar irradiation 〈K_T〉 (model 2) and c) the UV atmospheric transmittance index 〈K_TUV〉 is obtained by multiple regression of the air mass 〈m_r〉and 〈K_T〉 (model 3). Besides, they were modeled by two artificial neural networks: a) estimative of the (F_UV), considering the same physical variables of model 2 (model ANN1) and b) estimative of (K_TUV) from the same physical variables of model 3 (model ANN2). The statistical models and the artificial neural networks displayed a good statistical performance with RMSE% inferior to 5% and MBE between ?0.4%–2%. All the models can be used for estimating the UV radiation in places where there is only global irradiation data.     

Effect of sunshine and solar declination on the computation of monthly mean daily diffuse solar radiation

Several years of measured data for 17 European locations have been used to develop models for estimating monthly mean daily values of diffuse radiation (Hd) from combinations of the following: clearness index, sunshine fraction, and solar declination. Two models giving the highest correlation coefficients and the lowest standard errors of estimation are tested with data for 10 European locations not used in their development. From consideration of the MBE and RMSE values, a model which estimates Hd values from clearness index, relative sunshine duration and solar declination is found to be the most accurate. Comparison with Hd values predicted with the European Community solar radiation model (ECM) confirms this conclusion.     

Quality control of global solar radiation using sunshine duration hours

The aim of this study was to develop a new and automatic method for controlling the quality of daily global solar radiation, G_d, using sunshine duration hours. The new method has three levels of tests: first, G_d is compared against daily extraterrestrial radiation that is received on a horizontal surface (0.03×G_od?G_d<G_od); second, G_d should only exceed by a small amount of the daily clear sky irradiation that is observed under highly transparent clear skies (G_d<1.1G_cd); and third, the method uses a series of persistence checks that utilize the relation between daily global solar radiation and relative sunshine duration hours. The method is capable of identifying systematic and non-systematic errors and its ability has been shown in three different climates including semi-arid, coastal humid and very arid climates.     

Assessment of diffuse solar energy under general sky condition using artificial neural network

In this paper, artificial neural network (ANN) models are developed for estimating monthly mean hourly and daily diffuse solar radiation. Solar radiation data from 10 Indian stations, having different climatic conditions, all over India have been used for training and testing the ANN model. The coefficient of determination (R²) for all the stations are higher than 0.85, indicating strong correlation between diffuse solar radiation and selected input parameters. The feedforward back-propagation algorithm is used in this analysis. Results of ANN models have been compared with the measured data on the basis of percentage root-mean-square error (RMSE) and mean bias error (MBE). It is found that maximum value of RMSE in ANN model is 8.8% (Vishakhapatnam, September) in the prediction of hourly diffuse solar radiation. However, for other stations same error is less than 5.1%. The computation of monthly mean daily diffuse solar radiation is also carried out and the results so obtained have been compared with those of other empirical models. The ANN model shows the maximum RMSE of 4.5% for daily diffuse radiation, while for other empirical models the same error is 37.4%. This shows that ANN model is more accurate and versatile as compared to other models to predict hourly and daily diffuse solar radiation.     

A correlation for estimation of global solar radiation

We present a simple Ångstrom-type correlation for estimating the monthly average daily horizontal global radiation. We have developed this correlation using the bright sunshine and global radiation data of 48 locations around the world, with varied meteorological conditions and a wide distribution of geographical locations. Our study shows that this correlation provides good estimates of solar radiation. We have also statistically compared the performance of our correlation with Rietveld's equation, which is believed to be applicable anywhere in the world and has been found by Ma and Iqbal (1984) to give better estimates than other published correlations. Our correlation yields better estimates than Rietveld's equation for a majority of the stations considered.     

Validation of five global radiation models with measured daily data in China

Two sunshine based and three air temperature based global radiation models are calibrated using daily data in Jan. 1 1994–Dec. 31 1998 at 48 stations all over China. The Nash–Sutcliffe equation (NSE) is used as the model evaluation criterion. The sunshine based models are suitable for daily global radiation estimation. The averaged NSE value of the Angström model is 0.83, and the maximum value is 0.91. The maximum NSE value of the Bahel model is 0.92 with an averaged value of 0.84. The models that use air temperature as the input variable are not suitable for daily global radiation estimation in China. The averaged NSE values of the three air temperature based models (Bristow–Campbell model, Allen model and Hargreaves model) are not larger than 0.47. A logarithmic relationship between the daily global radiation/daily extra-terrestrial solar radiation (R_G/R_A) and the temperature difference between the maximum and minimum daily air temperature (T_M−T_m) is found in the present study. A new daily global radiation model that is a function of R_A, sunshine hours and T_M−T_m is designed, which gives an averaged NSE value of 0.85 and a maximum value of 0.92.     

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.     

Global solar radiation estimation from measurements of visibility and air temperature extremes

Solar radiation is the main source of energy for the survival of life and its associated activities. It is important to know accurate solar radiation value in areas such as agricultural activities, solar energy systems, heating, and meteorology. In this study, we present a model for the estimation of solar radiation value with other meteorological parameters in cases where solar radiation cannot be measured or not available. This model is based on the relationship between solar radiation and measured air temperature and visibility extremes. As is known, the incident global solar radiation is attenuated by clouds, aerosols, ozone layer, water vapor, etc.. In the model, the attenuation of the solar radiation is expressed by dew point temperature, visibility, and the maximum and minimum air temperatures. Dew-point temperature refers to the effect of water vapor on solar radiation, air temperature extremes are used to signify cloudiness. Visibility also gives the effect on the attenuation of solar radiation by air pollutants and aerosols in the model. The model was applied to the data taken from meteorological stations in Turkey. Error analysis was performed and compared with the models in the literature and satisfactory results were obtained.

Abbreviations H: Daily total global solar radiation, units of MJ ? m^?2 ? day^?1; H₀: Extraterrestrial solar radiation, units of MJ ? m^?2 ? day^?1; H_m: Measured daily total global solar radiation, units of MJ ? m^?2 ? day^?1; H_c: Calculated daily total global solar radiation, units of MJ ? m^?2 ? day^?1; T_min: Daily minimum temperature, units of °C; T_max: Daily maximum temperature, units of °C; RH: T_dew: Relative humidity, units of %rh; Dew-point temperature, units of °C     

Global,direct and diffuse solar radiation on horizontal and tilted surfaces in Jeddah,Saudi Arabia

The measured data of global and diffuse solar radiation on a horizontal surface, the number of bright sunshine hours, mean daily ambient temperature, maximum and minimum ambient temperatures, relative humidity and amount of cloud cover for Jeddah (lat. 21°42′37′′N, long. 39°11′12′′E), Saudi Arabia, during the period (1996–2007) are analyzed. The monthly averages of daily values for these meteorological variables have been calculated. The data are then divided into two sets. The sub-data set I (1996–2004) are employed to develop empirical correlations between the monthly average of daily global solar radiation fraction (H/H₀) and the various weather parameters. The sub-data set II (2005–2007) are then used to evaluate the derived correlations. Furthermore, the total solar radiation on horizontal surfaces is separated into the beam and diffuses components. Empirical correlations for estimating the diffuse solar radiation incident on horizontal surfaces have been proposed. The total solar radiation incident on a tilted surface facing south H_t with different tilt angles is then calculated using both Liu and Jordan isotropic model and Klucher’s anisotropic model. It is inferred that the isotropic model is able to estimate H_t more accurate than the anisotropic one. At the optimum tilt angle, the maximum value of H_t is obtained as ∼36 (MJ/m² day) during January. Comparisons with 22 years average data of NASA SSE Model showed that the proposed correlations are able to predict the total annual energy on horizontal and tilted surfaces in Jeddah with a reasonable accuracy. It is also found that at Jeddah, the solar energy devices have to be tilted to face south with a tilt angle equals the latitude of the place in order to achieve the best performance all year round.     

Global solar radiation estimation with sunshine duration in Tibet,China

Eight models using only the sunshine duration for estimating the global solar radiation on a horizontal surface are evaluated at Changdu, Geer, Lasa and Naqu stations in Tibet, China against the measured meteorological data during 1994–2008. Based on statistical error tests, results show that the simple linear Ångström–Prescott model is reasonably accurate in practice, and the modifications with complex expression are not necessary in Tibet. Then, two general Ångström–Prescott models for estimating the daily and monthly average daily global solar radiation respectively in Tibet are proposed.     

Diffuse solar radiation estimates from sunshine hours and clearness index for Karachi, Pakistan

Correlations for the estimation of monthly average daily diffuse solar radiation as a function of the sunshine hours and clearness index have been obtained from Karachi. Generally, two types of correlations are used: (a) diffuse radiation as a function of relative sunshine hours and extraterrestrial radiation, and (b) diffuse radiation as a function of global and extraterrestrial radiation. These correlations are mostly first- and second-order polynomials in the sunshine hours and clearness index, indicating the presence of the diffuse solar radiation component. The diffuse solar radiation shows a peak value during the monsoon months of July–August. The diffuse to global ratio is found to be 0.32 from the analysis, and the diffuse to extraterrestrial radiation ratio is nearly 0.19 throughout the year. Among the established relations, Iqbal and Stanhill overestimate the radiation value, while Liu and Jordan underestimate it.     

The potential of different artificial neural network (ANN) techniques in daily global solar radiation modeling based on meteorological data

The main objective of present study is to predict daily global solar radiation (GSR) on a horizontal surface, based on meteorological variables, using different artificial neural network (ANN) techniques. Daily mean air temperature, relative humidity, sunshine hours, evaporation, and wind speed values between 2002 and 2006 for Dezful city in Iran (32°16′N, 48°25′E), are used in this study. In order to consider the effect of each meteorological variable on daily GSR prediction, six following combinations of input variables are considered:

(I)

Day of the year, daily mean air temperature and relative humidity as inputs and daily GSR as output.

(II)

Day of the year, daily mean air temperature and sunshine hours as inputs and daily GSR as output.

(III)

Day of the year, daily mean air temperature, relative humidity and sunshine hours as inputs and daily GSR as output.

(IV)

Day of the year, daily mean air temperature, relative humidity, sunshine hours and evaporation as inputs and daily GSR as output.

(V)

Day of the year, daily mean air temperature, relative humidity, sunshine hours and wind speed as inputs and daily GSR as output.

(VI)

Day of the year, daily mean air temperature, relative humidity, sunshine hours, evaporation and wind speed as inputs and daily GSR as output.

Multi-layer perceptron (MLP) and radial basis function (RBF) neural networks are applied for daily GSR modeling based on six proposed combinations.The measured data between 2002 and 2005 are used to train the neural networks while the data for 214 days from 2006 are used as testing data.The comparison of obtained results from ANNs and different conventional GSR prediction (CGSRP) models shows very good improvements (i.e. the predicted values of best ANN model (MLP-V) has a mean absolute percentage error (MAPE) about 5.21% versus 10.02% for best CGSRP model (CGSRP 5)).     

Modeling of solar radiation using remote sensing and artificial neural network in Turkey

Artificial neural networks (ANNs) were used to estimate solar radiation in Turkey (26–45°E, 36–42°N) using geographical and satellite-estimated data. In order to train the Generalized regression neural network (GRNN) geographical and satellite-estimated data for the period from January 2002 to December 2002 from 19 stations spread over Turkey were used in training (ten stations) and testing (nine stations) data. Latitude, longitude, altitude, surface emissivity for ?_4, surface emissivity for ?_5, and land surface temperature are used in the input layer of the network. Solar radiation is the output. Root Mean Square Error (RMSE) and correlation coefficient (R²) between the estimated and measured values for monthly mean daily sum with ANN values have been found as 0.1630 MJ/m² and 95.34% (training stations), 0.3200 MJ/m² and 93.41% (testing stations), respectively. Since these results are good enough it was concluded that the developed GRNN tool can be used to predict the solar radiation in Turkey.     

Comprehensive study of solar conditions in Mozambique: the effect of trade winds on solar components

A new algorithm to simulate all solar components and optimum slopes, β_opt, based on new models for direct normal beam and diffuse radiation and an analytical model to predict β_opt, developed at the University of Botswana is applied for complete study of solar conditions in Mozambique. The components of solar radiation depend to a large extent on the number of h of sunshine. However, it is obvious that cloud-cover is determined mainly by the prevailing trade winds, which carry moisture and rain clouds. This is of especial concern in coastal areas. In the current work, hourly, I, daily, H and monthly mean, components of solar radiation and the optimum slopes of a north–south aligned collector are simulated and analyzed for 21 synoptic stations in Mozambique. Monthly mean daily direct normal, solar radiation maps are plotted for December and June and discussed. It is found that, to a great extent, isoinsolation curves are determined by the prevailing trade winds, mountain chains and coastal conditions. Plotted maps of annual mean daily direct normal and global solar radiation also show tremendous dependence on the prevailing winds. Several special locations in Mozambique with quite high or very low solar radiation components are pointed out and the reasons explained.