Statistical comparison of solar radiation correlations Monthly average global and diffuse radiation on horizontal surfaces

For most solar energy applications, it is necessary to predict the amount of global and diffuse radiation arriving on a horizontal surface at any specified location. Scientists have developed methods to achieve this using different input parameters. The purpose of this study is to compare statistically correlations for estimating the monthly average daily global/diffuse radiation incident on a horizontal surface and to recommend one in each catagory that best fits measured data from a number of locations chosen and is the simplest to use. The effects of using the new solar constant of 1367 W⁻² in these correlations are also investigated. As a result, Rietveld's and Page's correlations are recommended for estimating monthly average daily global and diffuse radiation incident on a horizontal surface, respectively. In addition, these correlations seem to be just as accurate with the new solar constant.     

Monthly average solar radiation in panama—Daily and hourly relations between direct and global insolation

Regressions are developed to estimate daily global and direct radiation and the hourly distribution of direct radiation for Barro Colorado Island, Panama from monthly mean values observed 35 km away at Chiva-Chiva. The ratio model of Liu and Jordan and the logarithmic model of Anderson for estimating direct from global radiation are compared. Both gave satisfactory results after accounting for “seasonal” variation, but the ratio model was preferred in this case for the smaller number of separate regressions required. The ratio model fitted for diffuse radiation at Chiva-Chiva agreed closely with regressions for stations at similar latitude. For a given value of the clearness index, the direct component of solar radiation was relatively (but not absolutely) reduced during the dry season compared with the wet season. A likely explanation for this unexpected result is increased marine and terrestrial aerosol during the dry season when offshore winds are stronger and burning of crop and wasteland occurs. The models of Whillier and of Garnier and Ohmura, which assume constant atmospheric transmittance throughout the day, gave unsatisfactory fits to the hourly distribution of direct radiation. They were also unable to mimic an observed morning/afternoon asymmetry that was strongest in the wet season. Hourly direct radiation was accurately estimated from hourly global radiation by quadratic polynomials fitted separately to the morning and afternoon data. The resulting regressions will enable estimation of radiation in forest understory from measurements of insolation in the open by computerized image analysis of hemispherical canopy photos.     

Prediction of hourly diffuse solar radiation from measured hourly global radiation on a horizontal surface

A statistical procedure has been employed to develop correlations between the hourly global horizontal radiation and its diffuse component. Several years', hourly radiation data from three Canadian stations and two French stations have been employed for this purpose. The relationships have been developed in dimensionless form which predict for particular solar altitudes when is given.Under heavily cloudy conditions or when the sky is completely covered ( ), diffuse radiation increases linearly with the global radiation. In this region, solar altitude has no bearing on the fraction of diffuse radiation.As goes beyond 0.35, the effect of solar altitude begins to appear and the region immediately following this may be considered as partly-cloudy-skies conditions. In the beginning of this region, the diffuse component increases briefly with the increase in global radiation and then begins to decrease as the partly cloudy skies become clearer. At particular solar altitudes, a minimum value of the diffuse radiation is reached. The value of where reaches its minimum value varies with solar altitude.The region beyond which a minimum value of is reached may be considered as mainly-clear-sky conditions. In this region, increases again with , lower solar altitudes giving a higher percentage of diffuse radiation.Under partly cloudy skies and under clear skies, solar altitudes lower than 30° had a marked effect on the fraction of diffuse radiation. However, solar altitudes greater than 30° had minimal influence on the fraction of diffuse radiation.     

Monthly and yearly average maps of total and direct solar radiation in Turkey

Total and direct solar radiation are calculated using the bright sunshine hours measurements from 83 stations over Turkey. The results are presented in the form of monthly and yearly mean maps. The values associated with the isoradiation lines, which pass throughout the frontiers of the country, are compared with the results obtained in some neighbourhood countries.     

A comparison of methods for estimating hourly diffuse solar radiation from global solar radiation

Four methods of estimating hourly diffuse irradiation from hourly global irradiation are compared, using global and diffuse irradiation data from the Australian Bureau of Meteorology for five widely separated Australian locations. A development of one of these methods with constants derived from the data for each place is found to perform best when judged on a criterion of absolute error, and this performance in maintained when constants averaged over the five locations are used. The derived constants are also given for all other Australian locations for which both global and diffuse data are available, and a method is suggested for deriving suitable values of the constants for places situated between 20° and 45° S for which only global radiation data are available. A previously reported dependence of the proportion of diffuse radiation on latitude is demonstrated.     

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°.     

Time series analysis of hourly global horizontal solar radiation

Accurate design and optimization of short response time solar energy systems with storage are sensitive to the stationary and sequential characteristics of hourly solar radiation. We perform monthly time series analyses of hourly global horizontal solar radiation for a wide range of climatic stations that span temperate and tropical conditions. The stationary statistics for individual hours are found to be very similar to the corresponding results for daily total global horizontal radiation, in keeping with a related fundamental observation of Liu & Jordan. Investigation of sequential properties shows that autocorrelation coefficients are, to a good approximation, independent of time of day and that persistence times are nearly as long as the entire daylight period, mainly due to the effect of very strong correlations at one-hour lag times. The isolated effect of two-hour and longer lag times, via the partial autocorrelation coefficients, is found to be negligible in most, but by no means all, instances. Finally, we find no universal correlation between hourly autocorrelation coefficients and monthly average radiation figures.     

Stochastic simulation model of hourly total solar radiation

A stochastic simulation model of hourly global solar radiation is presented in this paper. It is developed by introducing the concept of “time dependent frequency distribution” (TDFD) of hourly insolation values. In this model the two most critical aspects of time series simulation, i.e., the reproduced time series values which have the appropriate time dependent frequency distribution for the parameter being simulated and the correlation between successive values, are taken into account. The elimination of the TDFD of the data and the transformation of the data distribution to a Gaussian distribution (required for the stationary time series analysis) were carried out using a mapping technique. The autocorrelation function of the transformed data showed that the produced time series is stationary. Then, an antimapping coefficient matrix is developed, which provides a simple yet an effective simulation device. The described model has been applied in Athens (Greece) where hourly insolation data covering a period of two years are used. The theoretical results obtained using this simulation model, regarding both the TDFD and the correlation, are in agreement with the measured data.     

Comparative study of various correlations in estimating hourly diffuse fraction of global solar radiation

Proper design and performance predictions of solar energy systems require accurate information on the availability of solar radiation. The diffuse-to-global solar radiation correlation, originally developed by Liu and Jordan, has been extensively used as the technique providing accurate results, although it is latitude dependent. Thus, in the present study, empirical correlations of this type were developed to establish a relationship between the hourly diffuse fraction (k_d) and the hourly clearness index (k_t) using hourly global and diffuse irradiation measurements on a horizontal surface performed at Athalassa, Cyprus. The proposed correlations were compared against 10 models available in the literature in terms of the widely used statistical indicators, rmse, mbe and t test. From this analysis, it can be concluded that the proposed yearly correlation predicts diffuse values accurately, whereas all candidate models examined appear to be location-independent for diffuse irradiation predictions.     

Estimating monthly average daily diffuse solar radiation with multiple predictors: A case study

Solar radiation measurements are not easily available, especially for the diffuse solar radiation. In this study, two models for estimating the diffuse solar radiation are proposed based on multiple predictors including the clearness index, relative sunshine duration, ambient temperature and relative humidity. One of them aims to increase the estimation accuracy, and the other aims to estimate the diffuse solar radiation direct from other meteorological elements in the absence of the global solar radiation. For a case study, the performance of the proposed models is validated by comparing with eight existing models selected from literature against the measured data at Guangzhou station in China. Through the analysis based on statistical error tests, results show that the two models can estimate the monthly average daily diffuse solar radiation with good accuracy.     

The diffuse fraction of hourly solar radiation for Amman/Jordan

This paper presents various correlations of the hourly clearness index K_t with the hourly diffuse fraction K_d on a horizontal surface for Amman/Jordan. The first correlation is based on Orgill and Hollands method, but using weighted averages. The second correlation is based on hourly integrated values of K_t's and K_d's without any grouping. A refinement of the latter correlation is attempted by including a random shock.     

Computing diffuse fraction of global horizontal solar radiation: A model comparison

For simulation-based prediction of buildings’ energy use or expected gains from building-integrated solar energy systems, information on both direct and diffuse component of solar radiation is necessary. Available measured data are, however, typically restricted to global horizontal irradiance. There have been thus many efforts in the past to develop algorithms for the derivation of the diffuse fraction of solar irradiance. In this context, the present paper compares eight models for estimating diffuse fraction of irradiance based on a database of measured irradiance from Vienna, Austria. These models generally involve mathematical formulations with multiple coefficients whose values are typically valid for a specific location. Subsequent to a first comparison of these eight models, three better performing models were selected for a more detailed analysis. Thereby, the coefficients of the models were modified to account for Vienna data. The results suggest that some models can provide relatively reliable estimations of the diffuse fractions of the global irradiance. The calibration procedure could only slightly improve the models’ performance.     

Comparative study of various models in estimating hourly diffuse solar irradiance

This work presents a comparison among seventeen different proposals for estimating the hourly diffuse fraction of irradiance. Twelve of them are polynomial correlations of different orders, two are based on a logistic function and the three last ones consider the diffuse irradiance values in the previous and posterior hour to that of the calculation. In general, the proposals showing the more favourable statistics indexes are those that consider the process dynamics, as they behave better than the rest of the models even when the polynomial correlations and the logistic function are calibrated for the experimental data used in this work.The models Dirint and BRL are the ones recommended for the data of this study, as they exhibit the highest precision and generate a series of hourly diffuse irradiance values of which the distribution functions are very similar to those of the experimental data.     

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.     

A model for the diffuse fraction of hourly global radiation

Hourly values of diffuse and beam irradiance are often required in cases where, at best, only global irradiance is available. For use in the evaluation of the climatological potential for solar energy utilization in Norway, an analytical model is proposed expressing the hourly diffuse fraction of global irradiance in terms of hourly solar elevation and clearness index. This model, developed for average snow-free close to sea level conditions in Norway, fairly well fits the average picture of an extensive independent data base.     

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.     

Techniques for the precise estimation of hourly values of global, diffuse and direct solar radiation

The method usually used to compute solar radiation, when no measured data are available, is the well-known regression technique relating mean daily totals of global and diffuse solar radiation with the mean duration of sunshine. Using this method and taking into account the first order multiple reflections between the ground and the atmosphere, regression parameters were obtained from the monthly mean values of daily totals of global solar radiation and sunshine at a network of 16 stations in India. Daily values of global and diffuse solar radiation were then computed for 121 stations, where sunshine data are available for periods of 6–28 yr, using interpolated values of the regression parameters. Where no sunshine data were available, global and diffuse solar radiation were computed from cloud observations, using the inverse relationship between sunshine and cloudiness. Further, using the empirical relationship between daily totals and the corresponding hourly values of global and diffuse solar radiation, two sets of curves were prepared valid for the whole country, using which mean hourly values of global and diffuse radiation could be deduced from the corresponding daily totals, with a high degree of accuracy. The paper discusses the validity of the techniques used for computing daily and hourly values of global and diffuse solar radiation from sunshine and cloud amounts at an extended network of 145 stations in India and stresses the fact that such techniques are successful, only if accurate data on both radiation and sunshine are available at a widely distributed network of stations for a minimum period from at least 5 to 6 yr, using carefully calibrated and well-maintained instruments of the required quality. Theoretical models have also been used to compute clear sky noon values of global, diffuse and direct solar radiation from the solar constant, allowing for attenuation by atmospheric constituents such as ozone, water vapour, dust and aerosols. Using a simple model, calculations of global and diffuse solar radiation on clear days were made for 145 stations from values of the solar constant and measured values of ozone, water vapour and atmospheric turbidity. A method of extending the technique to overcast skies and partly clouded skies is discussed. The values of the mean annual transmission factor for global solar radiation under cloud-free conditions using the two methods show excellent agreement and establishes the soundness of the regression technique on one hand and the reliability of the theoretical model used for computing clear sky radiation, on the other.     

Evaluation and comparison of hourly solar radiation models

In this paper, an attempt has been made to develop a new model to evaluate the hourly solar radiation for composite climate of New Delhi. The comparison of new model for hourly solar radiation has been carried out by using various model proposed by others. The root mean square error (RMSE) and mean bias error (MBE) have been used to compare the accuracy of new and others model. The results show that the ASHRAE and new proposed model estimate hourly solar radiation better for composite climate of New Delhi in comparison to other models. Hourly solar radiation estimated by constants obtained by new model (modified ASHRAE model) for composite climate of India is fairly comparable with measured data. The percentage mean bias error with new constants for New Delhi was found as low as 0.15 and 0% for hourly beam and diffuse radiation, respectively. There is a 1.9–8.5% RMSE between observed and predicted values of beam radiation using new constants for clear days. The statistical analysis has been used for the present study. Copyright © 2008 John Wiley & Sons, Ltd.