A physical rationale for generalized Ångström-Prescott regression

The transparency of the terrestrial atmosphere has been related to the relative sunshine duration ever since the seminal work of Ångström [Ångström, A., 1924. Solar and terrestrial radiation. Q. J. Roy. Meteor. Soc. 50, 121-126]. Modified by Prescott [Prescott, J.A., 1940. Evaporation from water surface in relation to solar radiation. Trans. Roy. Soc. Austr. 40, 114-116], linear Ångström-Prescott regression has seen world-wide application in investigations concerned with solar irradiance of the surface at specific sites. Extensions of the linear formula to higher orders have been suggested as better suited in certain cases. A drawback of this kind of regressional modeling has been the lack of a clear link between the empirical formulae and the theory of radiative transfer. The coefficients involved are usually interpreted on an ad hoc basis. In the present work, a rationale for deriving and interpreting a polynomial relation between ground-level solar irradiance and relative sunshine duration is proposed.     

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.     

Quality control and estimation of global solar radiation in China

Measurements of surface radiation in China are too sparse to meet demand for scientific research and engineering applications. Moreover, the radiation data often include erroneous and questionable values though preliminary quality-check has been done before the data release. Therefore, quality control of radiation data is often a prerequisite for using these data. In this study, a set of quality-check procedures were implemented to control the quality of the solar radiation measurements at 97 stations in China. A hybrid model for estimating global solar radiation was then evaluated against the controlled data. The results show that the model can estimate the global radiation with accuracy of MBE less than 1.5 MJ m⁻² and RMSE less than 2.8 MJ m⁻² for daily radiation and RMSE less than 2.0 MJ m⁻² for monthly-mean daily radiation at individual stations over most of China except at a few stations where unsatisfactory estimates were possibly caused by severe air pollution or too dense clouds. The MBE averaged over all stations are about 0.7 MJ m⁻² and RMSE about 2.0 MJ m⁻² for daily radiation and RMSE about 1.3 MJ m⁻² for monthly-mean daily radiation. Finally, this model was used to fill data gaps and to expand solar radiation data set using routine meteorological station data in China. This data set would substantially contribute to some radiation-related scientific studies and engineering applications in China.     

Estimation of monthly global solar radiation from sunshine duration measurement in Elazi

In this study, the relation between a and b terms and / was investigated to estimate the global solar radiation in Elazi by using different regression analyses. Equations which contain the whole year and two different periods, winter and summer, were developed. Eqs. (5)–(7) which represent second, third and fourth degree equations respectively, gave the best results in all of the equations having an error less than 1%. Contrary to expectations, the equations developed for summer and winter periods had higher errors than the others.     

Models of solar radiation with hours of bright sunshine: A review

In the design and study of solar energy, information on solar radiation and its components at a given location is very essential. Solar radiation data are required by solar engineers, architects, agriculturists and hydrologists for many applications such as solar heating, cooking, drying and interior illumination of buildings. For this purpose, in the past, several empirical correlations have been developed in order to estimate the solar radiation around the world. The main objective of this study is to review the global solar radiation models available in the literature. There are several formulate which relate global radiation to other climatic parameters such as sunshine hours, relative humidity and maximum temperature. The most commonly used parameter for estimating global solar radiation is sunshine duration. Sunshine duration can be easily and reliably measured and data are widely available.     

The sun’s total and spectral irradiance for solar energy applications and solar radiation models

Using the most recent composite time series of total solar irradiance spaceborne measurements, a solar constant value of 1366.1 W m⁻² is confirmed, and simple quadratic expressions are proposed to predict its daily value from the Zurich sunspot number, the MgII index, or the 10.7 cm radio flux index. Whenever these three indices are available on a daily basis (since 1978), it is possible to predict the sun’s irradiance within 0.1% on average, as accurately as current measurements.Based on this value of the solar constant, an improved approximation of the extraterrestrial solar spectrum from 0 to 1000 μm is proposed. It is obtained by dividing the spectrum into nine bands and selecting representative (and recent) spectra, as well as appropriate scaling coefficients for each band. Comparisons with frequently used spectra are discussed, confirming previous findings of the literature.This synthetic and composite spectrum is proposed at 0.5-nm intervals in the UV (280–400 nm), 1-nm intervals between 0–280 and 400–1705 nm, 5-nm intervals between 1705 and 4000 nm, and progressively larger intervals beyond 4 μm, for a total of 2460 wavelengths.     

Statistical analysis of solar measurements in Algeria using beta distributions

A method of smoothing solar data by beta probability distributions is implemented in this paper. In the first step, this method has been used to process daily sunshine duration data recorded at thirty-three meteorological stations in Algeria for eleven year periods or more. In the second step, it has been applied to hourly global solar irradiation flux measured in Algiers during the 1987/89 period. For each location and each month of the year, beta probability density functions fitting the monthly frequency distributions of the daily sunshine duration measurements are obtained. Both the parameters characterising the resulting beta distributions are then mapped, enabling us to build the frequency distributions of sunshine duration for every site in Algeria. In the case of solar radiation for Algiers, the recorded data have been processed following two different ways. The first one consists in sorting the hourly global solar irradiation data into eight typical classes of the daily clearness index. The second one is based on the repartition of these data per month. The results of the first classification show that for each class of daily clearness index, the hourly data under consideration are modelled by only one beta distribution. When using the second classification, linear combinations of two beta distributions are found to fit the monthly frequency distributions of the hourly solar radiation data.     

Solar position algorithm for solar radiation applications

There have been many published articles describing solar position algorithms for solar radiation applications. The best uncertainty achieved in most of these articles is greater than ±0.01° in calculating the solar zenith and azimuth angles. For some, the algorithm is valid for a limited number of years varying from 15 years to a hundred years. This report is a step by step procedure for implementing an algorithm to calculate the solar zenith and azimuth angles in the period from the year −2000 to 6000, with uncertainties of ±0.0003°. The algorithm is described in a book written by Jean Meeus in 1998. This report is written in a step by step format to simplify the complicated steps described in the book, with a focus on the sun instead of the planets and stars in general. It also introduces some changes to accommodate for solar radiation applications. The changes include changing the direction of measuring azimuth angles to be measured from north and eastward instead of being measured from south and eastward, and the direction of measuring the observer’s geographical longitude to be measured as positive eastward from Greenwich meridian instead of negative. This report also includes the calculation of incidence angle for a surface that is tilted to any horizontal and vertical angle, as described by Iqbals in 1983.     

Quality control of solar radiation data within the RMIB solar measurements network

Assessment of the solar resource is based upon measured data, where available. However, with any measurement there exist errors. Consequently, solar radiation data do not exhibit necessarily the same reliability and it often happens that users face time series of measurements containing questionable values though preliminary technical control has been done before the data release. To overcome such a situation, a major effort has been undertaken at the Royal Meteorological Institute of Belgium (RMIB) to develop procedures and software for performing post-measurement quality control of solar data from the radiometric stations of our in situ solar monitoring network. Moreover, because solar energy applications usually need continuous time series of solar radiation data, additional procedures have also been established to fill missing values (data initially lacking or removed via quality checks).     

Empirical correlations as a means for estimating monthly average daily global radiation: A critical overview

In regions where solar energy is abundant, solar energy can play a vital role in attaining energy sustainability. Sizing solar energy systems requires the availability of solar radiation data on horizontal surface which can then be used to calculate solar radiation intensity on any tilted surface using appropriate conversion factors or formula. In many parts of the world, especially in developing countries, such data is not readily available. Many researchers have found that monthly average daily value of global solar radiation on horizontal surface can be estimated when meteorological parameters such as duration of sunshine, number of rainy days, relative humidity, etc. are available. Many empirical correlations have been developed based on this approach. The development of such a correlation has been made possible through the availability of solar and other meteorological data required for their validation. This paper presents a review on the existing empirical correlations and critically looks at the practicality of such correlations. This raises the question on the appropriateness of the past and present approaches adopted by researchers in this field. The paper also discusses various related aspects and proposes new directions for future research.     

Stochastic approach for daily solar radiation modeling

Mathematical modeling of solar radiation continues to be an important issue in renewable energy applications. In general, existing models are mostly empirical and data dependent. In this paper, a novel approach for solar radiation modeling is proposed and illustrated. The proposed application consists of hidden Markov processes, which are widely used in various signal processing topics including speech modeling with successful results. In the experimental work, mean of hourly measured ambient temperature values are considered as observations of the model, whereas mean of hourly solar radiation values are considered as the hidden events, which constitute the outcomes of the proposed mathematical model. Both solar radiations and temperatures are converted to quantized number of states. Finally, after a training stage that forms the transition probability values of the described states, the hidden Markov model parameters are obtained and tested. The tests are repeated for various numbers of states and observations are presented. Plausible modeling results with distinct properties in terms of accuracy are achieved.     

Reference luminous solar constant and solar luminance for illuminance calculations

A recently proposed extraterrestrial solar spectrum is used to derive reference values of the luminous solar constant. Two slightly different photopic curves, CIE’s V(λ) and V_M(λ), are used for the needed convolution with the spectrum. A historical perspective about these two curves is presented, with the conclusion that both curves can be useful, depending on application. Two reference values (one for each photopic curve) for the luminous solar constant, the Sun’s luminous efficacy and the average Sun’s luminance are proposed, consistent with the most recent determination of the solar constant. Comparisons are made with earlier determinations of these quantities, as well as of the average Sun’s radiance and the Sun’s effective temperature.     

Computation of monthly mean daily global solar radiation in China using artificial neural networks and comparison with other empirical models

In this paper, an artificial neural network (ANN) model is developed for estimating monthly mean daily global solar radiation of 8 typical cities in China. The feed-forward back-propagation algorithm is applied in this analysis. The results of the ANN model and other empirical regression models have been compared with measured data on the basis of mean percentage error (MPE), mean bias error (MBE) and root mean square error (RMSE). It is found that the solar radiation estimations by ANN are in good agreement with the measured values and are superior to those of other available empirical models. In addition, ANN model is tested to predict the same components for Kashi, Geermu, Shenyang, Chengdu and Zhengzhou stations over the same period. Data for Kashi, Geermu, Shenyang, Chengdu and Zhengzhou are not used in the training of the networks. Results obtained indicate that the ANN model can successfully be used for the estimation of monthly mean daily global solar radiation for Kashi, Geermu, Shenyang, Chengdu and Zhengzhou. These results testify the generalization capability of the ANN model and its ability to produce accurate estimates in China.     

A simple model for estimating monthly mean daily sums of solar irradiation and its local distribution

This paper deals with linear correlations between solar irradiation sums and sunshine duration for mapping global, diffuse and direct irradiation. All values represent long-term averages of monthly mean daily sums. The first part of this paper describes a set of fourteen correlation equations based on an earlier study. The constants of all correlations depend on a common numerical triple that describes the climatic conditions. The constants, correlation coefficients and the triple are determined and discussed with reference to the example of two stations in the Federal Republic of Germany. In the second part, a general method for generating solar irradiation maps is proposed and applied for the state of North-Rhine Westphalia (FRG). The distribution of global and diffuse irradiation in terms of yearly averages is shown and discussed. © 1997 John Wiley & Sons, Ltd.     

Development of a method for generating operational solar radiation maps from satellite data for a tropical environment

Despite a considerable number of publications which use satellite data to map solar radiation, relatively few studies have been undertaken in a tropical environment. In this study, we have developed a method to produce operational solar radiation maps from satellite data for this environment. The method is based on a physical model which relates the satellite-derived earth–atmospheric reflectivity from visible channel of GMS-4 and GMS-5 to the transmissivity of the atmosphere. Cloud reflectivity was determined from satellite data, while radiation absorbed by water vapour, ozone and aerosols and radiation scattered by aerosols were determined from ground-based meteorological data. Techniques for determining the radiation depleted by these atmospheric constituents over a whole country were also presented. Satellite data of a six-year period (1993–1998) with approximately ten thousand satellite images were used to construct the maps. When tested against an independent data set, monthly average of daily global irradiation calculated from this method agree with that obtained from the measurements with the relative root mean square difference of 6.8% with respect to the mean values. Solar radiation is presented as twelve maps showing the monthly average of global irradiation and one map showing the yearly average of global irradiation. Radiation patterns from the maps show a strong influence of the tropical monsoons.     

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.     

On the effects of solar radiation variations on solar heating system performances

The effect of solar radiation availability on the performance of different solar heating systems has been studied. The systems include a solar water heater, passive solar houses and district solar heating systems with seasonal heat storage. Also, different collector orientations and collector types have been investigated. The hourly radiation data were generated by a simple computational simulation procedure. It was found that district solar heating systems with concentrating collectors and passive solar houses showed the largest variations for the given conditions.     

A method of determining the time constant of the flat-plate solar collector

Analysis of the flat-plate solar water heating system indicates that the transient response of the system is determined by the time constants of the solar collector and storage tank. The time constants are dependent on the thermal capacitances and heat loss coefficients of the collector and storage tank and on the capacitance rate of the circulating liquid. This paper presents a method of determining the time constants of the system from test results on a solar simulator.     

An application of the multilayer perceptron: Solar radiation maps in Spain

In this work an application of a methodology to obtain solar radiation maps is presented. This methodology is based on a neural network system [Lippmann, R.P., 1987. An introduction to computing with neural nets. IEEE ASSP Magazine, 4–22] called Multi-Layer Perceptron (MLP) [Haykin, S., 1994. Neural Networks. A Comprehensive Foundation. Macmillan Publishing Company; Hornik, K., Stinchcombe, M., White, H., 1989. Multilayer feedforward networks are universal approximators. Neural Networks, 2(5), 359–366]. To obtain a solar radiation map it is necessary to know the solar radiation of many points spread wide across the zone of the map where it is going to be drawn. For most of the locations all over the world the records of these data (solar radiation in whatever scale, daily or hourly values) are non-existent. Only very few locations have the privilege of having good meteorological stations where records of solar radiation have being registered. But even in those locations with historical records of solar data, the quality of these solar series is not as good as it should be for most purposes. In addition, to draw solar radiation maps the number of points on the maps (real sites) that it is necessary to work with makes this problem difficult to solve. Nevertheless, with the application of the methodology proposed in this paper, this problem has been solved and solar radiation maps have been obtained for a small region of Spain: Jaén province, a southern province of Spain between parallels 38°25′ N and 37°25′ N, and meridians 4°10′ W and 2°10′ W, and for a larger region: Andalucía, the most southern region of Spain situated between parallels 38°40′ N and 36°00′ N, and meridians 7°30′ W and 1°40′ W.     

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.