Attenuation of solar radiation in the atmosphere

This paper presents the results of measurements of the solar radiant energy absorbed and scattered in the atmosphere. Since much of the information on solar irradiance at the ground is obtained by computation from extraterrestrial radiation data, it is important to know precisely the actual energy that is absorbed and scattered in its passage through the atmosphere for the accurate estimation of the radiant energy received at the ground. Various models exist for the estimation of daily totals of global solar radiation under clear sky and cloudy conditions, taking these effects into consideration and assuming average values for the ozone and water vapour content and the turbidity of the atmosphere. In the present investigation atmospheric attenuation of solar radiation has been calculated from measured values of ozone and water vapour content and turbidity in the atmosphere, at two stations Bangalore (950 metres above sea level) and Nandi Hills (1479 masl). Direct measurements of direct solar radiation for the whole spectrum and various spectral regions were made at Bangalore and Nandi using Ångström pyrheliometers fitted with broad-band pass filters during the clear months January–May 1979. Global solar radiation and sunshine duration measurements were also made at both stations. Using direct measurements of the total ozone and water vapour content and atmospheric turbidity, direct, diffuse and global solar radiation values at the ground were computed from extraterrestrial values of radiation for clear sky conditions. The results are compared with actual measurements and earlier observations of direct solar radiation at other high-level stations. The importance of atmospheric turbidity measurements in the computation of solar radiation is discussed.     

Dependence on cloudiness and solar altitude of global solar radiation received at 315 and 545 nm on horizontal surfaces

The study of monthly mean half hourly values of global radiation received at 315 (u.v.) and 545 nm (green) on a horizontal surface at Uccle (Belgium) in 1980 for clear (half hourly sunshine fraction σ = 1) and overcast (σ = 0) skies shows that for any solar altitude, global radiation received at 315 nm is less absorbed by clouds than radiation received at 545 nm. An explanation is given of the dependence on solar altitude for clear skies of the ratio between monthly mean half hourly values of global radiation received at both wavelengths, based on considerations concerning the direct and diffuse components.     

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.     

Computation of solar radiation from observations of cloud cover

Techniques of computation of global and diffuse solar radiation from the daily duration of bright sunshine and cloud cover are well-known. However, since radiation computations from cloud cover data provide rather imprecise results, this method is resorted to only when sunshine data are not available. To obtain a better idea of the inverse relationship between the long-term averages of sunshine duration and total cloud cover, an analysis of the monthly mean values of the fraction of the sky C, covered by clouds of all types and the duration of bright sunshine, n, was carried out. The relationship between C and (1−n/N′), where N′ is the maximum possible hours of sunshine, was found to be non-linear. The shape of the regression line connecting the two parameters also shows that ground observations of cloud cover always tend to be overestimates. The differences between such estimates and cloud cover values derived from sunshine duration tend to become zero when skies are either clear or overcast and are a maximum for cloud cover values in the range 0.4–0.7. A cubic regression equation was derived relating C and (1−n/N′) and using this relationship, it has been possible to compute sunshine duration from cloud cover data to an accuracy of about 4–7 per cent and from the cloud derived sunshine data, to compute monthly mean values of global solar radiation to an accuracy of about 6–10 per cent and diffuse solar radiation within an accuracy of about 10–15 per cent.     

The estimation of global and sky radiation in Austria

For obtaining the radiation values necessary for utilization of solar energy at as much possible locations in Austria, the monthly sums of global radiation at the horizontal surface are estimated after Angström from the relative duration of sunshine using the extraterrestrial radiations as maximum values. The thereby needed constants, which were evaluated for 19 stations in Austria with synchronous measurements of global radiation and duration of sunshine, are stated for the seasons as functions of altitude above sea level. The sky radiation is estimated by means of relationships after Liu-Yordan. These relationships were evaluated from the longterm measurements of global- and sky radiation at three stations in Austria for the mean monthly sums and for the mean hourly sums.     

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°.     

CLEAR SKY SOLAR INSOLATION DATA FOR ISLAMABAD

Monthly mean values of both integrated and instantaneous clear sky solar radiation components for Islamabad territory are presented and discussed. The components include global normal, direct normal, global horizontal, direct and diffuse horizontal radiations, sunshine duration, number of clear days and ambient temperature for solar energy applications. Direct normal irradiance values are used to get clear sky sunshine duration by ab-initio. The need for replacing the conventional sunshine recorder is discussed.     

Solar radiation on tilted south oriented surfaces: validation of transfer-models

Three transfer-models in use for estimating solar radiation on tilted surfaces are tested. A 12 year series of hourly global, diffuse, and reflected solar irradiation measured with horizontal pyranometers as well as hourly global solar irradiation measured with tilted south oriented pyranometers is available. One model uses daily irradiation, the other two use hourly irradiation. The models converting hourly solar irradiation on a horizontal surface to a tilted surface yield better results than that using daily irradiation. The best results are gained if pairs of hourly global and diffuse solar irradiation are available. The root mean square errors exceed 10% only if the sky is covered by more than 85% with clouds or if the solar elevation angle is less than 10°.     

Estimates of the Linke turbidity factor over Zimbabwe using ground-measured clear-sky global solar radiation and sunshine records based on a modified ESRA clear-sky model approach

This paper describes a procedure that can be used to calculate values for Linke atmospheric turbidity factors at air mass 2 (TL2) over Zimbabwe. Ground measured daily global solar radiation on clear days over 3years is used to evaluate TL2 for those stations that measure global radiation. The evaluation makes use of the clear-sky model of the European Solar Radiation Atlas (ESRA) combined with a diffuse transmittance model developed in the study. For those stations that do not measure global radiation but have sunshine duration records, global radiation values are generated through Angstrom type regression coefficients between the clearness index and relative sunshine duration. The TL2 values that are generated from the ESRA model are higher than those obtained from the study model (root mean square error (RMSE) up to 1.0 Turbidity Units). When compared to TL2 values from this study, the worldwide database SoDA, give significantly higher TL2 values (RMSE up to 2.2 Turbidity Units), underlining the value addition obtained in using measurement derived values in place of SoDA values.The values obtained from the study may be used to yield better estimates of clear-sky solar radiation for Zimbabwe. A better estimate of the clear-sky solar radiation will in turn improve the accuracy of the global radiation estimates from satellite based methods.     

A brief review of models for computing solar radiation on inclined surfaces

Modelling of solar energy systems requires estimation of the hourly radiation incident on surfaces of different tilts and orientations. Most meteorological stations report radiation values on a daily rather than hourly basis. Again, the value of the diffuse component may or may not be reported. Hence, different strategies may be encountered, for each location, with the common goal of computing hourly radiation on inclined surfaces.

In this study, five different schemes are presented to achieve this goal. In each scheme, certain correlations are required which are discussed in detail. The study is divided into five sections, each dealing with a specific type of correlation. These sections are: (i) correlations between daily diffuse and global radiation; (ii) correlations between hourly/daily global radiation; (iii) correlations between hourly/daily diffuse radiation; (iv) correlations between hourly diffuse and global radiation; and (v) models for computing diffuse sky radiation on inclined surfaces. The last section deals extensively with the anisotropic nature of sky diffuse radiation.

The important aspects of all correlation studies are highlighted, and the relative merits and demerits of their results are brought to light.

Mathematical expressions, where available, for models/correlations are provided so that the reader will have access to a comprehensive study. This information should be useful for modelling purposes in which computation of radiation on surfaces of different orientations and tilts is required.     

Estimation of direct illuminance on a horizontal surface for clear and intermediate skies

In the present work two simple models have been obtained which may be used to estimate mean hourly direct illuminance for clear skies as a function of solar elevation. Also a simple model has been developed valid for all sky conditions when direct illuminance is available, that is, clear and intermediate skies, using solar elevation and brightness index as input parameters. The sky conditions are defined by the clearness index and the brightness index, both calculated from solar irradiances.     

Generation of synthetic daily global solar radiation data based on ERA-Interim reanalysis and artificial neural networks

Four variables (total cloud cover, skin temperature, total column water vapour and total column ozone) from meteorological reanalysis were used to generate synthetic daily global solar radiation via artificial neural network (ANN) techniques. The goal of our study was to predict solar radiation values in locations without ground measurements, by using the reanalysis data as an alternative to the use of satellite imagery. The model was validated in Andalusia (Spain), using measured data for nine years from 83 ground stations spread over the region. The geographical location (latitude, longitude), the day of the year, the daily clear sky global radiation, and the four meteorological variables were used as input data, while the daily global solar radiation was the only output of the ANN. Sixty five ground stations were used as training dataset and eighteen stations as independent dataset. The optimum network architecture yielded a root mean square error of 16.4% and a correlation coefficient of 94% for the testing stations. Furthermore, we have successfully tested the forecasting capability of the model with measured radiation values at a later time. These results demonstrate the generalization capability of this approach over unseen data and its ability to produce accurate estimates and forecasts.     

Estimation of monthly mean daily diffuse radiation in China

In this study, several equations are employed to estimate monthly mean daily diffuse solar radiation for eight typical meteorological stations in China. Estimated values are compared with measured values in terms of statistical error tests such as mean percentage error (MPE), mean bias error (MBE), root mean square error (RMSE). All the models fit the data adequately and can be used to estimate monthly mean daily diffuse solar radiation from global solar radiation and sunshine hours. This study finds that the quadratic model performed better than the other models:     

Estimation of solar radiation from Australian meteorological observations

A carefully prepared set of Australian radiation and meteorological data was used to develop a system for estimating hourly or instantaneous broad band direct, diffuse and global radiation from meteorological observations. For clear sky conditions relationships developed elsewhere were adapted to Australian data. For cloudy conditions the clouds were divided into two groups, high clouds and opaque (middle and low) clouds, and corrections were made to compensate for the bias due to reporting practices for almost clear and almost overcast skies. Careful consideration was given to the decrease of visible sky toward the horizon caused by the vertical extent of opaque clouds. Equations relating cloud and other meteorological observations to the direct and diffuse radiation contained four unknown quatities, functions of cloud amount and of solar elevation, which were estimated from the data. These were the proportions of incident solar radiation passed on as direct and as diffuse radiation by high clouds, and as diffuse radiation by opaque clouds, and a factor to describe the elevation dependance of the fraction of sky not obscured by opaque clouds. When the resulting relationships were used to estimate global, direct and diffuse radiation on a horizontal surface, the results were good, especially for global radiation. Some discrepancies between estimates and measurements of diffuse and direct radiation were probably due to erroneously high measurements of diffuse radiation.     

A procedure to obtain global radiation maps from sunshine durations at isolated stations in a region with complex orography

In this paper the procedure followed to obtain preliminary maps of monthly average daily global radiation is discussed. The information on which these maps are based is monthly average daily percent sunshine durations at stations covering the considered territory with very irregular density. The possibility of correlations between monthly average percent sunshine and meteorological parameters, other than cloudiness, is examined but found to be absent. A local fit procedure (octant-search), followed by smoothing, is used to construct percent sunshine maps, over the entire territory, coherent with the values relative to the single stations. Finally we have considered the possibility of important variations in the elevation and the influence of this parameter on the global radiation. Hence, among the various relationships relating monthly average daily global radiation to average percent sunshine duration, we have chosen one in which the daily clear sky global radiation (which depends on elevation above sea level) appears instead of the daily extra-terrestrial radiation. The clear sky global radiation has been calculated with a model deduced from Hottel's transmission model which includes elevation dependence. When more data become available, an analogous procedure could be used to obtain definitive maps, employing more reliable values for parameters relating global radiation to percent sunshine tested with experimental data. This method has been applied to the territory of Ethiopia, in order to obtain preliminary maps of global radiation.     

Estimating solar irradiation sums from sunshine and cloudiness observations

A method is presented that offers the possibility of estimating solar irradiation sums on the basis of sunshine and cloudiness observations only. Its application requires the knowledge of the local hourly sums of global and diffuse solar irradiation by clear weather as well as the hourly sums of diffuse solar irradiation due to clouds. These quantities were determined for the actual radiation climate in Lisbon. Effective daily amount of sunshine and cloudiness are defined and compared with the usual daily sunshine and cloudiness concepts; the relationship between daily relative amount of sunshine and cloudiness is established for Lisbon.     

The relationship between global solar radiation and sunshine duration in Vietnam

Two approaches of the well-known modified Angstrom formula were developed from long term records of measured monthly mean daily global solar radiation and sunshine hour values obtained from 12 meteorological stations across Vietnam. These formulae were then used to estimate solar radiation for stations where only sunshine records were available. Three other commonly used correlations between solar irradiation and sunshine duration were also used and their results compared with those of two developed models. The procedure of measurement in Vietnamese weather stations was also indicated.     

Diffuse solar irradiation model evaluation in the North Mediterranean Belt area

The performance of daily and hourly diffuse horizontal solar irradiation models and correlations is examined using an assembled data set of multivariate meteorological time series from countries in the North Mediterranean Belt area. The correlations reviewed use only daily global, hourly global or daily diffuse irradiation as input, for the daily or hourly time scale. The best overall performance was presented by the Frutos correlation for the estimation of the daily diffuse radiation by an adapted version of the Liu and Jordan correlation for the mean daily diffuse radiation profile, and by the Hollands and Crha model for estimation of hourly diffuse values from the corresponding global values. The results show that the best correlation for each site varies. Two empirical piecewise correlations were also developed by the authors with the help of the data bank available, yielding models that showed even better fits to the data. The results show some seasonal and location dependence.     

A method for estimating monthly global solar radiation

In this paper a method is followed for estimating monthly totals of global solar radiation from a combination of calculations of monthly cloudless global solar radiation, surface meteorological observations, and empirical formulae relating sunshine duration to global solar radiation. The percent deviation of calculated from observed values is not negligible, but is much less than errors obtained by using extraterrestrial solar radiation totals. In case of values of monthly global solar radiation which are estimated for other regions, the resulted possible errors should be determined again. Some techniques leading to adaptation of the regression equations for other areas are argued.     

Comparative evaluation of SOLMET clear sky global solar radiation model

Selected aspects of the SOLMET solar data development project are discussed and the performance of the clear sky global radiation model used in the SOLMET project is compared to that of an alternative technique. Modeled values are compared to hourly observations from 1977 at 32 stations using r.m.s. and mean bias errors. The alternative model exhibits notably lower errors than the SOLMET approach which suggests that further improvement in the historical solar data base is possible.