A study of the division of global irradiance into direct and diffuse irradiance at thirty-three U.S. sites

Solar irradiance data obtained at 33 U.S. sites during parts or most of the period from January 1978 through December 1980 have been analyzed to study the division of global solar irradiance into its direct and diffuse components. New information concerning the dependence of this division upon the amount of global solar irradiance, solar elevation, surface albedo, atmospheric precipitable water and atmospheric turbidity has been obtained.     

Direct and indirect determination of the Linke turbidity coefficient

The Linke turbidity coefficient has been measured for the first time in the island of Crete, in the Mediterranean sea. Short time series data were used to calculate the beam irradiance through the global and diffuse irradiance on a horizontal plane. Strong seasonal effects on the monthly averaged T_L values are not observed, while their profile displays a smooth transition from lower to higher values. Examination of the daily averages reveals T_L values as low as 2.0 and as high as 4.0. The most frequent values of the turbidity are found in the range of 2.3–3.5. Archival global irradiance data from the same site are also used to estimate the turbidity with the aid of a robust estimator and two simple, analytical models. The usefulness of this approach is validated with data from a number of networks registering the solar radiation. The proposed method allows to estimate the turbidity with an rms error of 0.3, using only, good quality, global irradiance data. Large amounts of data can easily be processed with the proposed method.     

Direct solar transmittance and irradiance predictions with broadband models. Part II: validation with high-quality measurements

A thorough investigation of the performance of broadband direct irradiance predictions using 21 solar radiation models, along with carefully measured radiation data and ancillary meteorological data, is detailed here. A sensitivity study and a detailed error analysis show that precipitable water, and even more so, turbidity, are the two most critical inputs, whose accuracy conditions the resulting uncertainty in irradiance predictions. Large prediction uncertainties result from the use of time/space interpolated or extrapolated data of precipitable water and turbidity. So that the results of performance assessment studies like this one can be of any significance, it is necessary to rely on highly accurate precipitable water and turbidity data from collocated instruments with an appropriate sampling rate. An experimental assessment of the performance of all models has been conducted, using nearly 5000 data points from five different sites covering a large range of geographical and climatic conditions. Direct irradiance measured with first-class instruments at these sites are compared to model predictions where precipitable water and turbidity are determined from collocated sunphotometric measurements. This experimental assessment is found to be less stringent than the theoretical assessment (in Part 1 of this investigation), while confirming its main results. The same four high-performance models as in Part 1 are finally recommended: CPCR2, MLWT2, REST and Yang (in alphabetical order). Remarkably, they can predict direct irradiance under a variety of atmospheric conditions within the uncertainty of modern and well-maintained pyrheliometers, provided that good quality inputs of precipitable water and turbidity are used. The MLWT2 model produces the best results, with the lowest bias and variance for any irradiance value.     

Estimation of daily Linke turbidity factor by using global irradiance measurements at solar noon

This work presents a methodology for estimating daily Linke turbidity factor for clear sky days from global horizontal irradiance information at solar noon and monthly mean values of the Linke turbidity factor. The analysis of the method proposed here have been made using the ESRA clear sky model to recalculate the direct normal irradiance using as input the new Linke turbidities. Ground data of three BSRN and six AEMet radiometric meteorological stations have been used for assessing the method. Linke turbidity factor estimated here exhibits higher fluctuations than the monthly means and the comparison of the solar irradiance recalculated with the ground data have shown a noticeable reduction of the root mean square deviation. On the other hand the new Linke turbidity estimations have been compared to those values obtained from normal beam irradiance measures. The discrepancies found point out the high dependence of the reliability of this method with the quality of the ground measurements used.     

REST2: High-performance solar radiation model for cloudless-sky irradiance, illuminance, and photosynthetically active radiation – Validation with a benchmark dataset

REST2, a high-performance model to predict cloudless-sky broadband irradiance, illuminance and photosynthetically active radiation (PAR) from atmospheric data, is presented. Its derivation uses the same two-band scheme as in the previous CPCR2 model, but with numerous improvements. Great attention is devoted to precisely account for the effect of aerosols, in particular.Detailed research-class measurements from Billings, OK are used to assess the performance of the model for the prediction of direct, diffuse and global broadband irradiance. These measurements were made in May 2003 during a sophisticated radiative closure experiment, which involved the best radiometric instrumentation currently available and many ancillary instruments. As a whole, these exceptional measurements constitute the only known modern benchmark dataset made specifically to test the intrinsic performance of radiation models. Using this dataset as reference, it is shown that REST2 performs better than CPCR2 for irradiance, illuminance or PAR predictions. The availability of the turbidity data required by REST2 or other similar models is also discussed, as well as the effect that turbidity has on each component of broadband irradiance, PAR irradiance and illuminance, and on the diffuse/global PAR ratio.     

Diffuse and global solar spectral irradiance under cloudless skies

A simple empirical model to calculate solar spectral diffuse and global irradiance under cloudless skies is presented here. This formulation takes into account absorption of radiation by molecules such as O₃, H₂O and the uniformly-mixed gases. Attenuation by Rayleigh scattering and aerosol extinction are included. Aerosol attenuation is calculated through Ångström's turbidity parameters α and β. The diffuse radiation is assumed to be composed of three parts: (1) Rayleigh-scattered diffuse irradiance; (2) aerosol-scattered diffuse irradiance; and (3) irradiance arising out of multiple reflections between the atmosphere and the ground. The global irradiance is the sum of these three components of diffuse irradiance plus the direct irradiance. The input parameters include an extraterrestrial spectrum, zenith angle, turbidity coefficient β, wavelength exponent α, ground albedo _g, water vapor content and ozone content. The model is shown to yield very good results up to air mass two when compared to accurate theoretical calculations. No comparisons with measured spectra are presented because of a lack of accurate specifications of input parameters. Results are presented to show the effect of variation of certain of the input parameters.     

Comparison of eight clear sky broadband models against 16 independent data banks

A selection of eight high performance clear sky solar irradiance models is evaluated against a set of 16 independent data banks covering 20 years/stations, altitudes from sea level to 1600 m and a large range of different climates. Their performance evaluated on very clear condition measurements are within 4% in term of standard deviation.The conclusions are that the accuracy of the input parameters such as the turbidity is crucial in the validity of the obtained radiation components, and that the choice of a specific model is secondary. The model selection criteria should be based upon either implementation simplicity, input parameter availability (Linke turbidity or aerosol optical depth) or the capacity of the model to produce spectral radiation.     

Determination of atmospheric turbidity from the diffuse-beam broadband irradiance ratio

A semi-physical method is proposed to evaluate turbidity from broadband irradiance measurements and other atmospheric parameters. This method demonstrates the utility of diffuse data when estimating atmospheric composition with broadband irradiance data. An error analysis and various tests against measured data show that this method can predict accurate turbidities provided that the sky is perfectly cloudless and the diffuse irradiance data are very accurate. Yet, this method is insensitive to errors in input data such as precipitable water and ozone amount. Applications of this method to the quality control of radiation data are discussed. Tests with actual data from Florida and Oregon show good agreement with other methods. Evaluation of the model required a detailed discussion of the accuracy and cosine error of pyranometers, and the uncertainty in precipitable water estimates.     

Values of broad band turbidity coefficients in a mediterranean coastal site

The Angstrom turbidity coefficient, the Linke turbidity factor, and the Unsworth–Monteith coefficient have been determined and analysed based on measurements of normal direct irradiance and global horizontal irradiance taken in Valencia, Spain, between January 1990 and December 1996. The data, which were acquired automatically and continuously, have been filtered to select only those values corresponding to clear sky conditions. To determine the Angstrom turbidity coefficient the method proposed by Louche et al. has been used whilst the expression for δ_CDA proposed by Kasten was used to obtain the Linke turbidity coefficient. The Angstrom turbidity coefficient showed a minimum in winter with values between 0.06 and 0.12. It tended to increase in the spring and reach a maximum between 0.22 and 0.29 in summer before falling again in the autumn. The daily and annual evolution of all three coefficients were very similar with correlation coefficients between pairs of them close to 1.     

Experimental verification of some clear-sky insolation models

Clear-sky solar irradiance can be predicted when a number of essential atmospheric parameters are known. A number of parameterization methods to predict solar irradiance with various degrees of difficulty are available in the literature. In this study, three models called model A, model B and model C, with medium degree of difficulty, have been examined. In these models, the solar transmittance due to each atmospheric parameter is available in simple algebraic form. Based on these algebraic equations, the direct normal, diffuse, and global horizontal irradiance can be predicted. These models have been compared with measured data from Carpentras, a French radiometric station. At this station, several daily observations of the clear-sky irradiance are carried out. Corresponding instantaneous values of the Ångström turbidity coefficient β and several other necessary surface meteorological observations are also made. For diffuse irradiance, a value of 0.95 is assumed for the single-scattering albedo of the aerosols. Based on the calculation of the mean bias error and root mean square error, model C has the best correspondance with the measurements as for as direct irradiance is concerned. Model B appears to be more accurate for prediction of diffuse and global irradiance.Regression equations are provided to help the user of any one of the three models for better prediction of solar irradiance.     

Atmospheric turbidity in a semi-rural site—II influence of climatic parameters

Seasonal variations of Linke, Ångström and Schüepp turbidity coefficients and of α exponent as well as the influence of climatic factors on them are analyzed. For each of these turbidity coefficients, a typical annual evolution with summer maximum and winter minimum is found. The major weight of air mass origin is shown as well as the influence of wind velocity. Atmospheric water content effect is discussed from the analysis of direct irradiance, turbidity coefficients and precipitable water seasonal variations.     

Clear-sky classification procedures and models using a world-wide data-base

Clear-sky data need to be extracted from all-sky measured solar-irradiance dataset, often by using algorithms that rely on other measured meteorological parameters. Current procedures for clear-sky data extraction have been examined and compared with each other to determine their reliability and location dependency. New clear-sky determination algorithms are proposed that are based on a combination of clearness index, diffuse ratio, cloud cover and Linke’s turbidity limits. Various researchers have proposed clear-sky irradiance models that rely on synoptic parameters; four of these models, MRM, PRM, YRM and REST2 have been compared for six world-wide-locations. Based on a previously-developed comprehensive accuracy scoring method, the models MRM, REST2 and YRM were found to be of satisfactory performance in decreasing order. The so-called Page radiation model (PRM) was found to underestimate solar radiation, even though local turbidity data were provided for its operation.     

Angstrom turbidity and ozone column estimations from spectral solar irradiance in a semi-desertic environment in Spain

Angstrom parameters are commonly used for modelling the solar radiation extinction by aerosols. Detailed knowledge of these parameters in as many places as possible is desirable since many applications need this kind of information: satellite products assessment, clear sky models benchmarking, spectral modelling, etc. Experimental determinations of the Angstrom turbidity and wavelength exponent have been made for a semi-desertic area in the south-east of Spain using a double monochromator spectroradiometer. Experimental measurements of direct-beam spectral irradiance have been made about every 20 min during one year (from october 2005 to september 2006). Angstrom turbidity has a noticeable variability during the year, showing a seasonal characteristic behaviour. Low turbidity values were found during autumn and winter and quite large values can be observed in spring and summer days. The eventual values of high turbidity with low wavelength exponent found could indicate Saharan dust outbreaks events. In addition, total ozone column have been experimentally estimated from spectral measurements in the Huggins absorption band. The results showed a general agreement with the values extracted from the TOMS web site.     

Comparison and validation of three global-to-beam irradiance models against ground measurements

The study presents a comparison and validation of 3 state of the art-global-to-beam irradiance conversion models against ground measurements from 22 sites covering a wide range of latitudes, altitudes and climates. One of the 3 models takes into account a climatic turbidity and gives slightly better results in terms of bias and precision.

On a hourly time step basis, the validation on over 100,000 station-hour values shows that the normal beam irradiance can be evaluated from the global horizontal component with a negligible bias and a precision of 85 W m⁻² or 23%.

When the models are used on data with a shorter time step, the performance decreases, but remains acceptable. With a modification of the DirIndex (or the DirInt) model, the performance can slightly be increased and reach a bias of 2% and a precision of 28% for 10 min data.     

The effect of altitude upon the solar UV-B and UV-A irradiance in the tropical Chilean Andes

Using two Grasnick filter photometers measurements of the horizontal components of solar UV irradiance between 313 and 374 nm (mainly UV-A) and between 308 and 319 nm (mainly UV-B) were performed in the tropical Chilean Andes along the Tropic of Capricorn at different altitudes and cloudless skies in January and February 1992. A linear (but solar elevation dependent) increase (decrease) with altitude of the global and direct (diffuse) components in both the UV-A and UV-B ranges has been observed for altitudes up to 5500 m above mean sea level. At solar elevations between 20° and 90° the increase of the global irradiance was about 8–10%/1000 m for UV-B and changed from 15 to 7%/1000 m for UV-A. Thus, these changes in the comparatively clear and dry atmosphere over the Andes which show Linke turbidity factors between 1.06 and 1.70 are significantly smaller than in the Alps which are typical humid mountains. The increase of the direct component with altitude changes from 60 to 20%/1000 m for solar elevations between 20° and 90°. In contrast, the diffuse UV-A and UV-B irradiation show a decrease of 2–4%/1000 m between solar elevations of about 30–90°. The direct/diffuse ratio was found to increase with solar elevation and altitude, reaching values as high as about 5 for UV-A and about 4 for UV-B.     

Prediction of global irradiance on inclined surfaces from horizontal global irradiance

Knowledge of the radiation components incoming at a surface is required in energy balance studies, technological applications such as renewable energy and in local and large-scale climate studies. Experimental data of global irradiance on inclined planes recorded at Granada (Spain, 37.08°N, 3.57°W) have been used in order to study the pattern of the angular distribution of global irradiance. We have modelled the global irradiance angular distribution, employing horizontal global irradiance as the only radiometric input, and geometric information. We have obtained good results (root mean square deviation about 5%), except for surfaces affected by artificial horizon effects, which are not allowed for in this new model. The Skyscan'834 data set has also been used in order to test the model under completely different conditions from those in Granada, with respect to the amount of cloud, local peculiarities, experimental design and instrumentation. The results prove the validity of our model, even when compared with the Perez et al. model. The model offers a reliable tool for use when solar radiance data are scarce or limited to global horizontal irradiance.     

Forecast of solar irradiance using recurrent neural networks combined with wavelet analysis

In this paper, artificial neural network is combined with wavelet analysis for the forecast of solar irradiance. This method is characteristic of the preprocessing of sample data using wavelet transformation for the forecast, i.e., the data sequence of solar irradiance as the sample is first mapped into several time-frequency domains, and then a recurrent BP network is established for each domain. The forecasted solar irradiance is exactly the algebraic sum of all the forecasted components obtained by the respective networks, which correspond respectively the time-frequency domains. Discount coefficients are applied to take account of different effect of different time-step on the accuracy of the ultimate forecast when updating the weights and biases of the networks in network training. On the basis of combination of recurrent BP networks and wavelet analysis, a model is developed for more accurate forecasts of solar irradiance. An example of the forecast of day-by-day solar irradiance is presented in the paper, the historical day-by-day records of solar irradiance in Shanghai constituting the data sample. The results of the example show that the accuracy of the method is more satisfactory than that of the methods reported before.     

A study of atmospheric turbidity for Hong Kong

Clear skies are important in predicting the peak solar irradiance and daylight illuminance levels for active solar energy utilisation and passive energy-efficient building designs. The clearness of a sky is affected by the clarity of the atmosphere which is usually expressed in terms of a turbidity index. This study considers two common turbidity parameters including the Linke turbidity factor (T_L) and Angstrom turbidity coefficient (β). The annual and monthly average values, frequency of occurrence and cumulative frequency distribution of individual turbidity indices based on different approaches have been established to describe the clear sky atmospheric conditions in Hong Kong. The general features and characteristics of the findings are discussed.     

Investigating the effects of solar modelling using different solar irradiation data sets and sources within South Africa

When designing a solar photovoltaic (PV) system, the main aim of the designer is to optimise the system through the correct choice in sizing of system components (i.e.: size of PV array versus number of batteries for storage), whilst at the same time keeping the overall systems costs as low as possible. The choice of data provider and method for measuring the solar irradiance data in W/m² for a specific geographical location is therefore a critical determinant to ensure maintenance of the desired level of accuracy for the system design. The use of a data set which either over predicts or under predicts the amount of available solar irradiation at a specific location will therefore affect the electrical performance of the system, as the real world conditions may differ considerably to the data set used in the modelling of the system design. This paper specifically deals with the modelling of an off-grid photovoltaic power supply system using three different sources of solar irradiance data for two specific geographical locations within South Africa. The principal aim of the paper is to show that satellite data over-estimates solar irradiance and hence underestimates the initial cost of a solar PV system needed to meet the load in question.     

A method for correction of cosine errors in measurements of spectral UV irradiance

One of the sources contributing to the overall uncertainty of spectral UV radiation measurements is the cosine error of the spectroradiometer. It leads to measurement errors that depend on atmospheric conditions and on solar zenith angle, and thus time of the day and season. Though the foreoptics of modern instruments are designed such as to minimize cosine errors, there remain deviations from the ideal cosine response. We have worked out a method to further reduce that remaining cosine error in global spectral irradiance. This method was applied to spectra of global UV radiation taken with a Brewer spectroradiometer. The only additional input data needed to apply the method of cosine correction to spectral irradiance data are concurrent broad-band UV-B radiation measurements of diffuse and global radiation recorded with filter UV instruments, which are used to estimate the optical thickness referred to global UV radiation for the time when the spectral scan is taken. The method takes account of the variable conditions of cloudiness and turbidity. In the case of measurements taken with Brewer instrument No. 30, the cosine corrected global UV-B radiation was higher than the measured irradiance by 9–20%, and even its daily totals turned out to be higher than the uncorrected radiation by 13–18%. An estimate of the uncertainty of ±4 to ±8% was derived from a theoretical approach as well as from model calculations using a radiative transfer model.