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.     

Analysis and synthesis of the variability of irradiance and PV power time series with the wavelet transform

The irradiance fluctuations and the subsequent variability of the power output of a PV system are analysed with some mathematical tools based on the wavelet transform. It can be shown that the irradiance and power time series are nonstationary process whose behaviour resembles that of a long memory process. Besides, the long memory spectral exponent α is a useful indicator of the fluctuation level of a irradiance time series. On the other side, a time series of global irradiance on the horizontal plane can be simulated by means of the wavestrapping technique on the clearness index and the fluctuation behaviour of this simulated time series correctly resembles the original series. Moreover, a time series of global irradiance on the inclined plane can be simulated with the wavestrapping procedure applied over a signal previously detrended by a partial reconstruction with a wavelet multiresolution analysis, and, once again, the fluctuation behaviour of this simulated time series is correct. This procedure is a suitable tool for the simulation of irradiance incident over a group of distant PV plants. Finally, a wavelet variance analysis and the long memory spectral exponent show that a PV plant behaves as a low-pass filter.     

Evaluation of an innovative sensor for measuring global and diffuse irradiance,and sunshine duration

Delta-T Device Limited of Cambridge, UK have developed an integrated device which enables simultaneous measurement of horizontal global and diffuse irradiance as well as sunshine status at any given instance in time. To evaluate the performance of this new device, horizontal global and diffuse irradiance data were simultaneously collected from Delta-T device and Napier University's CIE First Class daylight monitoring station. To enable a cross check a Kipp & Zonen CM11 global irradiance sensor has also been installed in Currie, south-west Edinburgh. Sunshine duration data have been recorded at the Royal Botanical Garden, Edinburgh using their Campbell-Stokes recorder. Hourly data sets were analysed and plotted within the Microsoft Excel environment. Using the common statistical measures, Root Mean Square Difference (RMSD) and Mean Bias Difference (MBD) the accuracy of measurements of Delta-T sensor's horizontal global and diffuse irradiance, and sunshine duration were investigated. The results show a good performance on the part of Delta-T device for the measurement of global and diffuse irradiance. The sunshine measurements were found to have a lack of consistency and accuracy. It is argued herein that the distance between the respective sensors and the poor accuracy of Campbell-Stokes recorder may be contributing factors to this phenomenon.     

Prediction of daily global solar irradiance on horizontal surfaces based on neural-network techniques

In this study, a prediction model of global solar irradiance distribution on horizontal surfaces has been developed. The methodology is based on neural-network techniques and has been applied to the meteorological database of NTUA, Zografou Campus, Athens (37°58′26″N, 23°47′16″E). The investigation of the correlation between weather conditions, duration of daylight and the representative peak value of a Gaussian-type function plays an essential role in the development of the model. The weather conditions are categorized into six different states, whereas the daylight duration is obtained by familiar equations. Thereafter, a correction methodology for the Gaussian-type function—which stands for all six different states—is applied. Finally, the reliability of the developed model is investigated through a suitable validation procedure.     

Improved broadband solar irradiance from the multi-filter rotating shadowband radiometer

Approximations to total and diffuse horizontal and direct normal, broadband solar irradiance (280–4000 nm) can be obtained from the multi-filter rotating shadowband radiometer (MFRSR) using the unfiltered silicon channel of this seven-channel instrument. However, the unfiltered silicon channel only responds to wavelengths between 300 and 1100 nm and does not have a uniform spectral response. In contrast, the best, more expensive, first-class, thermopile-based radiometers respond fairly uniformly to all solar wavelengths. While the total horizontal and direct normal solar irradiance measurements made with the MFRSR unfiltered silicon channel are reasonable if carefully calibrated with a thermopile radiometer, the diffuse horizontal irradiance calibrated in this way has a large bias. These issues are common to all inexpensive, silicon-cell, solar pyranometers. In this paper we use a multivariate, linear regression technique for approximating the thermopile-measured total, diffuse, and direct broadband solar irradiances using the six, narrowband filters and the open-channel of an MFRSR. The calibration of the MFRSR for broadband solar by comparing various combinations of MFRSR channels to first-class thermopile instruments is illustrated, and methods to track the instrument response during field deployments are investigated. We also suggest an approach to calibrate the open-channel for all three components that could improve measurements that are made using typical, commercial, silicon-cell pyranometers.     

Interdisciplinary applications of a versatile spectral solar irradiance model: A review

A detailed review of different applications that have already been investigated with SMARTS, a versatile spectral solar irradiance model, is proposed here. This review provides examples of applications in many different disciplines, for which recent developments are discussed. Three main types of applications are considered, depending on their spectral range. Purely spectral applications encompass the determination of atmospheric constituents, the performance testing of spectroradiometers, and the improvement and validation of reference spectra for the rating of photovoltaic or glazing systems, or for new standards development in the field of weathering and material degradation. Narrow-band applications include the determination of different UV fluxes and of the UV index, and the prediction of illuminance on any horizontal or tilted surface, of the luminous efficacy of direct, diffuse or global radiation, of the photosynthetically active radiation, and of the irradiance transmitted by different bandpass filters. Finally, some specific broadband applications are reviewed: mesoscale predictions of radiation fluxes, evaluation of circumsolar effects in pyrheliometers, performance assessment of broadband radiation models, and turbidity determination from broadband irradiance data.     

Spectral solar irradiance before and during a Harmattan dust spell

Measurements of the ground-level spectral distributions of the direct, diffuse and global solar irradiance between 300 and 1100 nm were made at Akure (7.15°N, 5.5°E), Nigeria, in December 1991 before and during a Harmattan dust spell employing a spectroradiometer (LICOR LI-1800) with 6 nm resolution. The direct spectral solar irradiance which was initially reduced before the dust storm was further attenuated by about 50% after the spell. Estimated values of the Ångström turbidity coefficient β indicated an increase of about 146% of this parameter while the Ångström wavelength-exponent α decreased by about 65% within the 2-day study period. The spectral diffuse-to-direct and diffuse-to-global ratios suggest that the main cause of the significant reduction in solar irradiance at the surface was the scattering by the aerosol which led to an increase in the diffuse component. The global irradiance though reduced, was less sensitive to changing Harmattan conditions. It is recommended that solar energy devices that use radiation from Sun and sky be used under fluctuating Harmattan conditions. There are some deviations from the Ångström formula under very turbid Harmattan conditions which could be explained by the relative increase of the particle sizes.     

Evaluation of the estimation of diffuse irradiance from global and direct normal irradiance measurements

As part of a radiometer intercomparison experiment, different combinations of pyranometer and pyrheliometers were used to estimate diffuse solar irradiance on a horizontal surface. Sixteen combinations were possible with four pyranometers and four pyrheliometers. The values were intercompared and then compared to the measured values, obtained with a solar tracking/occulting disc system. The difference in estimated values using different radiometer combinations varied from 1 to 21 W/m². It was found that uncertainty in measuring the global irradiance accounted for most of the difference in estimated values. In the worst case, a 2.1 per cent difference in the global irradiance as measured by two different pyranometers caused a 12 per cent difference in estimates of the diffuse irradiance. It is shown that, if the estimated and measured values are analyzed statistically, agreement to within 1 per cent is possible.     

Prediction of direct and global solar irradiance using broadband models: Validation of REST model

In the present paper, three parametric models Yang, CPCR2 and REST (without considering transmittance due to nitrogen dioxide) have been analyzed for four Indian stations, namely New Delhi, Mumbai, Pune and Jaipur over the period of 1995–2002, under cloudless conditions. These stations have different climatic conditions. The beam radiation at normal incidence as well as global solar radiation at horizontal surface was computed for these locations during all seasons except monsoon (June to September). The computed values of beam and global irradiance was compared with reference values in case of beam and measured values in case of global solar radiation on the basis of percentage root mean square error (RMSE) and mean bias error (MBE). The maximum RMSE is 6.5% in REST model, as compare to 15% in Yang and 11% in CPCR2 model for predicting direct normal irradiance. The predicted global radiation at horizontal is showing maximum RMSE 7% in REST model, 13.4% in Yang and 25.9% in CPCR2 model. This shows that REST model has good agreement with measured data for these Indian stations as compare to other two models.     

Comparative building simulation study utilising measured and estimated solar irradiance for Australian locations

The focus of this paper is to investigate the impact of using estimated solar irradiance data in building energy simulations. A series of annual weather files were developed with the estimates from two global and three diffuse/direct irradiance models for three locations in Australia. A weather file was also developed using the modelled values of global, diffuse and direct irradiance as estimated by EnergyPlus' (Version 7.0.0) auxiliary weather generator program. In addition weather files were generated with measured irradiance data and satellite derived irradiance data from the Australian Bureau of Meteorology. The influence of irradiance data was tested via the simulation of a simple 15 × 15 × 3.5 m building under two construction scenarios with varying window to wall ratios (WWR). This study indicates that the level of bias and uncertainty in the simulation results was low when global irradiance was measured and only diffuse and direct irradiance were estimated. However, when global irradiance was unknown the level of bias and uncertainty increased significantly and was shown to be highly dependent on the WWR, whilst only the level of bias was shown to be dependent on the building envelope construction. The results also indicated that the Skartveit diffuse/direct irradiance model used in combination with the BOM's satellite derived global irradiance data set achieved better results than the complete (global and direct) satellite derived irradiance data set from the BOM. The worst correlation in the simulation results occurred for the case where the irradiance data was estimated by EnergyPlus' auxiliary weather generator program.     

Dependence of the spectral surface irradiance on aerosol properties and surface reflectivity

A reduction in global surface irradiance occurs with increasing aerosol loadings when the aerosols are absorbing. For scattering aerosols, a reduction is pronounced for isotropic scattering (characteristic of small particles) but reduction is not as significant for scattering with a high anisotropy of a large forward peak (characteristic of large particles). This distinction between isotropic and anisotropic scattering becomes small or null over highly reflecting terrain; and actually for reflectivities higher than 0.5 and solar elevation angles close to the zenith, the global irradiance can be slightly higher for isotropic scattering than in the case of an anisotropy of a forward peak. Under such conditions, which can be encountered in reflective infrared bands over dense vegetation or over sandy deserts (close to noon, in low latitudes) the surface irradiance becomes nearly independent of the aerosol optical thickness.The above conclusions are derived based on analytical treatment of simplified single scattering approximation to the radiative transfer through a turbid atmosphere, which is valid only for a low or a moderate optical thickness.Computations of the spectral irradiance using the explicit expression are presented in the form of tables and graphs, for two anisotropy parameters of aerosols and three surface reflectivities.     

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.     

Modelling slope irradiance at high latitudes

Irradiance on slopes is often required in cases where it is not directly measured and, consequently, has to be modelled from alternative data. In this paper three models for the derivation of hourly slope irradiances from hourly horizontal beam and diffuse sky irradiances are tested against 5 years of recorded slope irradiances at Bergen (60°24′N, 5°19′E). The test demonstrated the importance of accounting for sky radiance anisotropy both at overcast and cloudless weather. Moreover, a stepwise procedure for the derivation of long-term mean slope irradiance from various kinds of input data is outlined. Testing against observations demonstrated that, except for steeply south-facing slopes at low mid-winter sun, long-term slope irradiance is derived with reasonably accuracy from mean cloudiness. Moreover, observed horizontal irradiances, whether global or beam and diffuse, as input data yield satisfactory accuracy throughout the year on all slopes.     

Dependence of one-minute global irradiance probability density distributions on hourly irradiation

This paper analyzes the behavior of one minute global irradiance distributions as a function of hourly average solar global irradiance. For this purpose, we have used the clearness index k_t which describes the atmospheric transmittance. Our interest is in characterizing the intrahourly variability of solar global irradiance and the behavior of the instantaneous values as a function of hourly values of solar global irradiance. The distributions are unimodal and show a marked symmetry around a central value that is close to the corresponding hourly average value. The probability density functions have been modeled using functions based on the Boltzmann statistic used in recent studies of the one minute distributions of k_t conditioned to the optical air mass. These functions provide good fit of the distributions and are analytically integrable and can be inverted analytically. The one minute global irradiance data used in this study have been recorded during a three year period in a radiometric station located in south eastern Spain.     

A new approach for predicting vertical global solar irradiance

Solar irradiance, particularly on vertical surfaces, plays a major role in determining the thermal and energy performance of a building. It is important to the design and analysis of both active solar systems and passive solar buildings. Many mathematical models are mainly developed to predict the sky-diffuse irradiance on inclined surfaces from the measured horizontal diffuse component. This paper presents an approach to estimate the vertical global irradiance based on direct beam and ground-reflected components which can be accurately determined. Hourly data recorded from January 1996 to December 1998 in Hong Kong were used for the model development. The performance of the proposed model and two well-known anisotropic inclined surface models (Muneer and Perez) was evaluated against data measured in 1999. Statistical analysis indicated that the proposed model gives reasonably good agreement with measured data for all vertical planes. Although the new model has been found less effective than the Perez model, its simplicity nature provides buildings designers a convenient and reliable alternative in the estimation of vertical solar irradiance.     

Comparison of irradiance measurements made with the multi-filter rotating shadowband radiometer and first-class thermopile radiometers

The multi-filter rotating shadowband radiometer (MFRSR) uses a silicon photodiode sensor to measure shortwave global and diffuse horizontal irradiance from which direct normal irradiance is calculated. Silicon sensors are rugged, stable, and have a fast time response. However, silicon sensors are both thermally and spectrally sensitive. In addition they, as do all pyranometric sensors, have an imperfect cosine response, especially at high solar-incidence angles. In the MFRSR two of these sources of error are minimized: the cosine response of the MFRSR is measured, and the acquired data are corrected accordingly; an automatic heater maintains the MFRSR detector at a constant temperature near 40°C. This paper demonstrates that there is substantial agreement between first-class thermopile instruments and the MFRSR silicon sensor with the elimination of these two sources of error. Furthermore, this paper describes corrections, based on sky conditions, to lower the remaining errors. The data base for deriving and testing these corrections was collected in Albany, New York, during 1993. After correction equations are applied, the root-mean-square differences for 5 min averages of the global horizontal, diffuse horizontal, and direct normal irradiance are 8.8, 9.1, and 16.3 W/m², respectively. The differences in time response or time keeping between silicon and thermopile instruments may explain much of the remaining root-mean-square differences.     

Spectral and temperature correction of silicon photovoltaic solar radiation detectors

Silicon photovoltaic sensors are an inexpensive alternative to standard thermopile sensors for the measurement of solar radiation. However, their temperature and spectral response render them less accurate for global horizontal irradiance and unsuitable for direct beam and diffuse horizontal irradiance unless they can be reliably corrected. A correction procedure for the rotating shadowband radiometer, which measures all three components, based on a three-way parameterization of the solar position and sky conditions is proposed. After correction, root-mean-square errors for the global and diffuse horizontal irradiance and the direct normal irradiance are about 10, 12, and 13 W/m² in comparison with coincident, 5-minute thermopile measurements. While the numerical results are specific to the rotating shadowband instrument, the correction algorithm should apply universally.     

The spectral distribution of solar radiation at the earth's surface—elements of a model

The attenuating properties of the atmosphere are presented in a form that permits the calculation of direct, diffuse and global spectral solar irradiance at ground level, using the extraterrestrial irradiance values of Thekaekara. Input data describing the state of the atmosphere are obtained from standard meteorological information or from tabulated average values. Clear sky diffuse spectral irradiance on a horizontal surface is estimated from the direct beam by means of an empirical simplification. Examples of the agreement between calculated and measured values are shown.     

Spectral solar irradiance in the range 300–1100 nm measured at València, Spain

A programme of measurements aimed at originating a database of spectral solar irradiance which is representative of a wide range of optical masses and atmospheric conditions is described. A preliminary analysis of the measurements for clear-sky conditions is also presented.