A study of zenith luminance on Madrid cloudless skies

The zenith luminance (L_z) has been measured for cloudless skies at the IDMP station in Madrid. Mean values obtained at every 15 min have been fitted vs. solar elevation (α). A 5th degree polynomial connecting log (L_z) against (α) gives the best correlation in terms of the correlation coefficient (r=0.9358). A possible explanation of the dependence of the zenith luminance on solar elevation at low values is given.An exponential model obtained by other authors (Vázquez and Bernabeu, 1997) for a nearby temporary station in the same city does not account for the qualitative dependence of L_z vs. α for α<≈15°, and also overestimates experimental values for high solar elevations.The effect of turbidity on L_z is studied categorizing available data in three specified groups of T_v, the visual or luminous/illuminance turbidity. Best fits with 5th degree polynomials connecting log (L_z) against (α) are given for: T_v<3, 3<T_v<5, and T_v>5.     

Effect of atmospheric parameters on solar cell performance under global irradiance

The effect of incident sun angle and atmospheric conditions on solar-cell performance under global irradiance is investigated by theoretical analysis for reference-cell constructions of four kinds: module-packaged crystalline Si, module-packaged amorphous Si, unpackaged crystalline Si and inert gas-sealed crystalline Si. The dependence of solar-cell response on the incident beam angle (deviation from the cosine response) is quantitatively confirmed by calculations and measurements. The effect of deviation from the cosine response on cell sensitivity under global horizontal irradiance is investigated. The effect of incident sun angle and atmospheric conditions on solar-cell performance under global irradiance is then quantified.     

The aerosol effect on direct normal irradiance in Europe under clear skies

The effect of spatial and temporal variability of aerosol optical depth (AOD) on direct normal irradiance (DNI) under clear skies is studied, with the synergetic use of satellite and ground-based data as well as calculations from a radiative transfer model. The area of interest is Europe; data from May to September during 13 years (2000–2012) are analyzed. The aerosol effect on DNI is high in areas influenced by desert dust intrusions and intense anthropogenic activities, such as the Mediterranean basin and the Po Valley in Italy. In May, the attenuation of DNI from aerosols, over these areas, can reach values up to 35% and 45% respectively, which corresponds to 4 and 6 kWh m⁻² per day. In most areas, even for periods with lower values of AOD, the attenuation of DNI is found to be around 20%, which corresponds to about 2–3 kWh m⁻² less received DNI per day, compared to the corresponding value on an aerosol clean day. However, the DNI has increased during the recent years, due to the decreasing tendency of AOD over most areas of Europe. The increase is around 6–12%, which corresponds to an amount of 0.5–1.25 more kWh m⁻² received per day, compared to a clean day. The percentage differences of daily DNI from the corresponding monthly climatological value reveals that day-to-day differences (due to AOD changes) from the monthly mean, by ±20%, can occur. The significance of the aerosol changes in Europe reveals the necessity for near real-time measurements or forecasts of AOD when reliable estimations of DNI are required.     

The shade ring correction for measurements of diffuse irradiance under clear skies

Observed and estimated values of the shade ring correction in the measurement of diffuse irradiance are compared for a sample of days which were cloud-free or almost so. Corrections are determined observationally from measurements of diffuse irradiance using both a shade ring and an occulting disc, which are recorded every minute. Estimated corrections are calculated (a) from numerical integration of analytic radiance distributions and (b) from empirical formulae. The former method gives results that are sensitive to the choice of radiance distribution. Method (b) does not account for the variation in corrections throughout the day, but is adequate for most periods. Errors due to a misalignment of the shade ring are examined, using calculations from analytic radiance distributions.     

On the estimation for clear skies of the spectral distribution of diffuse solar radiation on a horizontal surface from global and diffuse broadband solar radiation

Using experimental data collected at Uccle (Belgium) in 1980, new relations are proposed which allow the spectral density distribution of diffuse solar radiation on a horizontal surface to be estimated for clear skies, as a function of the commonly measured broadband global and diffuse solar irradiances.     

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.     

A parameterized model for global insolation under partially cloudy skies

A simple and efficient parameterization of insolation under partially cloudy skies is discussed and compared with a set of exact radiative transfer results for clear skies, an empirical equation and observations. The parameterization is physically based and requires, as input variables, the ozone path length, precipitable water, Angstrom turbidity, surface air pressure and albedo, fractional cloud-cover and cloud thickness. Multiple reflection between the surface and the overlying atmosphere, and clouds are considered. The albedo of the earth-atmosphere system is also formulated and compared with a set of exact radiative transfer results. As compared to the exact radiative transfer results, the errors in the insolations are generally less than 1 per cent, and in the albedo of the earth-atmosphere system less than 10 per cent. The errors in the calculated insolations using climatological data are 2–3 per cent when compared with many years averaged observations at Maudheim (Antarctica) and at Rockville (U.S.A.). A parametric equation for calculating directly the daily total insolation is also given.     

A simple, solar spectral model for direct-normal and diffuse horizontal irradiance

A spectral model for cloudless days that uses simple mathematical expressions and tabulated look-up tables to generate direct-normal and diffuse horizontal irradiance is presented. The model is based on modifications to previously published simple models and comparisons with rigorous radiative transfer codes. This model is expected to be more accurate than previous simple models and applicable to a broader range of atmospheric conditions. The primary significance of this model is its simplicity, which allows it to be used on small desk-top computers. The spectrum produced by this model is limited to 0.3–4.0 μm wavelength with an approximate resolution of 10 nm.     

Directional spectral emissivities of clear skies

From the total spectral emissivities determined for clear skies in a preceding paper their directional values are obtained. The Bliss formulation still used for this doing is justified. The results point out the inefficiency of a large band around the horizon for cooling purposes. As an application, a natural focusing system to obtain dew is explained.     

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.     

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.     

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.     

Estimation of hourly direct normal from measured global solar irradiance in Spain

The availability of a good data set, registered in six Spanish locations, including several radiometric variables, has been used to test different approaches for estimating hourly direct normal irradiance by decomposition models. Models proposed by different authors have been tested. Following this preliminary study, to improve the k_b–k_t correlations, another geometric variable has been used as a predictor of hourly beam transmittance, k_b, by means of piecewise correlations. The new beam transmittance correlations, which include additional geometric information, reduce the root mean square deviation. In addition, they show a better performance in terms of the determination coefficient of the regression analysis of measured vs calculated values, providing an improved capture of the real world effects than models that are function of the clearness index only. A new model that uses only two ranges of clearness index is proposed. The proposed model shows seasonal dependence and thus we have developed a seasonal version of it. However, the performance of the seasonal version has proved to be similar to the corresponding annual model.     

Estimating solar irradiance and components

The performance of models to estimate solar irradiance and its components is assessed using data for six Canadian stations for nine years (1968–1976). Greatest emphasis is placed on a model, the MAC model, which uses cloud information from different layers. Here, effects on model estimates of using observed cloud layer opacities instead of amounts is examined because after 1976 the latter quantity is no longer recorded. Effects of aerosol are also examined. Two other models are considered here; a version of the MAC model which uses total cloud information rather than layer information, and Rietveld's[1] sunshine-based model.In general, the layer model yielded the best results. This is in agreement with a previous Canadian study[2]. RMSE values are between 11 and 15 percent for global irradiance on a daily basis and decrease below 10 percent for averaging periods greater than 2–4 days. Daily RMSE values for the direct beam and diffuse components are 25 per cent. These decrease below 10 per cent for averaging periods larger than 10–15 days. Errors increase when layer opacities are used but results are still acceptable.Aerosol effects can be neglected for much of the country except in Montreal and Toronto. Rietveld's model gives results of lower accuracy than the MAC model but may be useful for quick, easy estimates. The MAC model using total cloud amount performed poorly.     

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.     

Ground-level spectral distribution of solar direct-normal irradiance and marine aerosol attenuation coefficients at Reunion Island

The ground-level spectral distribution of direct solar irradiance at Reunion Island was measured for six bands covering the spectrum of solar radiation. The measurements, distributed over one year, were made under clear sky conditions with a pyrheliometer (Eppley, NIP) and six large pass-band flat filters. Good stability of spectral irradiances as a function of Solar height allows us to propose approximate relationships which significantly characterize the irradiance into each spectral band. Measurements at Reunion vary significantly from data obtained with the same apparatus in a northern hemisphere continental area (Lyon). The determination of aerosol attenuation coefficients, for different spectral bands, allows the establishment of a mean curve, for these coefficients as a function of wavelength, characteristic of marine aerosols.     

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.     

Investigation of cloudless solar radiation with PV module employing Matlab-Simulink

This paper focuses on a novel approach to the prediction of Voltage-Current (V-I) characteristics of a Photovoltaic panel under varying weather conditions and also the modelling of hourly cloudless solar radiation to provide the insolation on a PV module of any orientation, located at any site. The empirical model developed in this study uses standard specifications together with the actual solar radiation and cell temperature. This proposed work develops a Matlab-Simulink model to generate solar radiation at any location and for any time of the year. A new model for V-I characteristics and maximum power operation of a Photovoltaic (PV) module is also presented, which aims to model the effect on V-I and P-V curves of varying climatic conditions. Moreover, this model has been implemented using the Matlab-Simulink and is used to investigate the effect of meteorological conditions on the performance of a PV module generator. Thus the combined model of cloudless solar radiation and the photovoltaic module provides a tool that may be loaded in the library for analysis purpose. It is found that the predicted solar radiation strongly agrees with the experimental data.     

Simple models to compute solar global irradiance from the CMSAF product Cloud Fractional Coverage

Simple models are proposed to compute solar global irradiance by using the hourly Cloud Fractional Coverage (CFC) data provided by the Climate Monitoring Satellite Application Facility (CMSAF). The models are tested against measurements performed in five Romanian weather stations. The cloudy sky models based on CFC (n, for short) are compared with cloudy sky models based on ground-based estimates of point cloudiness (C, for short). Two models were proposed here for clear sky and overcast sky defined as n = 0 and n = 1, respectively. Two types of cloudy sky regression models were built on the basis of these clear sky and overcast sky models. Eight cloudy sky models based on n have been tested in a particular location. The bias error is good or good enough for all cloudiness classes. The spreading error is good for n = 0 ÷ 0.3; good enough for n = 0.3 ÷ 0.7 and poor for n > 0.7. For low zenith angle (Z = 0° ÷ 30°) the bias error of the eight models is generally good enough or poor. Generally, best fit models based on C perform better than best fit models based on n. One model (D1) has been selected for further testing. The sub-model D1TOT has been obtained by fitting the model D1 to all available measured data. The accuracy of sub-model D1TOT is good and good enough for all stations at low and intermediate zenith angles (Z < 70°). The performance of a model based on n is significantly better than that of a model based on C, for all zenith angle classes. D1 sub-models were developed by using data from particular stations. Generally, all sub-models have good or good enough performance when used in stations other than the origin one, for cloudiness classes n < 0.7. In case of skies with n = 0.3 ÷ 0.7, the performance of the sub-models based on n is obviously worse than that of sub-models based on C. For low zenith angles (Z = 0° ÷ 70°), the performance of D1 sub-models is good or good enough, when applied in the origin station or other stations, and it is comparable with that of models based on C.