Christian A. Gueymard

Parameterized transmittance model for direct beam and circumsolar spectral irradiance

Abstract An upgraded spectral radiation model called SMARTS2 (Simple Model of the Atmospheric Radiative Transfer of Sunshine) is introduced. The solar shortwave direct beam irradiance is calculated from spectral transmittance functions for the main extinction processes in the cloudless atmosphere: Rayleigh scattering, aerosol extinction, and absorption by ozone, uniformly mixed gases, water vapor, and nitrogen dioxide. Temperature-dependent or pressure-dependent extinction coefficients have been developed for all these absorbing gases, based on recent spectroscopic data obtained either directly from the experimental literature or, in a preprocessed form, from MODTRAN, a state-of-the-art rigorous code. The NO2 extinction effect, in both the UV and visible, is introduced in detail for the first time in a simple spectral model by taking into account temperature-dependent absorption coefficients. Aerosol extinction is evaluated using a two-tier Angstrom approach. Parameterizations of the wavelength exponents and single-scattering coefficient for different aerosol models (proposed by Shettle and Fenn, Braslau and Dave, and also in the Standard Radiation Atmosphere) are provided as a function of both wavelength and relative humidity. Moreover, aerosol turbidity can now be estimated from airport visibility data using a function based on the Shettle and Fenn aerosol model. SMARTS2 also has an optional circumsolar correction function and two filter smoothing functions which together allow the simulation of actual spectroradiometers. This facilitates comparison between modeled results and measured data. Preliminary performance assessment indicates that the direct-beam irradiance predicted by the proposed model compares well to published reference spectra obtained with rigorous radiative codes, and to measured spectroradiometric data.

Direct solar transmittance and irradiance predictions with broadband models. Part I: detailed theoretical performance assessment

A thorough investigation on the performance of broadband direct irradiance predictions using solar radiation models is detailed here. Nineteen models were selected from an extensive literature survey. In addition, two new models were specifically developed for this study to provide state-of-the-art modelling of the broadband transmittances associated with the most important extinction processes in the atmosphere. The SMARTS spectral radiative code has been selected to provide 2064 reference transmittance and irradiance values, corresponding to as many combinations of solar position and varied atmospheric conditions. Inconsistencies or errors in the modelling of different transmittance functions from existing models were found, and could be corrected in some cases. As a result of this theoretical assessment, it is concluded that detailed transmittance models normally perform better than bulk models, and that models using Linke’s turbidity coefficient in intermediate calculations performed poorly. Four high-performance models can be recommended as a result of this detailed investigation: CPCR2, MLWT2, REST and Yang (in alphabetical order). The new MLWT2 model provides the best performance in all tests, thanks to its elaborate multi-layer spectral weighting scheme.

A two-band model for the calculation of clear sky solar irradiance, illuminance, and photosynthetically active radiation at the earth's surface

Abstract A two-band radiation modelling technique is proposed for the clear sky case. The solar spectrum is divided into a UV/Visible band (0.29–0.7 μm) and an infra-red band (0.7–2.7 μm). In each band, the transmittance of each extinction layer (ozone, water vapor, mixed gases, molecules and aerosols) is parameterized using preliminary integrations of state-of-the-art spectral transmittance functions. The beam and diffuse radiation components are obtained as functions of these layer transmittances. The photosynthetically active radiation (0.4–0.7 μm) and illuminance (0.39–0.76 μm) components may be easily derived from the UV/Visible band irradiances. In the case of typical atmospheric conditions, the model predictions are generally in good agreement with results from three accepted rigorous spectral codes. The effect of changing the solar elevation, the Angstrom turbidity coefficient and the site altitude on the beam, diffuse and global components (or their ratio) is further discussed.

Critical analysis and performance assessment of clear sky solar irradiance models using theoretical and measured data

Eleven clear sky irradiance models have been selected for this analysis. All predict the beam, diffuse, and global radiation on a horizontal surface. Three types of analyses are made in order to test the validity of the models, their limitations, and their performance for standard or real conditions. First, a detailed analysis of the main equations of the models is performed. It is shown that atmospheric effects are not always correctly modeled. The modeling of water vapor absorption, and more importantly of aerosol extinction mostly conditions the overall model accuracy. Second, the performance of each model is statistically evaluated by comparison with a benchmark constituted by the predictions of three sophisticated spectral codes. Third, real life performance is evaluated by comparison with a large number of measured data from seven sites around the world, encompassing a wide range of atmospheric conditions. The more physical models are found to be generally of higher accuracy and greater flexibility than empirical models.

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

Abstract 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.

Analysis of monthly average atmospheric precipitable water and turbidity in Canada and Northern United States

Abstract Atmospheric turbidity and precipitable water data are necessary as inputs to solar radiation or daylight availability models, and to daylighting simulation programs. A new model is presented to obtain precipitable water from long-term averages of temperature and humidity. Precipitable water data derived from this model are tabulated for some Canadian and northern U.S. sites. A discussion on the available turbidity data is presented. An analysis of the datasets from the WMO turbidity network is detailed. The effect of volcanic eruptions is discussed, as well as the possible comparisons with indirect determinations of turbidity from radiation data. A tabulation of the monthly average turbidity coefficients for ten Canadian stations and seven northern U.S. stations of the WMO network is presented.

Mathermatically integrable parameterization of clear-sky beam and global irradiances and its use in daily irradiation applications

A simple parameterized clear-sky short-wave irradiance model is derived from a detailed two-band physical model presented earlier. The inputs for the parameterized model (called PSIM) are the solar elevation, the amount of precipitable water (w), the Angstrom turbidity coefficient (β), the stations pressure (or its altitude), and the zonal surface albedo (for which a simple submodel is provided for North America). PSIM is intended to give accurate irradiance estimates in any atmospheric condition whenever w < 5 cm and β < 0.45. The parameterization uses a function of solar elevation that is integrable with time, so that a parameterized daily irradiation model (called DIM) is also obtained. The seasonal variations of the daily clear-sky beam and global irradiations are presented for different combinations of w, β, and latitude. It is possible to use these irradiation estimates in different applications when dealing with solar energy or climatology. For example, a simple way to derive the mean monthly apparent solar elevation or air mass is given. It is also suggested that the original Angstroms equation (to derive the average global irradiation from the fraction of possible sunshine) be used more extensively with DIM. Finally, it is demonstrated (using data from Albany, NY) that the monthly average beam irradiation may be obtained with a very simple equation from the fraction of possible sunshine and DIM, yielding more accurate estimates than the existing best-performing method.

An atmospheric transmittance model for the calculation of the clear sky beam, diffuse and global photosynthetically active radiation

Abstract A physical model is proposed for the estimation of the photosynthetically-active-radiation (PAR) components. Transmittances corresponding to ozone absorption, Rayleigh scattering and aerosol extinction are parameterized after numerical integration of spectral formulae. The parameters used in the model are station pressure, ozone amount, Angstrom turbidity coefficients, single-scattering albedo, ground albedo and solar elevation. Knowledge of these parameters is necessary if the beam and diffuse PAR are to be estimated accurately; while the global PAR is essentially a function of solar elevation. Model estimates compare well with predictions obtained with rigorous spectral codes (LOWTRAN and BRITE) and to measurements in Uccle, Belgium. It may be used in any area where the turbidity climatology is sufficiently known, to compute instantaneous, hourly or daily PAR clear sky values, even if simultaneous solar radiation measurements are not available.

Revising and Validating Spectral Irradiance Reference Standards for Photovoltaic Performance Evaluation

In 1982, the American Society for Testing and Materials (ASTM) adopted consensus standard direct-normal and global-tilted solar terrestrial spectra (ASTM E891/E892). These standard spectra were intended to evaluate photovoltaic (PV) device performance and other solar-related applications. The International Standards Organization (ISO) and International Electrotechnical Commission (IEC) adopted these spectra as spectral standards ISO 9845-1 and IEC 60904-3. Additional information and more accurately representative spectra are needed by today’s PV community. Modern terrestrial spectral radiation models, knowledge of atmospheric physics, and measured radiometric quantities are applied to develop new reference spectra for consideration by ASTM.Copyright

Critical evaluation of precipitable water and atmospheric turbidity in Canada using measured hourly solar irradiance

Abstract Global and diffuse radiation and surface meteorological measurements at Edmonton, Montreal, Port Hardy, Toronto and Winnipeg for the years 1977–1984 are analyzed to yield estimates of atmospheric precipitable water and turbidity. Three methods of estimating the precipitable water and two methods of estimating the turbidy are used and compared. Laboratory measurements of pyranometer response as a function of zenith angle are used to correct the global radiation measurements. Circumsolar radiation is removed from the direct radiation obtained from the difference of measured global and diffuse radiation. The magnitude of this circumsolar correction is discussed in the light of recent measurements and calculations of the circumsolar ratio. Turbidity time series are presented, showing a clearly defined El Chichon eruption signature in 1983–1984. A comparison with earlier results in included.