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.     

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.     

Clear-sky irradiance predictions for solar resource mapping and large-scale applications: Improved validation methodology and detailed performance analysis of 18 broadband radiative models

The intrinsic performance of 18 broadband radiative models is assessed, using high-quality datasets from five sites in widely different climates. The selected models can predict direct, diffuse and global irradiances under clear skies from atmospheric data, and have all been (or still are) involved in large-scale applications, for instance to prepare solar resource maps and datasets, or to evaluate solar radiation in GIS software. The input data to the models include accurate aerosol and water vapor measurements by collocated sunphotometers, if needed. Cloud occurrences are meticulously scrutinized through the use of various tools to avoid cloud contamination of the test data. The intrinsic performance of the models is evaluated by comparison between their predictions and measurements at high frequency (1-minute time step at four sites, 3-minute at one site). The total expanded uncertainty of these measurements is estimated at 3% for direct irradiance, and 5% for diffuse and global irradiance.Various statistics are calculated to evaluate the systematic and random differences between the data series, as well as the agreement between the cumulative distribution functions. In the latter case, stringent statistics based on the Komolgorov–Smirnov (KS) test are used. Large differences in performance are apparent between models. Those that require more atmospheric inputs perform usually better than simpler models. Whereas many models can predict the global horizontal irradiance within uncertainty limits similar to those of the radiation measurements, the prediction of direct irradiance is less accurate. Moreover, the prediction of diffuse horizontal irradiance is particularly deficient in most models. The cumulative distribution functions also denote areas of concern.A ranking of all models is proposed, based on four statistical indicators: mean bias difference (MBD), root mean square difference (RMSD), total uncertainty with 95% confidence limits (U₉₅), and the newly introduced Combined Performance Index (CPI), which optimally combines two KS indices with RMSD. For direct irradiance, consistently high rankings are obtained with five models (REST2, Ineichen, Hoyt, Bird, and Iqbal-C, in decreasing order of performance) that require a relatively large number of atmospheric inputs. The inferior performance of models requiring little or no atmospheric inputs suggests that large-scale solar resource products derived from them may be inappropriate for serious solar applications. Additionally, prediction uncertainties under ideal clear-sky conditions can propagate and affect all-sky predictions as well—resulting in potential biases in existing solar resource maps at the continent scale, for instance.     

Clear-sky solar luminous efficacy determination using artificial neural networks

Under cloudless conditions, the effect of atmospheric variables, such as turbidity or water vapour, on luminous efficacy is an important source of variability, often limiting the use of simple empirical models to those sites where they were developed. Due to the complex functional relationship between these atmospheric variables and the luminous efficacy components, deriving a non-local model considering all these physical processes is nearly impossible if standard statistical techniques are employed. To avoid this drawback, the use of a new methodology based on artificial neural networks (ANN) is investigated here to determine the luminous efficacy of direct, diffuse and global solar radiation under cloudless conditions. In this purpose, a detailed spectral radiation model (SMARTS) is utilized to generate both illuminance and solar radiation values covering a large range of atmospheric conditions. Different input configurations using combinations of atmospheric variables and radiometric quantities are analyzed. Results show that an ANN model using direct and diffuse solar irradiance along with precipitable water is able to accurately reproduce the variations of the three components of luminous efficacy caused by solar zenith angle and the various atmospheric absorption and scattering processes. This proposed model is considerably simpler than the SMARTS radiation model it is derived from, but still can retain most of its predicting power and versatility. The proposed ANN model can thus be used worldwide, avoiding the need of using detailed atmospheric information or empirical models of the literature if radiometric measurements and precipitable water data (or temperature and relative humidity data) are available.     

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.     

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.     

Importance of atmospheric turbidity and associated uncertainties in solar radiation and luminous efficacy modelling

For many solar-related applications, it is important to separately predict the direct and diffuse components of irradiance or illuminance. Under clear skies, turbidity plays a determinant role in quantitatively affecting these components.In this paper, various aspects of the effect of turbidity on both spectral and broadband radiation are addressed, as well as the uncertainty in irradiance predictions due to inaccurate turbidity data, and the current improvements in obtaining the necessary turbidity data.     

Direct and indirect uncertainties in the prediction of tilted irradiance for solar engineering applications

Global radiation measured on fixed-tilt, south-facing planes (40° and vertical) and a 2-axis tracker at NREL’s Solar Radiation Research Lab. in Golden, CO is compared to predictions from ten transposition models, in combination with either optimal or suboptimal input data of horizontal irradiance. Suboptimal inputs are typically used in everyday engineering calculations, for which the necessary data are usually unavailable for the site under scrutiny, and must be estimated in some way. The performance of the transposition models is first evaluated for ideal conditions when optimal data are used. In this specific case, it is found that the Gueymard and Perez models provide the best estimates of global tilted irradiance under clear skies in particular.The performance of four direct/diffuse separation models is also evaluated. Their predictions of direct and diffuse radiation appear biased in most cases, with a model-dependent magnitude. Finally, the performance of the resulting combinations of separation and transposition models is analyzed in a variety of situations. When only global irradiance is known, the accuracy of the tilted irradiance predictions degrades significantly, and is mainly conditioned by the local performance of the direct/diffuse separation method. For the south-facing vertical surface, inaccuracies in the ground reflection calculations becomes another key factor and significantly increase the prediction error. The Reindl transposition algorithm appears to perform best in this case. When using suboptimal input data for the prediction of plane-of-array irradiance on a moderately tilted plane (40°S) or a 2-axis tracking plane, the Hay, Reindl and Skartveit models are less penalized than others and tend to perform better. It is concluded that further research should be conducted to improve the overall process of predicting irradiance on tilted planes in realistic situations where no local high-quality irradiance or albedo measurements are available.     

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.     

Solar cells efficiency variations with varying atmospheric conditions

The resuls of model simulations and analyses of operating solar cell efficiencies are reported. Defined as the ratio (%) between the electrical output power of the device and the total incident radiant power, this efficiency is somewhat ambiguous as it ignores the effects of temperature, total irradiance, and the spectral distribution of the light source. Since the total intensity and spectral distribution of sunlight varies with atmospheric conditions such as cloudiness, total column ozone, turbidity, and precipitable water, the efficiency of a cell operating in a field installation may also be a function of the above factors. This paper examines variation of modeled and observed cell efficiencies with atmospheric variations. Variations in turbidity and water vapor content drive the SPCTRAL2 solar spectral radiation model of Bird and Riordan (1986). Model output, coupled with prescribed spectral response functions representing monocrystalline and amorphous solar cells, is used to model the efficiency of these cell types. The modeled efficiency rises with increasing humidity, especially for the simulated amorphous cell. Simulated efficiency decreases with increasing turbidity for both modeled cell types. The amount of increase or decrease dependents on the spectral response specified. The measured performance of different solar cells operating at the PVUSA site in Davis, California is also analyzed. The major factors found to cause variations in operational efficiency are ambient temperature and total irradiance intensity. The authors also observed increases of the apparent efficiency of amorphous cells with decreasing energy in the red portion of the solar spectrum which are consistent with model predictions.     

Semi-empirical models for the estimation of clear sky solar global and direct normal irradiances in the tropics

This paper presents semi-empirical models for estimating global and direct normal solar irradiances under clear sky conditions in the tropics. The models are based on a one-year period of clear sky global and direct normal irradiances data collected at three solar radiation monitoring stations in Thailand: Chiang Mai (18.78°N, 98.98°E) located in the North of the country, Nakhon Pathom (13.82°N, 100.04°E) in the Centre and Songkhla (7.20°N, 100.60°E) in the South. The models describe global and direct normal irradiances as functions of the Angstrom turbidity coefficient, the Angstrom wavelength exponent, precipitable water and total column ozone. The data of Angstrom turbidity coefficient, wavelength exponent and precipitable water were obtained from AERONET sunphotometers, and column ozone was retrieved from the OMI/AURA satellite. Model validation was accomplished using data from these three stations for the data periods which were not included in the model formulation. The models were also validated against an independent data set collected at Ubon Ratchathani (15.25°N, 104.87°E) in the Northeast. The global and direct normal irradiances calculated from the models and those obtained from measurements are in good agreement, with the root mean square difference (RMSD) of 7.5% for both global and direct normal irradiances. The performance of the models was also compared with that of other models. The performance of the models compared favorably with that of empirical models. Additionally, the accuracy of irradiances predicted from the proposed model are comparable with that obtained from some rigorous physical models.     

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.     

Validation of models for global irradiance on inclined planes

The accuracy of models to estimate irradiance on inclined planes is tested by comparing the predictions to measurements taken with four instruments of various tilt and azimuth angles in Sede Boqer, Israel. The three models investigated are: the Perez model, Hay's anisotropic model, and the isotropic model. The Perez model is found to perform significantly better than the other two, with residual errors that are comparable to the accuracy of the measuring instruments themselves. The same data are also used to evaluate the precision of empirical correlations to estimate the direct component from global horizontal radiation, and to assess the sensitivity of the predicted irradiance on tilted surfaces to the errors associated with these correlations.     

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.     

Modeling the luminous efficacy of direct and diffuse solar radiation using information on cloud,aerosol and water vapor in the tropics

This paper presents luminous efficacy models for direct and diffuse solar irradiance using information on cloud, aerosol and water vapor in the tropics. The model is based on five years (2007–2011) of diffuse illuminance and irradiance measurements and two years of direct illuminance and irradiance measurements, April 2010–March 2012. Data are taken at four solar radiation monitoring stations in Thailand, specifically Chiang Mai (18.78 °N, 98.98 °E) in the Northern region, Ubon Ratchathani (15.25 °N, 104.87 °E) in the Northeastern region, Nakhon Pathom (13.82 °N, 100.04 °E) in the Central region and Songkhla (7.20 °N, 100.60 °E) in the Southern region. The models express luminous efficacy as functions of the aerosol optical depth and precipitable water, obtained from the AERONET network, and a cloud index for hourly time scales derived from the MTSAT-1R satellite. The model performance is good when validated against independent data from these stations. Root mean square differences (RMSD) of 9.7% and 6.8% for direct normal efficacy and diffuse efficacy, respectively are obtained. The models compared favorably with most existing models when tested against these independent data.     

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.     

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.     

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.     

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.     

Evaluation of conventional and high-performance routine solar radiation measurements for improved solar resource, climatological trends, and radiative modeling

The solar renewable energy community depends on radiometric measurements and instrumentation for data to design and monitor solar energy systems, and develop and validate solar radiation models. This contribution evaluates the impact of instrument uncertainties contributing to data inaccuracies and their effect on short-term and long-term measurement series, and on radiation model validation studies. For the latter part, transposition (horizontal-to-tilt) models are used as an example. Confirming previous studies, it is found that a widely used pyranometer strongly underestimates diffuse and global radiation, particularly in winter, unless appropriate corrective measures are taken. Other types of measurement problems are also discussed, such as those involved in the indirect determination of direct or diffuse irradiance, and in shadowband correction methods. The sensitivity of the predictions from transposition models to inaccuracies in input radiation data is demonstrated. Caution is therefore issued to the whole community regarding drawing detailed conclusions about solar radiation data without due attention to the data quality issues only recently identified.