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.     

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.     

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.     

Empirical validation of models to compute solar irradiance on inclined surfaces for building energy simulation

Accurately computing solar irradiance on external facades is a prerequisite for reliably predicting thermal behavior and cooling loads of buildings. Validation of radiation models and algorithms implemented in building energy simulation codes is an essential endeavor for evaluating solar gain models. Seven solar radiation models implemented in four building energy simulation codes were investigated: (1) isotropic sky, (2) Klucher, (3) Hay–Davies, (4) Reindl, (5) Muneer, (6) 1987 Perez, and (7) 1990 Perez models. The building energy simulation codes included: EnergyPlus, DOE-2.1E, TRNSYS-TUD, and ESP-r. Solar radiation data from two 25 days periods in October and March/April, which included diverse atmospheric conditions and solar altitudes, measured on the EMPA campus in a suburban area in Duebendorf, Switzerland, were used for validation purposes. Two of the three measured components of solar irradiances – global horizontal, diffuse horizontal and direct-normal – were used as inputs for calculating global irradiance on a south-west façade. Numerous statistical parameters were employed to analyze hourly measured and predicted global vertical irradiances. Mean absolute differences for both periods were found to be: (1) 13.7% and 14.9% for the isotropic sky model, (2) 9.1% for the Hay–Davies model, (3) 9.4% for the Reindl model, (4) 7.6% for the Muneer model, (5) 13.2% for the Klucher model, (6) 9.0%, 7.7%, 6.6%, and 7.1% for the 1990 Perez models, and (7) 7.9% for the 1987 Perez model. Detailed sensitivity analyses using Monte Carlo and fitted effects for N-way factorial analyses were applied to assess how uncertainties in input parameters propagated through one of the building energy simulation codes and impacted the output parameter. The implications of deviations in computed solar irradiances on predicted thermal behavior and cooling load of buildings are discussed.     

Accuracies achievable with indirect measurements of the direct solar irradiance component

Calculated direct solar irradiances from recording of global and diffuse irradiance are possible. However, to achieve the desired accuracy of 2 per cent of direct solar irradiance, corrections for the cosine error of the pyranometer to measure global irradiance and of the error induced by the shadowband in the diffuse irradiance have to be applied. Results then are satisfactory to zenith angles of approx. 80°.     

A comparison of luminous efficacy models with illuminance and irradiance measurements

Several luminous efficacy models have been tested against simultaneous illuminance and irradiance measurements in Helsinki, Finland (60°11′N, 24°50′E). When compared with the measured values, the Perez luminous efficacy model had the lowest relative root mean square difference (RMSD) of 6.7%. All tested models had an RMSD within 2% of the constant model which used the measured yearly average of 110 lm/W as the constant. For all models, the error was smaller for high solar altitudes but greater for the low altitudes. The monthly average luminous efficacy was fairly constant between April and October but it was clearly lower during the winter months when the sun is very low.     

Predicting the spectral and broadband aerosol transmittance in the atmosphere for solar radiation modelling

Calculations of the spectral transmittance of the atmospheric aerosol, using Mie theory, for wavelengths between 0 and 40 μm is presented. The chemical composition of the aerosol particles has been modelled in order to correspond to the atmospheric conditions of medium and large coastal or near coastal cities with important industrial and other anthropogenic emission sources. Individual size distributions and optical properties for each aerosol constituent have been considered.Based on the detailed aerosol model, and using parameterization techniques, analytical broadband aerosol transmission functions for the absorption and total attenuation are obtained. The accuracy of the proposed expressions are verified with various tests, using data from the National Observatory of Athens (NOA). The proposed broadband aerosol transmission functions can be incorporated directly into solar radiation models to predict accurately the beam, diffuse and global solar radiation at a given place.     

Solar irradiance estimation from geostationary satellite data: II. Physical models

The use of satellite data to estimate solar irradiance at ground level represents a valid alternative to ground measurements of solar radiation. This paper continues the analysis and evaluation, started in a previous paper, of the best known methods for calculating solar irradiance at the earth's surface using geostationary satellite data. In the previous paper, we examined and compared the so-called statistical models. Now we will consider the physical models and point out the differences between them. Finally, a summary will be made of the assessments and comparisons carried out on the methods described.     

Direct beam and hemispherical terrestrial solar spectral distributions derived from broadband hourly solar radiation data

Multiple junction and thin film photovoltaic (PV) technologies respond differently to varying terrestrial spectral distributions of solar energy. PV device and system designers are concerned with the impact of spectral variation on PV specific technologies. Spectral distribution data are generally very rare, expensive, and difficult to obtain. We modified an existing empirical spectral conversion model to convert hourly broadband global (total hemispherical) horizontal and direct normal solar radiation to representative spectral distributions. Hourly average total hemispherical and direct normal beam solar radiation, such as provided in Typical Meteorological Year (TMY) data, are spectral model input data. Default or prescribed atmospheric aerosols and water vapor are possible inputs. Individual hourly and monthly and annual average spectral distributions are computed for a specified tilted surface. The spectral range is from 300 nm to 1800 nm. The model is a modified version of the Nann and Riordan SEDES2 model. Measured hemispherical spectral distributions for a wide variety of conditions at the Solar Radiation Research Laboratory at the National Renewable Energy Laboratory, Golden, Co. and Florida Solar Energy Center (Cocoa, FL) show that reasonable spectral accuracy of about ±10% is obtainable with exceptions for weather events such as snow. Differing cloud climatology and variable albedo and aerosol optical depth atmospheric conditions can lead to spectral model differences of 30–40%.     

Monthly average clear-sky broadband irradiance database for worldwide solar heat gain and building cooling load calculations

This paper establishes the formulation of a new clear-sky solar radiation model appropriate for algorithms calculating cooling loads in buildings. The aim is to replace the ASHRAE clear-sky model of 1967, whose limitations are well known and are reviewed. The new model is derived in two steps. The first step consists of obtaining a reference irradiance dataset from the REST2 model, which uses a high-performance, validated, two-band clear-sky algorithm. REST2 requires detailed inputs about atmospheric conditions such as aerosols, water vapor, ozone, and ground albedo. The development of global atmospheric datasets used as inputs to REST2 is reviewed. For the most part, these datasets are derived from space observations to guarantee universality and accuracy. In the case of aerosols, point-source terrestrial measurements were also used as ground truthing of the satellite data. The second step of the model consists of fits derived from a REST2-based reference irradiance dataset. These fits enable the derivation of compact, but relatively accurate expressions, for beam and diffuse clear-sky irradiance. The fitted expressions require the tabulation of only two pseudo-optical depths for each month of the year. The resulting model, and its tabulated data, are expected to be incorporated in the 2009 edition of the ASHRAE Handbook of Fundamentals.     

Extraterrestrial solar irradiance variability two and one-half years of measurements from Nimbus 7

A cavity pyrheliometer aboard the Nimbus Spacecraft has been making solar irradiance measurements since 16 November 1978. The data has shown short term variability in the solar flux reaching the earth at the fractional percentage level. A long term downward trend at the 0.02 per cent per year level is also indicated. Inverse correlation between sunspot number and the measured irradiance has been found for a number of events. The data presented here is from a preliminary analysis through 13 July 1981.     

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.     

Combining solar irradiance measurements,satellite-derived data and a numerical weather prediction model to improve intra-day solar forecasting

Isolated power systems need to generate all the electricity demand with their own renewable resources. Among the latter, solar energy may account for a large share. However, solar energy is a fluctuating source and the island power grid could present an unstable behavior with a high solar penetration. Global Horizontal Solar Irradiance (GHI) forecasting is an important issue to increase solar energy production into electric power system. This study is focused in hourly GHI forecasting from 1 to 6 h ahead. Several statistical models have been successfully tested in GHI forecasting, such us autoregressive (AR), autoregressive moving average (ARMA) and Artificial Neural Networks (ANN). In this paper, ANN models are designed to produce intra-day solar forecasts using ground and exogenous data. Ground data were obtained from two measurement stations in Gran Canaria Island. In order to improve the results obtained with ground data, satellite GHI data (from Helioclim-3) as well as solar radiation and Total Cloud Cover forecasts provided by the European Centre for Medium-Range Weather Forecasts (ECMWF) are used as additional inputs of the ANN model. It is shown that combining exogenous data (satellite and ECMWF forecasts) with ground data further improves the accuracy of the intra-day forecasts.     

Experimental solar radiation measurements and their effectiveness in setting up a real-sky irradiance model

The present work investigates the effectiveness of an innovative procedure to calculate the global real sky irradiance of a mountain urban region, the city of Trento (Italy). The proposed methodology improves the predictive Bird’s real-sky model by introducing in it both atmospheric parameters, specifically defined for the analyzed site, and a local cloud cover factor, based on experimental data, to calculate the global real sky irradiance. The experimental data have been measured at the meteorological station of the University of Trento located in the city center. At first, a selection of the global irradiance measurements, representative of daily clear-sky conditions of each season, is presented and compared with the corresponding values obtained by the improved Bird’s clear-sky model. Making use of the improved procedure, the monthly mean daily irradiation is then calculated and compared both with experimental measurements covering the years from 2003 to 2006 and available models as well as data banks. The results, presented in terms of statistical functions, demonstrate that the generalized calculation procedures usually adopted, also available from commercial software tools, reach a satisfactory accuracy if compared with an experimental methodology approach as the one proposed in this work.     

Spectral measurements of visible solar direct-normal irradiance and air pollutant attenuation coefficients at Helwan

Solar radiation spectra were measured by a ground-level pyrheliometer (Eppley NIP) equipped with a filter wheel. Three flat, circular, Schott filters were used to define three spectral bands. The filters were large band-pass filters of the types OG530, RG630 and RG695. The experiment was conducted from June 1991 to May 1992 on the roof of the new building of the National Research Institute of Astronomy and Geophysics (NRIAG) at Helwan. The Linke turbidity factor for the integrated radiation, and the spectral attentuation coefficients of solar energy caused by aerosols were computed. In comparison with earlier measurements in 1910, 1967 and 1987, it is clear that there is a continuous increase in the turbidity factor, due to an increase of industrial waste in the Helwan atmosphere. A correlation analysis between the turbidity factors and the total suspended particles, smoke and sulphur dioxide was carried out. Meteorological elements and sand storms have been taken into consideration in the correlation analysis.     

Satellite based estimates of solar irradiance at the earth''s surface—II. Mapping of solar radiation

This paper reviews the theoretical basis of relatively simple models that use widely available meteorological data to determine the solar irradiation at the earth's surface. Spectral and non-spectral models for clear and cludy sky conditions are considered. A sample of validation results is presented. These indicate that most of the models studied are capable of estimating the global irradiation with acceptable accuracy, especially for time intervals of a month of more.     

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.