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.     

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

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.     

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.     

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.     

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.     

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.     

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.     

Monthly ratios of PAR to global solar radiation measured at northern Tibetan Plateau, China

Using narrowband and broadband solar radiation measurements collected at Wudaoliang (WDL) site in northern Tibetan Plateau (NTP) from September 1993 to December 1998, the relationship between monthly photosynthetically active radiation (Q_P) and global solar radiation (R_S) values is analyzed. Temporal variability of the ratio (Q_P/R_S) and its further dependence on several meteorological variables are presented. The narrowband ratio exhibited diurnal and seasonal variability with high values during morning and afternoon hours and low values around noon in winter time, whereas during summer period the ratio was decreased from morning to afternoon. The ratio (Q_P/R_S) was correlated positively with several atmospheric parameters such as water vapor pressure and low-level cloud amount; in contrast, the ratio was negatively correlated with clearness index, relative sunshine duration and atmospheric turbidity. It was also found that both the relative sunshine duration and water vapor pressure are the most influential parameters on the estimations of the spectral PAR ratio. Finally, an empirically derived model is proposed for estimating monthly average PAR values over the northern Tibetan Plateau. Verification results further ensured that the proposed model predicts monthly global PAR values accurately.     

Computing global and diffuse solar hourly irradiation on clear sky. Review and testing of 54 models

Fifty-four broad band models for computation of global and diffuse irradiance on horizontal surface are shortly presented and tested. The input data for these models consist of surface meteorological data, atmospheric column integrated data and data derived from satellite measurements. The testing procedure is performed for two meteorological stations in Romania (South-Eastern Europe). The testing procedure consists of forty-two stages intended to provide information about the sensitivity of the models to various sets of input data. There is no model to be ranked “the best” for all sets of input data. Very simple models as well as more complex models may belong to the category of “good models”. The best models for solar global radiation computation are, on equal-footing, ESRA3, Ineichen, METSTAT and REST2 (version 81). The second best models are, on equal-footing, Bird, CEM and Paulescu & Schlett. The best models for solar diffuse radiation computation are, on equal-footing, ASHRAE2005 and King. The second best model is MAC model. The best models for computation of both global and diffuse radiation are, on equal-footing, ASHRAE 1972, Biga, Ineichen and REST2 (version 81). The second best is Paulescu & Schlett model.     

Luminous efficacy models and their application for calculation of photosynthetically active radiation

From a spectral radiative transfer model, an algorithm is developed for the conversion of illuminance to different measures of Photosynthetically Active Radiation (PAR) (in W m⁻² or in μEm⁻²s⁻¹). This illuminance to PAR conversion may even be used in combination with a luminous efficacy model and, thus, form a photosynthetic efficacy model. In this work, two luminous efficacy models are chosen, one empirical and one derived from the above radiative transfer model. Observed PAR energy flux and PAR photon flux from seven Nordic stations (56–70°N) and illuminance from one U.S. station (43°N) are, together with observed all-wave solar irradiance from all stations, used for verification.Observed and modelled luminous efficacies agree on the average within 1% at high solar elevation under cloudless sky, while it is indicated that the illuminance, PAR energy flux, and PAR photon flux radiometers are mutually inconsistent by some 6–16%. Even differences in cosine response between radiometer types are apparent at low solar elevation under cloudless sky. In the present climates, the global radiation efficacy is 10–12% higher under an average cloudless atmosphere than it is outside the atmosphere. By introducing an average cloud deck in this cloudless atmosphere, a further efficacy increase, slightly exceeding these 10–12%, is observed. However, observations indicate that the cloud transmittance algorithm used in the radiative transfer model significantly overestimates the global radiation efficacy increase caused by horizontally inhomogeneous cloud decks.     

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.     

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 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.     

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.     

Luminous efficacy of direct solar radiation for all sky types

Three models for the luminous efficacy of direct solar radiation on a horizontal surface, valid for all sky conditions, have been developed in the present work, and two of them are proposed. In all the models a function for the direct luminous efficacy for all sky conditions relative to the direct luminous efficacy for clear skies is obtained, using the function for the direct luminous efficacy for clear skies given in a previous work, and the brightness index as a new independent variable. One of the two models is obtained by fitting the values of the relative luminous efficacy as a function of the brightness index. The other proposed model is developed by obtaining in the first place models for direct illuminance and direct irradiance, both relative to the corresponding clear sky models, and then finding the ratio between the relative direct illuminance and irradiance models. Statistical assessment of the direct illuminance values estimated with the proposed models gives similar values for the MBE and the RMSE. However, the model obtained from illuminance and irradiance models is mathematically coherent.     

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.     

Comparative study on different models for estimation of direct normal irradiance (DNI) over Egypt atmosphere

The results obtained by using seven-parameterization broadband models to estimate Direct Normal Irradiance (DNI) along with two spectral models for four sites in Egypt atmosphere were compared with ground DNI measurements. Some statistical indicators (MBE, RMSE and R²) have been used to measure the performance of the used models. MBE for all dataset is <1% to both spectral models (SPCTRAL2, SMARTS2) and broadband models (MLWT1, MLWT2 and REST) while is equal to 1.2% to YANG model. However, RMSE are around 2% for spectral models and 3% to the broadband models. The error in prediction of DNI to such models is below experimental errors a part from the big number of observations. On the other hand, Louche, Dogniaux and Rodgers models provide relatively bad performance, RMSE are at most cases >4%. Determination coefficient (R²) results to all models are near 1.0. If we excluded spectral models, the broadband models MLWT1, MLWT2 and REST along with YANG models provide the best performance in all tests, therefore, those models can be used in Egypt atmosphere.     

Discourses on solar radiation modeling

All solar energy applications require readily available, site-oriented and long-term solar radiation data. A typical database comprises of global, direct and diffuse solar irradiance, duration of sunshine and complementary data like cloud cover, atmospheric turbidity, humidity, temperature, etc. However, most of these stations do not provide complete if any information on solar data, chiefly due to the capital and maintenance costs that measuring instruments incur. For instance, global radiation is the most frequently measured parameter, its two components, i.e. diffuse and direct irradiance are often not measured.Improvements have been made to the meteorological radiation model MRM which, had been developed by Muneer et al. as a simple broadband irradiance estimation model based on synoptic information, by incorporating the sunshine information in the model's regressions. The result of the improvement of the model is a considerable reduction in biases and scatter in the comparison between estimated and measured data. The improved meteorological radiation model, IMRM is more accurate, by up to 70% in some cases, than its predecessor in estimating, global and diffuse horizontal irradiance.When sunshine, atmospheric pressure and temperature are not measured by a nearby station, yet cloud information is recorded, radiation estimation models based on cloud cover, CRM, can be used. Three CRMs have been compared to newly proposed models. It was found that models with locally fitted coefficients gave a more accurate estimation of the solar radiation than CRMs with generalized coefficients. The newly proposed model performed better that the older generation models.The third section of the article deals with estimation of diffuse radiation and possible improvements in its modeling. In this section, apart from clearness index (k_t), influence of the synoptic parameters of sunshine fraction (SF), cloud cover (CC) and air mass (m) on diffuse fraction of global radiation (k) is studied both qualitatively and quantitatively. It is found that, SF shows a strong bearing on the k–k_t relationship followed by CC and then m. As a next step, a series of models are developed for k as a polynomial function of k_t, SF, CC and m. After an extensive evaluation procedure, a regression model is selected such that the diffuse radiation can be estimated with reasonable accuracy without making the model overtly complex. It was found that among all the models, the composite model involving all parameters provides the most accurate estimation of diffuse radiation. The site-specific models are further investigated for any appreciable correlations between different locations and their possible attributions. It was also found that a single model could more than adequately estimate the diffuse radiation for the locations within a given region. Three optimum models are also recommended for each region, in view of the fact that information on all parameters is not necessarily available for all sites. This study reveals a significant improvement from the conventional k–k_t regression models to the presently proposed models, therefore, leading to more accurate estimation of diffuse radiation by approximately 50%.     

Comparing diffuse radiation models with one predictor for partitioning incident PAR radiation into its diffuse component in the eastern Mediterranean basin

In the photosynthesis process, solar radiation energy is converted to chemical energy by using atmospheric CO₂. That is, almost all living species depend on energy produced through photosynthesis for their nourishing components thus making photosynthesis vital to the earth's life. Nevertheless, the knowledge of photosynthetic photon flux density Q_P (PAR, 400–700 nm) is important in several applications dealing with plants physiology, biomass production, natural illumination in greenhouses and agricultural research. This study aiming to explore the applicability of several diffuse radiation empirical models, hourly measurements of diffuse PAR and global PAR irradiation collected at Athens (37°N, 23°E, 250 m above MSL) from 1 January 2000 to 31 December 2002, are employed. These data were used to establish an empirical model relating the spectral diffuse fraction, k_dP (ratio of the diffuse-to-global PAR) with the fractional transmission of global PAR k_tP (ratio of the global PAR-to-extraterrestrial solar PAR). The performance of the proposed empirical model was further compared with those of twelve other diffuse–global correlation models available in the literature in terms of the widely used statistical indicators mbe, rmse and t-test. From the overall analysis, it can be concluded that the proposed model predicts diffuse PAR values accurately, whereas most of the candidate empirical models examined here appear to be location-independent for the diffuse PAR predictions.