Radiometric Stations Research Articles

Validating Hourly Satellite Based and Reanalysis Based Global Horizontal Irradiance Datasets over South Africa

This study validates the hourly satellite based and reanalysis based global horizontal irradiance (GHI) for sites in South Africa. Hourly GHI satellite based namely: SOLCAST, Copernicus Atmosphere Monitoring Service (CAMS), and Satellite Application Facility on Climate Monitoring (CMSAF SARAH) and two reanalysis based, namely, fifth generation European Center for Medium-Range Weather Forecasts atmospheric reanalysis (ERA5) and Modern-Era Retrospective Analysis for Research and Applications (MERRA2) were assessed by comparing in situ measured data from 13 South African Weather Service radiometric stations, located in the country’s six macro climatological regions, for the period 2013–2019. The in situ data were first quality controlled using the Baseline Surface Radiation Network methodology. Data visualization and statistical metrics relative mean bias error (rMBE), relative root mean square error (rRMSE), relative mean absolute error (rMAE), and the coefficient of determination (R2) were used to evaluate the performance of the datasets. There was very good correlation against in situ GHI for the satellite based GHI, all with R2 above 0.95. The R2 correlations for the reanalysis based GHI were less than 0.95 (0.931 for ERA5 and 0.888 for MERRA2). The satellite and reanalysis based GHI showed a positive rMBE (SOLCAST 0.81%, CAMS 2.14%, CMSAF 2.13%, ERA5 1.7%, and MERRA2 11%), suggesting consistent overestimation over the country. SOLCAST satellite based GHI showed the best rRMSE (14%) and rMAE (9%) combinations. MERRA2 reanalysis based GHI showed the weakest rRMSE (37%) and rMAE (22%) combinations. SOLCAST satellite based GHI showed the best overall performance. When considering only the freely available datasets, CAMS and CMSAF performed better with the same overall rMBE (2%), however, CAMS showed slightly better rRMSE (16%), rMAE (10%), and R2 (0.98) combinations than CMSAF rRMSE (17%), rMAE (11%), and R2 (0.97). CAMS and CMSAF are viable freely available data sources for South African locations.

Diffuse irradiance on tilted planes in urban environments: Evaluation of models modified with sky and circumsolar view factors

Numerous studies have analyzed existing irradiance models for estimating sky diffuse irradiance on tilted planes. However, few have evaluated the suitability of these models for estimating irradiance in obstructed environments, specifically considering the effects of obstacles. In this study, three irradiance models —one of them with five variants— for estimating diffuse irradiance on tilted planes located in urban environments were evaluated. All models have been adapted to consider the effect of an urban canyon on the diffuse irradiance received on a tilted plane through the sky view factor and the circumsolar view factor. All the models were evaluated against the diffuse irradiance values obtained by the ISO 15469:2004(E)/CIE S 011/E:2003 angular distribution model. Therefore, it was necessary to determine the standard sky type corresponding to each record of the measurements performed by a sky scanner at the radiometric station of UPNA (Spain). A total of 4,864 scenarios were considered to occur from the combination of different orientations and inclinations of the plane, and different orientations and aspect ratios of the urban canyon. The results revealed that the Perez model considering a 35° half-angle circumsolar region has the best performance, followed by the Perez model considering a 45° half-angle circumsolar region.

Surface albedo spatial variability in North America: Gridded data vs. local measurements

Considering the current booming interest for the large-scale deployment of bifacial photovoltaic modules, the solar industry now requires accurate estimates of broadband surface albedo at high spatial resolution. In this context, the present study evaluates the adequacy and performance over North America of two Moderate Resolution Imaging Spectroradiometer (MODIS) white-sky albedo products (at 500-m and 1-km resolution) and the National Solar Radiation Database (NSRDB) product at 4-km resolution. Two variations of the 500-m MODIS product are also considered: black-sky albedo and all-sky albedo. Albedo observations from 36 radiometric stations during 2011–2015 are analyzed while considering the apparent homogeneity of the surface characteristics over the 4x4 km NSRDB pixel in which they are located. Even at sites where the albedo around the station has been found “homogeneous” in the literature, marked differences are found between the daily observations and the gridded estimates at any spatial resolution. Differences in seasonal behavior and between the three different albedo types also impact the accuracy of the albedo estimates, with overtones caused by local specificities and inhomogeneities. All this precludes the desirable evaluation of the local albedo at a specific site of relatively small size compared to its corresponding 4x4-km pixel if only the mean albedo over that pixel is known. Significant discrepancies are also found at snow-impacted sites, most importantly in the case of the NSRDB albedo estimates, which are typically much too high.

Twenty-Four-Hour Ahead Probabilistic Global Horizontal Irradiance Forecasting Using Gaussian Process Regression

Probabilistic solar power forecasting has been critical in Southern Africa because of major shortages of power due to climatic changes and other factors over the past decade. This paper discusses Gaussian process regression (GPR) coupled with core vector regression for short-term hourly global horizontal irradiance (GHI) forecasting. GPR is a powerful Bayesian non-parametric regression method that works well for small data sets and quantifies the uncertainty in the predictions. The choice of a kernel that characterises the covariance function is a crucial issue in Gaussian process regression. In this study, we adopt the minimum enclosing ball (MEB) technique. The MEB improves the forecasting power of GPR because the smaller the ball is, the shorter the training time, hence performance is robust. Forecasting of real-time data was done on two South African radiometric stations, Stellenbosch University (SUN) in a coastal area of the Western Cape Province, and the University of Venda (UNV) station in the Limpopo Province. Variables were selected using the least absolute shrinkage and selection operator via hierarchical interactions. The Bayesian approach using informative priors was used for parameter estimation. Based on the root mean square error, mean absolute error and percentage bias the results showed that the GPR model gives the most accurate predictions compared to those from gradient boosting and support vector regression models, making this study a useful tool for decision-makers and system operators in power utility companies. The main contribution of this paper is in the use of a GPR model coupled with the core vector methodology which is used in forecasting GHI using South African data. This is the first application of GPR coupled with core vector regression in which the minimum enclosing ball is applied on GHI data, to the best of our knowledge.

Short-Term Solar Power Forecasting Using Genetic Algorithms: An Application Using South African Data

Renewable energy forecasts are critical to renewable energy grids and backup plans, operational plans, and short-term power purchases. This paper focused on short-term forecasting of high-frequency global horizontal irradiance data from one of South Africa’s radiometric stations. The aim of the study was to compare the predictive performance of the genetic algorithm and recurrent neural network models with the K-nearest neighbour model, which was used as the benchmark model. Empirical results from the study showed that the genetic algorithm model has the best conditional predictive ability compared to the other two models, making this study a useful tool for decision-makers and system operators in power utility companies. To the best of our knowledge this is the first study which compares the genetic algorithm, the K-nearest neighbour method, and recurrent neural networks in short-term forecasting of global horizontal irradiance data from South Africa.

The Performance Assessment of Six Global Horizontal Irradiance Clear Sky Models in Six Climatological Regions in South Africa

This study assesses the performance of six global horizontal irradiance (GHI) clear sky models, namely: Bird, Simple Solis, McClear, Ineichen–Perez, Haurwitz and Berger–Duffie. The assessment is performed by comparing 1-min model outputs to corresponding clear sky reference 1-min Baseline Surface Radiation Network quality controlled GHI data from 13 South African Weather Services radiometric stations. The data used in the study range from 2013 to 2019. The 13 reference stations are across the six macro climatological regions of South Africa. The aim of the study is to identify the overall best performing clear sky model for estimating minute GHI in South Africa. Clear sky days are detected using ERA5 reanalysis hourly data and the application of an additional 1-min automated detection algorithm. Metadata for the models’ inputs were sourced from station measurements, satellite platform observations, reanalysis and some were modelled. Statistical metrics relative Mean Bias Error (rMBE), relative Root Mean Square Error (rRMSE) and the coefficient of determination (R2) are used to categorize model performance. The results show that each of the models performed differently across the 13 stations and in different climatic regions. The Bird model was overall the best in all regions, with an rMBE of 1.87%, rRMSE of 4.11% and R2 of 0.998. The Bird model can therefore be used with quantitative confidence as a basis for solar energy applications when all the required model inputs are available.

Intelligent techniques, harmonically coupled and SARIMA models in forecasting solar radiation data: A hybridization approach

The unsteady and intermittent feature (mainly due to atmospheric mechanisms and diurnal cycles) of solar energy resource is often a stumbling block, due to its unpredictable nature, to receiving high-intensity levels of solar radiation at ground level. Hence, there has been a growing demand for accurate solar irradiance forecasts that properly explain the mixture of deterministic and stochastic characteristic (which may be linear or nonlinear) in which solar radiation presents itself on the earth’s surface. The seasonal autoregressive integrated moving average (SARIMA) models are popular for accurately modelling linearity, whilst the neural networks effectively capture the aspect of nonlinearity embedded in solar radiation data at ground level. This comparative study couples sinusoidal predictors at specified harmonic frequencies with SARIMA models, neural network autoregression (NNAR) models and the hybrid (SARIMA-NNAR) models to form the respective harmonically coupled models, namely, HCSARIMA models, HCNNAR models and HCSARIMA-NNAR models, with the sinusoidal predictor function, SARIMA, and NNAR parts capturing the deterministic, linear and nonlinear components, respectively. These models are used to forecast 10-minutely and 60-minutely averaged global horizontal irradiance data series obtained from the RVD Richtersveld solar radiometric station in the Northern Cape, South Africa. The forecasting accuracy of the three above-mentioned models is undertaken based on the relative mean square error, mean absolute error and mean absolute percentage error. The HCNNAR model and HCSARIMA-NNAR model gave more accurate forecasting results for 60-minutely and 10-minutely data, respectively.
 Highlights
 
 HCSARIMA models were outperformed by both HCNNAR models and HCSARIMA-NNAR models in the forecasting arena.
 HCNNAR models were most appropriate for forecasting larger time scales (i.e. 60-minutely).
 HCSARIMA-NNAR models were most appropriate for forecasting smaller time scales (i.e. 10-minutely).
 Models fitted on the January data series performed better than those fitted on the June data series.

Evolutionary artificial neural networks for accurate solar radiation prediction

This paper evaluates the performance of different evolutionary neural network models in a problem of solar radiation prediction at Toledo, Spain. The prediction problem has been tackled exclusively from satellite-based measurements and variables, which avoids the use of data from ground stations or atmospheric soundings. Specifically, three types of neural computation approaches are considered: neural networks with sigmoid-based neurons, radial basis function units and product units. In all cases these neural computation algorithms are trained by means of evolutionary algorithms, leading to robust and accurate models for solar radiation prediction. The results obtained in the solar radiation estimation at the radiometric station of Toledo show an excellent performance of evolutionary neural networks tested. The structure sigmoid unit-product unit with evolutionary training has been shown as the best model among all tested in this paper, able to obtain an extremely accurate prediction of the solar radiation from satellite images data, and outperforming all other evolutionary neural networks tested, and alternative Machine Learning approaches such as Support Vector Regressors or Extreme Learning Machines.

Estimation of solar radiation using stepwise multiple linear regression with principal component analysis in Algeria

For the modelling of solar systems, reliable and complete time series of solar radiation are required. However, solar radiation data from ground measurements or satellite images may be available only for limited time periods and often have data quality issues or/and data gaps. It is possible to get reasonably accurate radiation estimates of solar radiation from meteorological parameters, which can complement or extend existing data. In this paper, a model based on eight meteorological parameters (evaporation, temperature, wind speed, visibility, cloud cover, sunshine duration, sunshine ratio and global solar radiation) is developed to predict the global solar radiation using 29-year (1986–2014) data from Oran radiometric station in Algeria. Two versions of the multiple regression analysis are used: the first with original observation variables (called as manifest variables) and the second by PCs called as latent variables or (common) factors. Separate analyses have been carried out for two scenarios: overall and partial study. The first scenario uses all climatic dataset, but the last scenario uses three subsets which are sunny, partly cloudy and cloudy days. This classification has been obtained using certain statistical properties that we have considered as thresholds. Stepwise multiple linear regression analysis is used to fit global solar radiation data using meteorological variables as predictors. A variable selection method based on PCA technique are used to obtain the subsets of predictors to be included in the regression model of global solar radiation data. Hence, the proposed relationships may be considered useful for predicting global solar radiation rate in other sites of Algeria that have climatic conditions similar to the study area.

Most relevant input parameters selection for 10-min global solar irradiation estimation on arbitrary inclined plane using neural networks

ABSTRACT This paper propounds the use of ‘Weights’ method to assess the relative importance of input features for estimating 10-min global solar irradiation on an arbitrary tilted plane, using artificial Neural Networks (ANNs). Two different data sources are exerted: satellite data, including different inclinations, are used for learning, while ground data, measured at Bouzaréah radiometric station (Algeria), are used for testing. ‘Weights’ method allowed to identify the relative importance of input variables and rank them according to their order of contribution, thus significantly improving the performance of the model by eliminating the parameters that are poorly correlated with the network output. The results show that the most relevant input data are in the following order: the global horizontal irradiation 35.9%, extraterrestrial irradiation 25.08%, declination 15.81%, elevation of the sun 12.60% and inclination 10.61%. The optimal configuration includes 16 neurons in the hidden layer with nRMSE = 6.37% and R 2 = 0.992.

Bright-Sun: A globally applicable 1-min irradiance clear-sky detection model

Clear-sky detection (CSD) is a crucial process in numerous solar energy applications. Many CSD models have been proposed over the years, though model performance is generally found unsatisfactory for worldwide use. We demonstrate this qualitatively on 22 CSD models at five climatologically-diverse radiometric stations; all exhibit one or more limitations: (1) unreliability at high zenith; (2) unrealistic “clear” periods immediately before or after cloudy conditions; (3) relaxed (short-term false positives); (4) over-relaxed during clear conditions (longer-term false positives); (5) conservative (short-term false negatives); and (6) over-conservative during clear conditions (longer-term false negatives).A new globally applicable CSD methodology is proposed for a posteriori detection of apparent “cloudless sky” conditions on 1-min irradiance time series, named the Bright-Sun model. This new tool requires measured global horizontal irradiance (GHI) and diffuse horizontal irradiance (DIF), and consists of three stages: (1) clear-sky irradiance optimisation, (2) tri-component CSD analysis with the newly derived Modified-Reno method, and (3) a cascading durational filters to determine periods of apparent cloudless sky. Through qualitative evaluation and exploring sensitivity to clear-sky model selection, the Bright-Sun model does not suffer any of the aforementioned limitations at any of the five stations, despite their distinctive climates. Due to the significant influence of bright or dark clouds on DIF, which have much lower impact on GHI, the new model also exhibits extra discretionary power by including analysis on DIF and can thus identify apparently clear periods with zero or near-zero cloudiness.The Bright-Sun CSD model is coded in Matlab®and freely available (future releases in R and Python are anticipated). A script is attached as supplementary material in the original form. For a supported and version controlled release of the Bright-Sun model, as well as other CSD models mentioned within this document, the reader can refer to the CSD Library at https://jamiembright.github.io/csd-library/.

Prediction of Solar Radiation According to Aerosol Optical Depth

The dependencye of aerosol optical depth on wavelength as well as the fit of the humidity, temperature and pressure approximation under atmoshperic condition at Biskra city of Algeria has been investigated. Our work consists of measuring and modeling solar radiation on the horizontal area to create a mathematical model of global solar radiation which depends on the aerosol optical depth data between two wavelengths: 550 and 1250 nm. Simultaneous measurements of global solar radiation were carried out and recorded on the horizontal zone on an urban site (Biskra, Algeria) to characterize the radiative effect of atmospheric aerosols from January to December 2013. In addition, the effect of meteorological parameters such as: humidity, ambient temperature, and time durations were studied. This relationship constitutes an alternative tool to estimate AOD at the routine lighting measurements available at many radiometric stations around the world. Finally, a comparative study was established between the theoretical results and the experimental data which leads at an excellent correlation by a low relative error which is limited by the interval 2 and 15%.

Forecasting Hourly Global Horizontal Solar Irradiance in South Africa Using Machine Learning Models

Solar irradiance forecasting is essential in renewable energy grids amongst others for back-up programming, operational planning, and short-term power purchases. This study focuses on forecasting hourly solar irradiance using data obtained from the Southern African Universities Radiometric Network at the University of Pretoria radiometric station. The study compares the predictive performance of long short-term memory (LSTM) networks, support vector regression and feed forward neural networks (FFNN) models for forecasting short-term solar irradiance. While all the models outperform principal component regression model, a benchmark model in this study, the FFNN yields the lowest mean absolute error and root mean square error on the testing set. Empirical results show that the FFNN model produces the most accurate forecasts based on mean absolute error and root mean square error. Forecast combination of machine learning models' forecasts is done using convex combination and quantile regression averaging (QRA). The predictive performance we found is statistically significant on the Diebold Mariano and Giacomini-White tests. Based on all the forecast accuracy measures used in this study including the statistical tests, QRA is found to be the best forecast combination method. QRA was also the best forecasting model compared with the stand-alone machine learning models. The median method for combining interval limits gives the best results on prediction interval widths analysis. This is the first application of LSTM on South African and African solar irradiance data to the best of our knowledge. This study has shown that providing adequate and detailed evaluation metrics, including statistical tests in forecasting gives more insight into the developed forecasting models.

Day Ahead Hourly Global Horizontal Irradiance Forecasting—Application to South African Data

Due to its variability, solar power generation poses challenges to grid energy management. In order to ensure an economic operation of a national grid, including its stability, it is important to have accurate forecasts of solar power. The current paper discusses probabilistic forecasting of twenty-four hours ahead of global horizontal irradiance (GHI) using data from the Tellerie radiometric station in South Africa for the period August 2009 to April 2010. Variables are selected using a least absolute shrinkage and selection operator (Lasso) via hierarchical interactions and the parameters of the developed models are estimated using the Barrodale and Roberts’s algorithm. Two forecast combination methods are used in this study. The first is a convex forecast combination algorithm where the average loss suffered by the models is based on the pinball loss function. A second forecast combination method, which is quantile regression averaging (QRA), is also used. The best set of forecasts is selected based on the prediction interval coverage probability (PICP), prediction interval normalised average width (PINAW) and prediction interval normalised average deviation (PINAD). The results demonstrate that QRA gives more robust prediction intervals than the other models. A comparative analysis is done with two machine learning methods—stochastic gradient boosting and support vector regression—which are used as benchmark models. Empirical results show that the QRA model yields the most accurate forecasts compared to the machine learning methods based on the probabilistic error measures. Results on combining prediction interval limits show that the PMis the best prediction limits combination method as it gives a hit rate of 0.955 which is very close to the target of 0.95. This modelling approach is expected to help in optimising the integration of solar power in the national grid.

Prediction of diffuse horizontal irradiance using a new climate zone model

Knowledge on the diffuse horizontal irradiance (DHI), and direct normal irradiance (DNI) is crucial for the estimation of the irradiance on tilted surfaces, which in turn is critical for photovoltaic (PV) applications and for designing and simulating concentrated solar power (CSP) plants. Since global horizontal irradiance (GHI) is the most commonly measured solar radiation variable, it is advantageous for establishing a suitable method that uses it to compute DHI and DNI. In this way, a new model for predicting the diffuse fraction (Kd) based on the climate zone is proposed, using only the clearness index (Kt) as the predictor and 1-min resolution GHI data. A review of the literature on models that use hourly and sub-hourly Kt values to compute Kd was also carried out, and an extensive performance assessment of both the proposed model and the models from the literature was conducted using ten statistical indicators and a global performance index (GPI). A set of model parameters was determined for each climate zone considered in this study (arid, high albedo, temperate and tropical) using 48 worldwide radiometric stations. It was found that the best overall performing model was the model proposed in this work.

Machine learning regressors for solar radiation estimation from satellite data

In this paper we evaluate the performance of several Machine Learning regression techniques in a problem of global solar radiation estimation from geostationary satellite data. Different types of neural networks, Support Vector Regression and Gaussian Processes have been selected as regression techniques to be evaluated, due to their good performance in similar problems in the past. The study area is located in the surroundings of the radiometric station of Toledo, Spain. In order to train the regression techniques considered, one complete year of hourly global solar radiation data is used as the target of the experiments, and different input variables are considered: a cloud index, a clear-sky solar radiation model and several reflectivity values from Meteosat visible images. To assess the results obtained by the Machine Learning algorithms, we have selected as a reference three different physical-based methods, a model based on the Heliosat-2 method (Heliosat-2), the Copernicus Atmosphere Monitoring Service (CAMS) and the SolarGIS model (Soevaluate the performance of Machine Learning regressors when the physical models are included as input variables, in a class of post-processing of these physical approaches. The results obtained show the capacity of Machine Learning regressors to obtain reliable global solar radiation estimation by using satellite measurements.

ANN-based modelling and prediction of daily global solar irradiation using commonly measured meteorological parameters

The aim of this work is to develop an artificial neural network (ANN) based model for accurately predicting the daily global solar irradiation in the city of Fez. The potential of the developed model is verified and appraised through the local collected database for the period 2009-2015 from the radiometric station of the Faculty of Sciences and Technology of Fez. The obtained model is MLP with feed forward back-propagation algorithm containing three input parameters and a single hidden layer with nine neurons. Coefficient of determination R2, the mean absolute percentage error MAPE and the relative root mean square error RRMSE are respectively equal to 97.16%, 21.77% and 18.79%.

Downscaling solar irradiance using DEM-based model in young volcanic islands with rugged topography

Many small island developing states are adopting solar photovoltaic technologies as a solution to curtail their overreliance on fossil fuels. Some of these islands are young and of volcanic origin, characterised by intricate topographic heterogeneity. Since they are mostly small, flat land is scarce and valuable. As a result, solar photovoltaic projects are usually developed at sites with complex terrain where frequent changes in elevation, slope and shadows cast by topographic features can significantly attenuate the amount of solar irradiance received. The existence of strong local solar radiation gradients on such islands implies that any solar resource assessment must be performed at a small enough spatial and temporal resolution in order to provide a reliable basis for investment decisions. Ground-based measurements of solar irradiance are accurate but are widely dispersed geographically. Although satellite-derived solar resource data have better spatial and temporal resolution than those recorded by radiometric stations, they are less accurate. Moreover, their spatial resolution is still too large with respect to the small size of the islands. In this work, a downscaling methodology is used to derive monthly and annual average global solar irradiance maps at a resolution of 250 m × 250 m using satellite hourly datasets, spanning over the period 1999 to 2015 and having a spatial resolution of 0.05° × 0.05°. The combined effects of horizon blocking and sky obstruction resulting from heterogeneous topography are considered by applying a binary blocking factor and sky view factor respectively. The downscaled maps are then refined by convolving them with ground-based measurements through a kriging procedure. The methodology is validated using leave-one-out kriging procedure and illustrated successfully with the case of Reunion Island, where strong local gradients of solar irradiance were easily distinguished in regions marked by uneven topographic features.

Solar irradiation from the energy production of residential PV systems

Abstract Considering the dense network of residential photovoltaic (PV) systems implemented in Belgium, the paper evaluates the opportunity of deriving global horizontal solar irradiation data from the electrical energy production registered at PV systems. The study is based on one year (i.e. 2014) of hourly PV power output collected at a representative sample of roughly 1500 residential PV installations. Validation is based on ground-based measurements of solar radiation performed within the network of radiometric stations operated by the Royal Meteorological Institute of Belgium and the method's performance is compared to the satellite-based retrieval approach. Our results indicate that the accuracy of the derived solar irradiation data depends on a number of factors including the efficiency of the PV system, the weather conditions, the density of PV systems that can be used for the tilt to horizontal conversion, other data sources that can be accessed to complement the PV data. In particular, the computed solar irradiation data degrade as the information about the orientation and tilt angles of the PV generator becomes more inaccurate. It is also found that there are certain sun positions (i.e. low solar elevations) for which the method fails to produce a valid estimation.

Modeling the erythemal surface diffuse irradiance fraction for Badajoz, Spain

Abstract. Despite its important role on the human health and numerous biological processes, the diffuse component of the erythemal ultraviolet irradiance (UVER) is scarcely measured at standard radiometric stations and therefore needs to be estimated. This study proposes and compares 10 empirical models to estimate the UVER diffuse fraction. These models are inspired from mathematical expressions originally used to estimate total diffuse fraction, but, in this study, they are applied to the UVER case and tested against experimental measurements. In addition to adapting to the UVER range the various independent variables involved in these models, the total ozone column has been added in order to account for its strong impact on the attenuation of ultraviolet radiation. The proposed models are fitted to experimental measurements and validated against an independent subset. The best-performing model (RAU3) is based on a model proposed by Ruiz-Arias et al. (2010) and shows values of r2 equal to 0.91 and relative root-mean-square error (rRMSE) equal to 6.1 %. The performance achieved by this entirely empirical model is better than those obtained by previous semi-empirical approaches and therefore needs no additional information from other physically based models. This study expands on previous research to the ultraviolet range and provides reliable empirical models to accurately estimate the UVER diffuse fraction.