Relative Mean Bias Error Research Articles

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.

An improved method for calculating the freezing/thawing index using monthly and annual temperature data

AbstractChanges in soil thermal regimes in cold climates have widespread impacts on hydrology, ecology, and the carbon cycle. The annual freezing and thawing index, which is generally calculated using daily temperature, has been widely used to estimate the freezing depth, active layer thickness, and the distribution of permafrost. However, continuous and reliable daily temperature data are scarce in cold climates, while monthly and annual temperature data are more readily available. If daily temperature data are unavailable, these indices can be estimated based on monthly or annual temperature data. In this study, we developed a resampling method for estimating the annual freezing and thawing index and compared the results with those produced by the existing methods. Daily temperature data with a 0.5° resolution over the Northern Hemisphere during 1901–2012 were used to calculate the freezing/thawing index, and then the monthly and annual temperature were calculated and three different approaches were used to estimate the daily temperature and the freezing/thawing index. When the monthly data were used, the resampling method produced the smallest relative error (RE) and mean bias error (MBE), and the largest correlation in estimating the two indices, compared to the two other methods. Although the annual temperature data usually underestimate the freezing/thawing index, the RE is still <5% over most of the high‐latitude regions. The results suggest that if the daily temperature can be reliably estimated using the resampling method, the thermal regimes of permafrost can be reliably estimated using modelled monthly temperature and/or reconstructed past monthly/annual temperature. These estimations can also be used to validate modelled paleo‐permafrost and its variations. Additionally, our results indicate that after the 1970s the annual freezing index (DDF) increased substantially, while the frost index (FI) decreased substantially.

A novel combined multi-task learning and Gaussian process regression model for the prediction of multi-timescale and multi-component of solar radiation

A novel combined multi-task learning and Gaussian process regression (MTGPR) model is proposed to predict the multi-time scale (daily and monthly mean daily) and multi-component (global and diffuse) solar radiation simultaneously. Compared to conventional Gaussian process regression (GPR) which can only be used for specific solar radiation component prediction on a specific timescale, the MTGPR can utilize the correlated information between different tasks to improve the model generalization and accuracy. Meteorological data from ten stations in China were used to train and validate the GPR and MTGPR models for daily global, monthly mean daily global, daily diffuse and monthly mean daily diffuse solar radiation prediction. The results showed that the GPR and MTGPR models are highly accurate in estimating daily and monthly mean daily solar radiation with coefficient of determination (R2), root mean square error (RMSE), relative root mean square error (rRMSE) and mean bias error (MBE) of GPR in ranges of 0.4623–0.9892, 0.5542–4.1591 MJm−2d−1, 4.70–39.75% and −1.1750–1.5347 MJm−2d−1, respectively. Because the MTGPR learned the intercorrelated information between different tasks, compared to GPR models, the MTGPR models performed better. For daily prediction, the average R2, RMSE and rRMSE of the MTGPR improved by 0.19–0.48%, 0.57–0.65% and 0.51–0.52%, respectively. In terms of monthly mean daily prediction, the corresponding values of MTGPR improved by 2.62–2.65%, 5.50–12.07% and 5.21–12.08%, respectively. This paper provides a compact guide for the simultaneous prediction of combined parameters.

The Ångström–Prescott Regression Coefficients for Six Climatic Zones in South Africa

The South African Weather Service (SAWS) manages an in situ solar irradiance radiometric network of 13 stations and a very dense sunshine recording network, located in all six macroclimate zones of South Africa. A sparsely distributed radiometric network over a landscape with dynamic climate and weather shifts is inadequate for solar energy studies and applications. Therefore, there is a need to develop mathematical models to estimate solar irradiation for a multitude of diverse climates. In this study, the annual regression coefficients, a and b, of the Ångström–Prescott (AP) model, which can be used to estimate global horizontal irradiance (GHI) from observed sunshine hours, were calibrated and validated with observed station data. The AP regression coefficients were calibrated and validated for each of the six macroclimate zones of South Africa using the observation data that span 2013 to 2019. The predictive effectiveness of the calibrated AP model coefficients was evaluated by comparing estimated and observed daily GHI. The maximum annual relative Mean Bias Error (rMBE) was 0.371%, relative Mean Absolute Error (rMAE) was 0.745%, relative Root Mean Square Error (rRMSE) was 0.910%, and the worst-case correlation coefficient (R2) was 0.910. The statistical validation metrics results show that there is a strong correlation and linear relation between observed and estimated GHI values. The AP model coefficients calculated in this study can be used with quantitative confidence in estimating daily GHI data at locations in South Africa where daily observation sunshine duration data are available.

Worldwide evaluation and correction of irradiance measurements from personal weather stations under all-sky conditions

Personal weather stations (PWS) are gaining popularity since they provide open meteorological data with high spatial resolution. However, a number of factors may affect the quality of the measurements of these stations. PWS provide irradiance measurements using silicon-photodiode sensors, which are a low-cost and lower-maintenance option compared to thermopile-type pyranometers. Silicon-photodiode sensors present, however, several limitations related to the spectral bandwidth, the device’s temperature and other affecting factors, which increase the error in the measurements. This article evaluates the accuracy of irradiance measurements from PWS under all-sky conditions. We propose a calibration method to reduce the uncertainty in the measurements based on the solar zenith angle, the temperature of the device and the clear-sky index. The proposed calibration model is evaluated in 30 personal weather stations from different producers located in 5 climate zones worldwide over several years. An average reduction of the relative mean bias error from 18.4% to 2.8% is achieved based on 5-min instantaneous irradiance samples for clear-sky instances and it is within a ±5% tolerance for all-sky conditions, where other metrics are also improved 1–4%. This study helps understanding the nature of uncertainty of irradiance measurements in this increasingly used data source and provides a practical calibration method to increase accuracy of PWS data.

Validation of global irradiance derived from INSAT-3D over India

Geostationary satellites offer the possibility of producing high-frequency time series irradiance datasets, covering a large geographical area. Here, we derive half-hourly global irradiance (GHI) at 4 km spatial resolution from visible channel radiance of INSAT-3D satellite using a semi-empirical model and validate it against 19 ground stations over 2015–16, across India. Our model uses the Advanced Solis clear-sky model with monthly climatological values of modern-era retrospective analysis for research and applications-2 (MERRA-2) aerosol optical depth (AOD) and precipitable water (PW) as inputs. The relative root mean squared error (rRMSE) and relative mean bias error (rMBE) are 24.02% and −0.05%, respectively. Over the validation period, INSAT-3D derived GHI outperformed SARAH-E model and MERRA-2 reanalysis GHI.

Evaluation of the reanalysis surface solar radiation from NCEP, ECMWF, NASA, and JMA using surface observations for Balochistan, Pakistan

Solar radiation from reanalysis datasets can be used to estimate solar energy potential in the absence of long-term surface measured data. Comprehensive validation of reanalysis data against short-term measurements of solar radiation is necessary to find uncertainties. The evaluation of the performance of seven reanalysis datasets (ERA-5, MERRA-2, ERA-Interim, JRA-55, NCEP-NCAR, NCEP-DOE, and CFSR) for Balochistan against high-quality surface measured data was performed using statistical analysis. The relative mean bias error (rMBE), relative mean absolute error (rMAE), and relative root mean square error of reanalysis solar radiation range from −4 to 7%, 8 to 14%, and 16 to 21%, respectively, using sub-daily data of six datasets except for NCEP-NCAR. Seasonal statistical analysis was performed to study seasonal variation of performance of datasets, which reveals the significant variation of errors in different seasons. Analysis of monthly mean data shows that rMBE and rMAE are less than 3 and 5% for ERA-5, respectively. The performance of the dataset changes by changing the temporal resolution of the data used for comparison. The monthly mean values of data show better performance, but the accuracy of data is compromised. The solar radiation data of ERA-5 can be used for preliminary solar resource assessment and power estimation.

Global horizontal irradiance forecast for Finland based on geostationary weather satellite data

Global horizontal irradiance (GHI) estimates and forecasts are necessary for the efficient use of a naturally fluctuating energy source like solar energy. However, few forecasting methods exist for high latitudes. In this study we present the development and validation of a satellite-based GHI forecast for southern Finland, called Solis-Heliosat. The forecast is formed by combining information from the clear sky (CS) model Pvlib Solis with consecutive geostationary weather satellite imagery, using the Heliosat method. Forecasts are produced up to 4 h with a 15-min temporal resolution. The CS model, the satellite-based all-sky estimate, and the GHI forecast have been compared and validated against other methods and in situ GHI measurements. An additional comparison was made for two datasets representing a changing cloud environment.The CS model estimates had an average rMBE (relative Mean Bias Error) of −6% to 1% and a rRMSE (relative Root Mean Square Error) of 6–10%. For the all-sky estimates the rMBE was −4% to −2%, and rRMSE 2–33%. With increasing forecast time the Solis-Heliosat rMBE descends to −9% and rRMSE reaches 50% at 4 h. Solis-Heliosat performs better than the persistence forecasts in most cases, particularly in a changing cloud environment.Our study indicates the use of satellite-based forecasts as a viable tool for forecasting GHI for the solar energy industry also in the high latitudes. In high latitudes geostationary satellite-based methods are at their limit; however, the information they can provide will enable efficient solar energy production.

Wind turbine power output very short-term forecast: A comparative study of data clustering techniques in a PSO-ANFIS model

The emergence of new sites for wind energy exploration in South Africa requires an accurate prediction of the potential power output of a typical utility-scale wind turbine in such areas. However, careful selection of data clustering technique is very essential as it has a significant impact on the accuracy of the prediction. Adaptive neurofuzzy inference system (ANFIS), both in its standalone and hybrid form has been applied in offline and online forecast in wind energy studies, however, the effect of clustering techniques has not been reported despite its significance. Therefore, this study investigates the effect of the choice of clustering algorithm on the performance of a standalone ANFIS and ANFIS optimized with particle swarm optimization (PSO) technique using a synthetic wind turbine power output data of a potential site in the Eastern Cape, South Africa. In this study a wind resource map for the Eastern Cape province was developed. Also, autoregressive ANFIS models and their hybrids with PSO were developed. Each model was evaluated based on three clustering techniques (grid partitioning (GP), subtractive clustering (SC), and fuzzy-c-means (FCM)). The gross wind power of the model wind turbine was estimated from the wind speed data collected from the potential site at 10 min data resolution using Windographer software. The standalone and hybrid models were trained and tested with 70% and 30% of the dataset respectively. The performance of each clustering technique was compared for both standalone and PSO-ANFIS models using known statistical metrics. From our findings, ANFIS standalone model clustered with SC performed best among the standalone models with a root mean square error (RMSE) of 0.132, mean absolute percentage error (MAPE) of 30.94, a mean absolute deviation (MAD) of 0.077, relative mean bias error (rMBE) of 0.190 and variance accounted for (VAF) of 94.307. Also, PSO-ANFIS model clustered with SC technique performed the best among the three hybrid models with RMSE of 0.127, MAPE of 28.11, MAD of 0.078, rMBE of 0.190 and VAF of 94.311. The ANFIS-SC model recorded the lowest computational time of 30.23secs among the standalone models. However, the PSO-ANFIS-SC model recorded a computational time of 47.21secs. Based on our findings, a hybrid ANFIS model gives better forecast accuracy compared to the standalone model, though with a trade-off in the computational time. Since, the choice of clustering technique was observed to play a vital role in the forecast accuracy of standalone and hybrid models, this study recommends SC technique for ANFIS modeling at both standalone and hybrid models.

Satellite Retrieval of Downwelling Shortwave Surface Flux and Diffuse Fraction under All Sky Conditions in the Framework of the LSA SAF Program (Part 2: Evaluation)

High frequency knowledge of the spatio-temporal distribution of the downwelling surface shortwave flux (DSSF) and its diffuse fraction (fd) at the surface is nowadays essential for understanding climate processes at the surface–atmosphere interface, plant photosynthesis and carbon cycle, and for the solar energy sector. The European Organization for the Exploitation of Meteorological Satellites (EUMETSAT) Satellite Application Facility for Land Surface Analysis operationally delivers estimation of the MDSSFTD (MSG Downwelling Surface Short-wave radiation Fluxes—Total and Diffuse fraction) product with an operational status since the year 2019. The method for retrieval was presented in a companion paper. Part 2 now focuses on the evaluation of the MDSSFTD algorithm and presents a comparison of the corresponding outputs, i.e., total DSSF and diffuse fraction (fd) components, against in situ measurements acquired at four Baseline Surface Radiation Network (BSRN) stations over a seven-month period. The validation is performed on an instantaneous basis. We show that the satellite estimates of DSSF and fd meet the target requirements defined by the user community for all-sky (clear and cloudy) conditions. For DSSF, the requirements are 20 Wm−2 for DSSF < 200 Wm−2, and 10% for DSSF ≥ 200 Wm−2. The mean bias error (MBE) and relative mean bias error (rMBE) compared to the ground measurements are 3.618 Wm−2 and 0.252%, respectively. For fd, the requirements are 0.1 for fd < 0.5, and 20% for fd ≥ 0.5. The MBE and rMBE compared to the ground measurements are −0.044% and −17.699%, respectively. The study also provides a separate analysis of the product performances for clear sky and cloudy sky conditions. The importance of representing the cloud–aerosol radiative coupling in the MDSSFTD method is discussed. Finally, it is concluded that the quality of the aerosol optical depth (AOD) forecasts currently available is accurate enough to obtain reliable diffuse solar flux estimates. This quality of AOD forecasts was still a limitation a few years ago.

Power curve modeling for wind turbine systems: a comparison study

ABSTRACT The main goal of this study is to determine which one of the current methods is the most appropriate in representing the power curve of commercial Wind Turbine Systems (WTSs). For this purpose, the adequacy of various power curve methods is quantitatively evaluated with reference to three well-known statistical indices; Root Mean Square Error (RMSE), Coefficient of determination (R 2) and relative Mean Bias Error (rMBE). The capabilities of these methods in representing power curve of commercial WTSs are also evaluated on predicting the mean power of these WTSs assuming that they were located at a specified wind site. Several WTSs (about 100 wind turbines) with their experimental data are undertaken in the analyses. Results indicate that the methods based on capacitor charging voltage equation (M 10) and quadratic form of wind speed (M 4) are more effective than the remaining ones in predicting the output power of WTSs.

Solar irradiance modelling using an offline coupling procedure for the Weather Research and Forecasting (WRF) model

The research proposed herein seeks to improve solar irradiance magnitude and variability results produced by the Weather Research and Forecasting (WRF) model using a novel offline coupling procedure (OCP). The OCP includes simulations in clear sky conditions, where the effects from varying atmospheric composition depend on the broadband clear sky model used, on cloud attenuation and on decomposition techniques to accurately separate the global irradiance into direct and diffuse components. Furthermore, shadowing and slope effects from orographic features and other obstacles are included with much greater detail. Benefits of the offline coupling procedure were quantified by comparison against local solar radiation measurements over a period of one year. A baseline test to explore the different configuration options was implemented. It considers two aerosol databases, three broadband clear sky models, two cloud attenuation corrections based on clear sky index (either global or by components) and four decomposition models. Given the amount of results from baseline tests, the relative root-mean-square error (rRMSE) was used as the criterion to identify the most suitable OCP configuration, which was subsequently used in the performance analysis. The current baseline test comprises seven sites selected from the Baseline Radiation Network (BSRN) in different terrain complexities and atmospheric conditions. Statistical indicators associated with the annual global horizontal irradiance reveal that OCP improved WRF results by 88.4% in terms of the relative mean bias error (rMBE) and by 5.0% in the value of the Nash-Sutcliffe efficiency (NSE). A standard OCP configuration to model global horizontal irradiance only is proposed. The rMBE of annual hourly global horizontal irradiance oscillated between −3.6% and 3.9%, whilst the NSE varied between 0.608 and 0.939. The analogous quantities for diffuse horizontal irradiance were -19.3%⩽rMBE⩽4.6% and 0.371⩽NSE⩽0.717, while for direct normal irradiance -6.5%⩽rMBE⩽23.2% and 0.101⩽NSE⩽0.656.

Evaluation of WRF parameterizations for global horizontal irradiation forecasts: A study for Turkey

This study deals with the evaluation of the Weather Research and Forecast (WRF) model’s parameterization schemes when used for global horizontal irradiation (GHI) forecasts, to assess the feasibility of solar energy utilization. The study area is the southeastern Anatolia (SEA) region of Turkey, with favorable weather conditions for solar energy generation. The results indicate that the values in the hourly output of GHI in the model were overestimated for all configurations at all stations compared to observations. The relative mean bias error values at five stations for all configurations vary between 10-21% for clear-sky and 17-30% for partly-cloudy conditions. Similarly, the relative RMSE values at the five stations vary between 20-39% for clear sky and 41-70% for partly-cloudy conditions. However, there are noticeable differences among the various configurations of the WRF parameterizations.

Assessment of Hourly Solar Direct Normal Irradiance using Eight Broadband Clear Sky Models: Study of Four Moroccan Arid Sites

This paper presents a statistical comparative study of eight important parametric broadband clear sky models, against Meteosat-derived data, to estimate solar hourly direct normal irradiance (DNI) for four Moroccan arid zone sites. To achieve this aim, four sites well spread across this climatic zone were selected, and four references days were chosen. The statistical parameters such as relative mean bias error (rMBE), the relative root mean square error (rRMSE), and the determination coefficient are calculated. According to these results, the Bird model produces acceptable estimates with 62.5% of good results of rMBE ranging between 0 and 6%; 25% of average results of rRMSE ranging between 11% and 14%, and 62.5% of good results of ranging between 0.90 and 0.96. The comparison of both means of DNI, calculated and measured for a given site and day of reference, using the paired t-test, states that for a level of significance of 1%, the Bird model and the REST2 model give in the quarter of the studied cases conforming means of hourly DNI. For a level of significance of 0.1%, the Bird model is more proficient and gives conforming means in almost half of the cases studied. Despite all these performances displayed by the Bird Model, it remains average and does not reach the required level in some sites at certain times. The elaboration of a new simpler DNI estimation model giving higher performances for this zone of high solar potential is of great interest.

On modeling reference crop evapotranspiration under lack of reliable data over Iran

This study was conducted to evaluate the performance of temperature-based models i.e. temperature-based Penman-Monteith FAO 56 fed with average wind speed (U) value (TPMU) and default U quantity (TPM2), Hargreaves-Samani (HS) and FAO Blaney-Criddle (FBC) against Penman-Monteith FAO 56 (PM) using data recorded in 1993–2015 at 146 sites over Iran. Two statistics i.e. normalized Root Mean Square (nRMSE) and relative Mean Bias Error (rMBE) were calculated to analyze the absolute error and bias magnitude of the temperature-based ET0 estimation, respectively. Except for the December-January-February (DJF), the models gave reliable seasonal estimates (i.e. nRMSE of 30 > %) for the majority of studied areas. At monthly scale, FBC gave poor estimates of ET0 in DJF for more than 60% of semi-arid and sub/humid-humid sites. ET0 in December and January was not also modeled reliably by TPM2 for 61 and 52% of the semi-arid and sub/humid-humid sites, respectively. Hence, application of FBC and TPM2 appears not to be recommendable in cold areas and months over Iran. Overall, TPMU and HS are better suited at all temporal scales under data limitation over the studied areas. In the case of data availability, calculation of TPM with local average U (instead of default quantity of 2 m s−1) is highly likely to improve the estimation accuracy. Seasonal and monthly ET0 were mostly underestimated over the hyper-arid/arid sites during the March-April-May (MAM) and June-July-August (JJA). However, TPM2 and HS overestimated ET0 for the majority of semi-arid and sub-humid/humid areas. The U anomalies were identified as the primary contributing factor to the error in temperature-based ET0 estimation for most cases. TPM2, HS and FBC provided more accurate estimates for the U range of 1.5–2.5 m s−1. These findings are of significant practical importance for agricultural, hydrological and climatic studies and applications under data sparse condition.

Bias correction of global irradiance modelled with weather and research forecasting model over Paraguay

The estimation of solar irradiance is performed by means of numerical weather prediction (NWP) models that include all the necessary information to solve the temporal, geographical and atmospheric conditions variability being this the basis of solar energy applications. However, the radiative transfer schemes implemented in meteorological models show systematic errors in the simulation of global horizontal irradiance (GHI). In this contribution, we present a post-process analysis of Weather and Research Forecasting (WRF-ARW) model which combines a Kalman Filter with Model Output Statistics (MOS) for bias correction in order to improve the overall predicted values of GHI simulations over Paraguay. The hourly GHI is simulated at 4 × 4 km2 of spatial resolution. The annual evaluation of the hourly WRF model without post process shows relative mean bias error (rMBE) of 21% and relative root mean square error (rRMSE) of 81%. The results using several ground stations and combinations of post-process show an annual correction of systematic errors with rMBE of −0.7% and rRMSE of 70%.

Robust cloud motion estimation by spatio-temporal correlation analysis of irradiance data

The main contributor to spatio-temporal variability in the solar resource is clouds passing over photovoltaic (PV) modules. Cloud velocity is a principal input to many short-term forecast and variability models. In this paper spatio-temporal correlations of irradiance data are analyzed to estimate cloud motion. The analysis is performed using two spatially and temporally resolved simulated irradiance datasets generated from large eddy simulation. Cloud motion is estimated using two different methods; the cross-correlation method (CCM) applied to two or a few consecutive time steps and cross-spectral analysis (CSA) where the cloud speed and direction are estimated by cross-spectral analysis of a longer time series. CSA is modified to estimate the cloud motion direction as the case with least variation for all the velocities in the cloud motion direction. To ensure reliable cloud motion estimation, quality control (QC) is added to the CSA and CCM analyses. The results show 33% (52°) and 21% (6°) improvement in the cloud motion speed (direction) estimation using the modified CSA and CCM over the original methods (without QC), respectively. In general, CCM results are accurate for all the different cloud cover fractions with average relative mean bias error (rMBE) of cloud speed and mean absolute error of cloud direction equal to 3% and 3°, respectively. For low cloud cover fractions, CSA estimates the cloud motion speed and direction with rMBE and mean absolute error equal to 10% and 11°, respectively. However, for high cloud cover fractions and unsteady cloud speed, CSA results are not reliable for 3–4 h time series; however, splitting the whole time series into shorter time intervals reduces the rMBE and mean absolute error to 15% and 16° respectively.

Comparative Assessment of PV Plant Performance Models Considering Climate Effects

The climate conditions can affect the accuracy of photovoltaic (PV) system performance models that can be used for monitoring and diagnostic purposes. In this paper, an improved energetic physical model has been considered to estimate the power production of PV systems. Specifically, in this model, special attention has been devoted to the modeling of optical losses (IAM losses) and to the inverter efficiency under low-power conditions.A comparative analysis of the proposed model applied to two PV plants installed respectively in the north of Denmark (Aalborg) and in the south of Italy (Agrigento) has been performed. The different ambient, operating and installation conditions allow to understand how these factors impact the precision and effectiveness of such model. The experimental results show that the proposed model allows us to have a good estimation of AC power in terms of Relative Mean Bias Error, normalized Root-Mean-Square Error, and the Correlation Coefficient. Further in order to have the possibility to analyze and compare the performance of the studied PV plants with others, the efficiency of the systems has been estimated by both Performance Ratio and Corrected Performance Ratio.

Validating nine clear sky radiation models in Australia

There have been many validation studies of clear sky solar radiation models, however, to date, no such analysis has been completed for Australia. Clear sky models are essential for estimating the generation potential of various solar energy technologies, the basic calibration of radiation measuring equipment, quality control of solar radiation datasets, engineering design (e.g. heating and cooling of buildings) and in agricultural and biological sciences (e.g. forestry). All of these areas are of considerable interest to the Australian economy and will benefit from an assessment of clear sky radiation models. With the recent provision of one-minute interval radiation data by the Australian Bureau of Meteorology for 20 sites across Australia, such a study can now be undertaken at a level not previously possible. Using up to ten years of data from each of 14 of these sites, clear sky periods are extracted through an automated detection algorithm. With these clear sky periods identified, nine of the most prominent beam and global clear sky radiation models are assessed using the relative Mean Bias Error, relative Root Mean Square Error and Coefficient of Determination as metrics. Further testing assessed model performance as a function of solar zenith angle and apparent solar time. Results show that for global clear sky simulations, the Solis, Esra and REST2 approaches perform best, while the Iqbal, Esra and REST2 methods are the most proficient clear sky beam models.

Impact of local broadband turbidity estimation on forecasting of clear sky direct normal irradiance

Clear-sky modeling is of critical importance for the accurate determination of Direct Normal Irradiance (DNI), which is the relevant component of the solar irradiance for concentrated solar energy applications. Accurate clear-sky modeling of DNI is typically best achieved through the separate consideration of water vapor and aerosol concentrations in the atmosphere. Highly resolved temporal measurements of such quantities is typically not available unless a meteorological station is located in close proximity. When this type of data is not available, attenuating effects on the direct beam are modeled by Linke turbidity-equivalent factors, which can be obtained from broadband observations of DNI under cloudless skies. We present a novel algorithm that allows for a time-resolved estimation of the average daily Linke turbidity factor from ground-based DNI observations under cloudless skies. This requires a method of identifying clear-sky periods in the observational time series (in order to avoid cloud contamination) as well as a broadband turbidity-based clear-sky model for implicit turbidity calculations. While the method can be applied to the correction of historical clear-sky models for a given site, the true value lies in the forecasting of DNI under cloudless skies through the assumption of a persistence of average daily turbidity. This technique is applied at seven stations spread across the states of California, Washington, and Hawaii while using several years of data from 2010 to 2014. Performance of the forecast is evaluated by way of the relative Root Mean Square Error (rRMSE) and relative Mean Bias Error (rMBE), both as a function of solar zenith angle, and benchmarked against monthly climatologies of turbidity information. Results suggest that rRMSE and rMBE of the method are typically smaller than 5% for both historical and forecasted CSMs, which compare favorably against the 10–20% range that is typical for monthly climatologies.