Solar radiation analysis and regression coefficients for the Vhembe Region, Limpopo Province, South Africa

Given the limited observed and reliable data for solar irradiance in rural parts in South Africa, a correlation equation of the Angström-Prescott linear type has been used to estimate the regression coefficients in the Vhembe District, Limpopo Province, South Africa. Five stations were selected for the study, with the greatest distance between stations less than 180 km. Monthly regression coefficients were derived for each station based on an observation dataset of sunshine duration hours and global horizontal irradiance. The correlation coefficients appear to be above 0.9. The representative Angström-Prescott model for the Vhembe Region was found by collating the data for each station and then averaging the respective correlation coefficients. This paper presents the generated regression coefficients for each station and for the Vhembe Region

Comparison of Satellite-Based and Ångström–Prescott Estimated Global Horizontal Irradiance under Different Cloud Cover Conditions in South African Locations

The study compares the performance of satellite-based datasets and the Ångström–Prescott (AP) model in estimating the daily global horizontal irradiance (GHI) for stations in South Africa. The daily GHI from four satellites (namely SOLCAST, CAMS, NASA SSE, and CMSAF SARAH) and the Ångström–Prescott (AP) model are evaluated by validating them against ground observation data from eight radiometric stations located in all six macro-climatological regions of South Africa, for the period 2014-19. The evaluation is carried out under clear-sky, all-sky, and overcast-sky conditions. CLAAS-2 cloud fractional coverage data are used to determine clear and overcast sky days. The observed GHI data are first quality controlled using the Baseline Surface Radiation Network methodology and then quality control of the HelioClim model. The traditional statistical benchmarks, namely the relative mean bias error (rMBE), relative root mean square error (rRMSE), relative mean absolute error (rMAE), and the coefficient of determination (R2) provided information about the performance of the datasets. Under clear skies, the estimated datasets showed excellent performance with maximum rMBE, rMAE, and rRMSE less than 6.5% and a minimum R2 of 0.97. In contrast, under overcast-sky conditions there was noticeably poor performance with maximum rMBE (24%), rMAE (29%), rRMSE (39%), and minimum R2 (0.74). For all-sky conditions, good correlation was found for SOLCAST (0.948), CMSAF (0.948), CAMS (0.944), and AP model (0.91); all with R2 over 0.91. The maximum rRMSE for SOLCAST (10%), CAMS (12%), CMSAF (12%), and AP model (11%) was less than 13%. The maximum rMAE for SOLCAST (7%), CAMS (8%), CMSAF (8%), and AP model (9%) was less than 10%, showing good performance. While the R2 correlations for the NASA SSE satellite-based GHI were less than 0.9 (0.896), the maximum rRMSE was 18% and the maximum rMAE was 15%, showing rather poor performance. The performance of the SOLCAST, CAMS, CMSAF, and AP models was almost the same in the study area. CAMS, CMSAF, and AP models are viable, freely available datasets for estimating the daily GHI at South African locations with quantitative certainty. The relatively poor performance of the NASA SSE datasets in the study area could be attributed to their low spatial resolution of 0.5° × 0.5° (~55 km × 55 km). The feasibility of the datasets decreased significantly as the proportion of sky that was covered by clouds increased. The results of the study could provide a basis/data for further research to correct biases between in situ observations and the estimated GHI datasets using machine learning algorithms

Comparison of Satellite-Based and Ångström–Prescott Estimated Global Horizontal Irradiance under Different Cloud Cover Conditions in South African Locations

The study compares the performance of satellite-based datasets and the Ångström–Prescott (AP) model in estimating the daily global horizontal irradiance (GHI) for stations in South Africa. The daily GHI from four satellites (namely SOLCAST, CAMS, NASA SSE, and CMSAF SARAH) and the Ångström–Prescott (AP) model are evaluated by validating them against ground observation data from eight radiometric stations located in all six macro-climatological regions of South Africa, for the period 2014-19. The evaluation is carried out under clear-sky, all-sky, and overcast-sky conditions. CLAAS-2 cloud fractional coverage data are used to determine clear and overcast sky days. The observed GHI data are first quality controlled using the Baseline Surface Radiation Network methodology and then quality control of the HelioClim model. The traditional statistical benchmarks, namely the relative mean bias error (rMBE), relative root mean square error (rRMSE), relative mean absolute error (rMAE), and the coefficient of determination (R2) provided information about the performance of the datasets. Under clear skies, the estimated datasets showed excellent performance with maximum rMBE, rMAE, and rRMSE less than 6.5% and a minimum R2 of 0.97. In contrast, under overcast-sky conditions there was noticeably poor performance with maximum rMBE (24%), rMAE (29%), rRMSE (39%), and minimum R2 (0.74). For all-sky conditions, good correlation was found for SOLCAST (0.948), CMSAF (0.948), CAMS (0.944), and AP model (0.91); all with R2 over 0.91. The maximum rRMSE for SOLCAST (10%), CAMS (12%), CMSAF (12%), and AP model (11%) was less than 13%. The maximum rMAE for SOLCAST (7%), CAMS (8%), CMSAF (8%), and AP model (9%) was less than 10%, showing good performance. While the R2 correlations for the NASA SSE satellite-based GHI were less than 0.9 (0.896), the maximum rRMSE was 18% and the maximum rMAE was 15%, showing rather poor performance. The performance of the SOLCAST, CAMS, CMSAF, and AP models was almost the same in the study area. CAMS, CMSAF, and AP models are viable, freely available datasets for estimating the daily GHI at South African locations with quantitative certainty. The relatively poor performance of the NASA SSE datasets in the study area could be attributed to their low spatial resolution of 0.5° × 0.5° (~55 km × 55 km). The feasibility of the datasets decreased significantly as the proportion of sky that was covered by clouds increased. The results of the study could provide a basis/data for further research to correct biases between in situ observations and the estimated GHI datasets using machine learning algorithms

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

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

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

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