Engerer2: Global re-parameterisation, update, and validation of an irradiance separation model at different temporal resolutions

Abstract

The Engerer2 separation model estimates the diffuse fraction Kd from inputs of global horizontal irradiance, UTC time, latitude, and longitude. The model was initially parameterized and validated on 1-min resolution data for Australia and performed best out of the 140 models in global validation studies. This research reparameterizes Engerer2 on a global training dataset and at many common temporal resolutions (1-min, 5-min, 10-min, 15-min, 30-min, 1-h, and 1-day), so that it may be more easily implemented in the future; the need for the user to perform prerequisite calculations of solar angles and clear-sky irradiance has also been removed for ease of use. Comparing the results of the new 1-min parameterization against the original Engerer2 parameterization on a global testing dataset, the root mean squared error (RMSE) improves from 0.168 to 0.138, the relative RMSE from 30.4% to 25.1%, the mean bias error from 8.01% to -0.30%, and the coefficient of determination (R2) from 0.80 to 0.86; hence, there is a significant improvement to the model. Engerer2 was unsuited to 1-day averages; however, it performed remarkably well at all other averaging periods. A climate specific analysis found poor suitability of Engerer2 in polar climates; however, improvement and suitability were found for all other climates and temporal averaging periods. Code for the model are provided as supplementary material in languages R, Python, and Matlab® - selected for their wide-adoption in academia and industry - and they can also be found in the Github repository: Engerer2-separation-model.