Very short-term reactive forecasting of the solar ultraviolet index using an extreme learning machine integrated with the solar zenith angle

Abstract

Exposure to erythemally-effective solar ultraviolet radiation (UVR) that contributes to malignant keratinocyte cancers and associated health-risk is best mitigated through innovative decision-support systems, with global solar UV index (UVI) forecast necessary to inform real-time sun-protection behaviour recommendations. It follows that the UVI forecasting models are useful tools for such decision-making. In this study, a model for computationally-efficient data-driven forecasting of diffuse and global very short-term reactive (VSTR) (10-min lead-time) UVI, enhanced by drawing on the solar zenith angle (θ_s) data, was developed using an extreme learning machine (ELM) algorithm. An ELM algorithm typically serves to address complex and ill-defined forecasting problems. UV spectroradiometer situated in Toowoomba, Australia measured daily cycles (0500-1700h) of UVI over the austral summer period. After trialling activations functions based on sine, hard limit, logarithmic and tangent sigmoid and triangular and radial basis networks for best results, an optimal ELM architecture utilising logarithmic sigmoid equation in hidden layer, with lagged combinations of θ_s as the predictor data was developed. ELM's performance was evaluated using statistical metrics: correlation coefficient (r), Willmott's Index (WI), Nash-Sutcliffe efficiency coefficient (E_NS), root mean square error (RMSE), and mean absolute error (MAE) between observed and forecasted UVI. Using these metrics, the ELM model's performance was compared to that of existing methods: multivariate adaptive regression spline (MARS), M5 Model Tree, and a semi-empirical (Pro6UV) clear sky model. Based on RMSE and MAE values, the ELM model (0.255, 0.346, respectively) outperformed the MARS (0.310, 0.438) and M5 Model Tree (0.346, 0.466) models. Concurring with these metrics, the Willmott's Index for the ELM, MARS and M5 Model Tree models were 0.966, 0.942 and 0.934, respectively. About 57% of the ELM model's absolute errors were small in magnitude (±0.25), whereas the MARS and M5 Model Tree models generated 53% and 48% of such errors, respectively, indicating the latter models' errors to be distributed in larger magnitude error range. In terms of peak global UVI forecasting, with half the level of error, the ELM model outperformed MARS and M5 Model Tree. A comparison of the magnitude of hourly-cumulated errors of 10-min lead time forecasts for diffuse and global UVI highlighted ELM model's greater accuracy compared to MARS, M5 Model Tree or Pro6UV models. This confirmed the versatility of an ELM model drawing on θ_sdata for VSTR forecasting of UVI at near real-time horizon. When applied to the goal of enhancing expert systems, ELM-based accurate forecasts capable of reacting quickly to measured conditions can enhance real-time exposure advice for the public, mitigating the potential for solar UV-exposure-related disease.

Keywords: Extreme learning machine; M5 Model Tree; Multivariate adaptive regression splines; Real-time solar forecasting; Solar ultraviolet index (UVI).