Despite advances in NWP, models still yield biased and under-scattered forecasts. To mitigate this, past attempts have explored nonparametric methods such as quantile regression neural networks (QRNN) and their variants, which are designed to output quantiles that reflect value ranks in the forecast distribution. However, these methods often face "quantile crossing," hindering forecast interpretation.

Ad hoc solutions, such as naive sorting, didn't address the core problem. Enter the team's breakthrough: the non-crossing quantile regression neural network (NCQRNN) model. 

This innovation, developed by Prof. YANG Dazhi of the Harbin Institute of Technology and his collaborators from the Karlsruhe Institute of Technology, the Institute of Atmospheric Physics (IAP) of the Chinese Academy of Sciences, and the National University of Singapore, etc., tweaks the traditional QRNN structure. 

The NCQRNN model modifies the structure of the traditional QRNN by adding a new layer that preserves the rank order of the output nodes, such that the lower quantiles are constrained to be perpetually smaller than the higher ones without losing accuracy. 

Their results were published in Advances in Atmospheric Sciences on Mar. 1.

"Our NCQRNN model maintains the natural order of forecast values, ensuring that lower quantiles remain smaller than higher ones. This increases the accuracy and significantly improves forecast interpretability," said Prof. YANG.  

"The idea is simple but effective: The neural network indirectly learns the differences between the quantiles as intermediate variables and uses these non-negative values in an additive way to estimate the quantiles, which inherently guarantees their increasing order. Moreover, this non-crossing layer can be added to a wide range of different neural network structures, ensuring the wide applicability of the proposed technique," said Dr. Martin J. Mayer of the Budapest University of Technology and Economics.

Indeed, successfully applied to solar irradiance prediction, this innovative machine learning approach showcased substantial improvements over existing models. Its adaptable design allows for seamless integration into various weather forecasting systems, promising clearer and more reliable predictions for a range of weather variables. 

"The proposed neural network model for quantile regression is very general and can be applied to other target variables with minimal adaptations. Therefore, the method will also be of interest for other weather and climate applications beyond solar irradiance forecasting," said Dr. Sebastian Lerch from the Karlsruhe Institute of Technology.

"Machine learning has important application prospects in the field of weather and climate research. This study provides an instructive case study on how to apply advanced machine learning methods to numerical weather prediction models to improve the accuracy of weather forecasts and climate predictions," said Prof. XIA Xiang'ao from IAP.

The international research team includes individuals with diverse backgrounds in atmospheric sciences, solar energy, computational statistics, engineering, and data science. Notably, some of the team members involved in this study have collaborated on a review paper elucidating fundamental concepts and recent advances in solar power curves.  

Published on the same day as the original "quantile crossing" paper, this review paper not only provides a robust understanding of solar power curve modeling principles, but also serves as a bridgehead for atmospheric scientists to connect their knowledge of radiation to the practical use of solar power.

The review paper featured on the cover of the 8th issue of Advances in Atmospheric Sciences aims to assist readers in the field of atmospheric sciences in gaining a thorough understanding of solar power curve modeling and staying updated on relevant research advancements. (Image by AAS)