Mixture Gram–Charlier series method for modelling wind velocity probability distribution in actual urban environments

Abstract

Understanding probabilistic features in urban wind environments is crucial. While previous studies have used the Gram–Charlier series (GCS) method to model the probability distribution functions (PDFs) of wind speed, their accuracy is often limited for bimodal or highly-skewed PDFs. This issue becomes more pronounced when large moments cause fluctuations in the modeled PDFs. This study introduces the mixture GCS method for modeling the PDFs of wind velocity components and wind speed. Time-series data derived from a large eddy simulation (LES) of an actual urban area (Niigata City, Japan), were analyzed. This study focuses on two mixture GCS methods: GCS2-2 (combining two Gaussian distributions) and GCS2-3 (combining a Gaussian distribution and a third-order GCS model). While GCS methods effectively model symmetric PDFs, the mixture GCS methods excel at capturing bimodal and skewed PDFs, with GCS2-3 proving more accurate than GCS2-2. Compared to GCS-6th, GCS2-3 achieves a more accurate maximum mean absolute error ($\text{MAE}$), reducing it by over 50%. For nearly symmetric unimodal PDFs, traditional GCS methods suffice, but for cases with large higher-order moments, mixture GCS methods are recommended to avoid accuracy loss. This study is expected to provide valuable insights for probabilistic modeling of urban wind environments.