Rician Distribution as a Physically Interpretable Model for Wind-Speed Statistics

Abstract

The statistics of atmospheric wind variations are commonly modeled using Gaussian or Weibull forms, which often trade physical interpretability against statistical accuracy, especially in the distribution tails. Here we derive a Rician distribution for wind speed from a simple physical model based on two orthogonal Gaussian velocity components with a non-zero mean in the preferred direction. Using wind-speed records from four geographically distinct wind farms, we show that the Rician model consistently outperforms the Gaussian model and remains competitive with the Weibull model. The same behavior persists when the data are partitioned into monthly windows, where the Rician parameters also provide a transparent description of seasonal and geographic variability, compared to Weibull parameters. In addition, the model naturally connects Gaussian-like and Weibull-like regimes through the Rician parameter ratio $μ/σ$, making the Rician distribution a compact and physically interpretable two-parameter model for wind-speed statistics.