Statistical models incorporating mean and standard deviation to predict probability distributions of pedestrian-level wind speed in a realistic urban area

Understanding the probabilistic characteristics of urban wind environments is crucial for pedestrian safety and comfort. Previous studies have used various distribution functions based on statistics to evaluate gusty winds; however, the prediction accuracy of gusts and plausibility of the various distribution functions have not been discussed. This paper models the probability density function (PDF) using four distribution functions: Gaussian, Lognormal, Weibull, and Gamma, with parameters determined by the method of moments based on only two statistics: mean and standard deviation. The large-eddy simulations (LES) results of a realistic urban case were used to assess their effectiveness in estimating PDFs and quantiles of wind speed. The key findings indicate that while all distributions accurately modeled the mean and standard deviation, none effectively captured skewness and kurtosis. The Gamma distribution provided the best global fit of PDFs, followed by the Weibull distribution. The Lognormal and Gaussian distributions performed less effectively, with the Gaussian distribution showing the largest errors due to its constrained, symmetric bell-shaped PDF, which struggles to capture the asymmetry in wind speed data. Although the Gamma distribution had the highest overall accuracy in modelling PDFs, other distributions occasionally provided more accurate estimates at specific locations. For wind speed quantiles, particularly extreme values with an exceedance probability of 1 % (i.e., $s_{1\%}$), the Weibull and Gamma distributions showed superior accuracy, while the Gaussian and Lognormal distributions had larger errors. This study is expected to provide valuable insights into modeling wind speed PDFs, serving as a foundation for further developments of statistical models.