Probability Distribution and Extreme Characteristics of Tree Wind-Induced Responses Under Various Approaching Flow Turbulences

Trees play a critical role in urban ecological protection and wind disaster mitigation, yet conventional Gaussian-based wind engineering models often underestimate extreme tree motions under turbulent flows. This study aims to clarify the statistical characteristics of tree wind-induced responses and develop a quantitative framework to distinguish Gaussian and non-Gaussian behaviors. Scaled aeroelastic tree models were tested in a boundary-layer wind tunnel under controlled turbulence intensity (0.05–0.19), mean wind speeds of 3.9–9.3 m/s, and leaf area index (LAI) of 0–2.46. Acceleration and displacement time histories of branches, crown center, and trunk were recorded. A Gaussian discrimination criterion was established using cumulative probability thresholds of skewness and kurtosis, supplemented by time-history and probability density verification. Results reveal that branch accelerations exhibit strong non-Gaussianity with heavy-tailed and asymmetric distributions, crown displacements show moderate non-Gaussianity, while trunk responses remain near-Gaussian due to higher stiffness. Under weak turbulence, Gamma and Lognormal distributions fit best; under strong turbulence, the Generalized Extreme Value (GEV) distribution prevails. A high-quantile GEV-based framework markedly reduces extreme response prediction bias compared with Gaussian assumptions. These findings provide a probabilistic basis for more accurate assessment of tree wind stability and the design of wind-resistant urban vegetation and shelterbelts.