Atmospheric near surface wind speed and wind direction play an important role in many applications, ranging from air quality modeling, building design, wind turbine placement to climate change research. It is therefore crucial to accurately estimate the joint probability distribution of wind speed and direction. In this work we develop a conditional approach to model these two variables, where the joint distribution is decomposed into the product of the marginal distribution of wind direction and the conditional distribution of wind speed given wind direction. To accommodate the circular nature of wind direction a von Mises mixture model is used; the conditional wind speed distribution is modeled as a directional dependent Weibull distribution via a two-stage estimation procedure, consisting of a directional binned Weibull parameter estimation, followed by a harmonic regression to estimate the dependence of the Weibull parameters on wind direction. A Monte Carlo simulation study indicates that our method outperforms an alternative method that uses periodic spline quantile regression in terms of estimation efficiency. We illustrate our method by using the output from a regional climate model to investigate how the joint distribution of wind speed and direction may change under some future climate scenarios.

翻译：大气近地面风速和风向在诸多应用中发挥着重要作用，涉及空气质量建模、建筑设计、风力涡轮机选址以及气候变化研究等领域。因此，精确估计风速与风向的联合概率分布至关重要。本研究开发了一种条件方法来对这两个变量进行建模，将联合分布分解为风向边缘分布与给定风向条件下风速条件分布的乘积。为适应风向的环形特性，采用了冯·米塞斯混合模型；风速条件分布则通过两阶段估计过程建模为方向依赖的威布尔分布，包括方向分箱威布尔参数估计，以及后续的谐波回归以估计威布尔参数对风向的依赖性。蒙特卡洛模拟研究表明，本方法在估计效率上优于使用周期样条分位数回归的替代方法。我们利用区域气候模式的输出数据，应用本方法研究了未来气候情景下风速与风向联合分布可能发生的变化。