基于混合分布与Gaussian Copula的风速——空气密度联合概率建模研究
Wind Speed Based on Mixed Distribution and Gaussian Copula—A Study on Joint Probability Modeling with Air Density
摘要: 该研究旨在提高风能资源评估的精度，提出了一种基于混合分布与Gaussian Copula的风速–空气密度联合概率建模方法。研究使用中国青海省莫合风电场2021~2024年的日尺度气象数据，首先通过理想气体状态方程计算空气密度。随后，研究对风速和空气密度的边缘分布采用多种单分布(Weibull、对数正态、Gamma)和混合分布(双组分、三组分)进行拟合，并使用对数似然值、AIC、BIC、RMSE和R2等指标进行评估。在确定最优边缘分布(三组分对数正态分布)的基础上，构建了Gaussian Copula模型来刻画风速与空气密度之间的负相关依赖结构。最后，基于该联合模型对风功率密度进行了估算，并分析了其年际与月度变化特征。研究发现，该风电场平均风功率密度为50.55 W·m−2，且春季风能资源显著优于夏冬季。
Abstract: This study aims to improve the accuracy of wind energy resource assessment and proposes a joint probability modeling method for wind speed and air density based on a hybrid distribution and Gaussian Copula. The study uses daily-scale meteorological data from the Mohe Wind Farm in Qinghai Province, China, from 2021 to 2024. Air density is first calculated using the ideal gas law. Subsequently, the marginal distributions of wind speed and air density are fitted using various single distributions (Weibull, lognormal, Gamma) and mixed distributions (two-component, three-component), and evaluated using log-likelihood, AIC, BIC, RMSE, and R2 indicators. Based on the determination of the optimal marginal distribution (three-component lognormal distribution), a Gaussian Copula model is constructed to characterize the negative correlation dependence between wind speed and air density. Finally, wind power density is estimated based on this joint model, and its interannual and monthly variation characteristics are analyzed. The study finds that the average wind power density of this wind farm is 50.55 W·m−2, and that spring wind energy resources are significantly superior to those in summer and winter.
文章引用：方圆, 闫在在. 基于混合分布与Gaussian Copula的风速——空气密度联合概率建模研究[J]. 统计学与应用, 2026, 15(4): 374-386. https://doi.org/10.12677/sa.2026.154098

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