[论文解读] A Generalized Richardson Number Diagnostic for Turbulence in the Free Atmosphere

Mohamed Foudad, Miguel A. C. Teixeira+2 more|arXiv (Cornell University)|Feb 25, 2026

Meteorological Phenomena and Simulations被引用 0

一句话总结

论文引入 Ri_new，一种通用的 Richardson 数，除了垂直剪切外还包括水平风剪切，并在使用 ERA5 数据和 2.47 亿条飞行器报告的情境下，展示其在预测航空颠簸方面优于 Ri_old 和 TI1。

ABSTRACT

A new Richardson number formulation, Ri_new, is introduced to improve the diagnosis of turbulence in the stratified free atmosphere, particularly near jet stream regions. The formulation is derived from the turbulent kinetic energy budget and accounts for both vertical wind shear and horizontal shear (deformation and divergence), weighted by the ratio of horizontal to vertical eddy viscosities (Kmh/Kmv). This extends the classical Richardson number Ri_old, which includes only vertical shear, and provides a physically based measure of the balance between stratification and three-dimensional shear production. The diagnostics Ri_new, Ri_old, and the widely used Turbulence Index 1 (TI1), computed from ERA5 reanalysis, are evaluated using more than 247 million automated turbulence reports from commercial aircraft (2017-2024). Across various turbulence intensity thresholds, Ri_new consistently outperforms the other diagnostics, resulting in higher AUC values and improved probability of detection at operationally relevant false-alarm rates. Sensitivity analyses show that the predictive skill of Ri_new is maximized for Kmh/Kmv values in the range 10^3-10^4, with peak performance near 5000 and weak dependence on horizontal resolution. Seasonal and regional evaluations indicate that the added value of Ri_new is largest where turbulence generation involves both vertical and horizontal shear, such as over the contiguous United States and during summer. Over oceans, performance remains high and Ri_new still provides the best overall discrimination skill. These results demonstrate that incorporating horizontal wind shear into the Richardson number yields a physically consistent and statistically robust improvement in turbulence diagnostics, with relevance for research and operational applications.

研究动机与目标

• 为层化自由对流层，尤其在喷气流附近，推动改进的颠簸诊断。
• 从包含水平变形和散度的完整湍动能预算推导 Ri_new。
• 使用 ERA5再分析和大规模 MADIS ACARS 颠簸数据，评估 Ri_new 相对于 Ri_old 与 TI1 的表现。
• 识别水平—垂直涡扩粘性比（Kh/Kv）对预测技能的影响。
• 评估在不同季节、区域和颠簸强度上的适用性。

提出的方法

• 从完整的 TKE 预算推导 Ri_new，保留水平梯度并引入一阶湍流闭合。
• 将 Ri_new 表达为 Ri_g 除以 Pr_t，其中 Ri_g 融合 N^2 和增强的水平形变项。
• 定义 Ri_g = N^2 / [Sv^2 + (Kh/ Kv)(Div^2 + D_ST^2 + D_SH^2)]，其中 Sv 为垂直剪切，形变项捕捉水平剪切。
• 通过设定 Kh/Kv = 0 将 Ri_new 与 Ri_old 相关联，回到经典的 Ri_old。
• 使用插值匹配 ACARS 观测的 ERA5 场对 Ri_new、Ri_old 和 TI1 进行比较。
• 利用 2.47 亿条 MADIS 颠簸报告（2017–2024）并以 ROC/AUC 作为主要验证指标。

Figure 1: Spatial distribution of ACARS turbulence reports from the NOAA MADIS archive for the period 1 January 2017 to 31 December 2024. Shading indicates the number of reports on a logarithmic scale, binned onto a 1° × 1° latitude–longitude grid. Only reports above 8 km flight altitude are include

实验结果

研究问题

• RQ1 Ri_new 相对于经典 Ri_old 与 TI1 在不同颠簸强度下是否提高了颠簸区分能力？
• RQ2 获得最大预测技能的最佳 Kh/Kv 比值是多少，Ri_new 对水平分辨率的敏感度如何？
• RQ3 Ri_new 在区域性和季节性上的表现如何，尤其在三维（垂直+水平）剪切主导颠簸产生的区域？
• RQ4 Ri_new 在海洋与陆地上层对流层/下平流层颠簸的鲁棒性如何？
• RQ5 基于 Ri_new 的诊断与全球大规模 ACARS 颠簸报告之间的对齐程度如何？

主要发现

• Ri_new 在多种颠簸强度阈值下持续优于 Ri_old 和 TI1，表现为更高的 AUC 值。
• 最佳 Kh/Kv 比值约为 5×10^3，能为 Ri_new 提供最佳 ROC 性能，10^3–10^4 范围的取值也能提升技能。
• Ri_new 在分辨率上表现鲁棒，且当颠簸由垂直和水平剪切共同驱动时（例如美大陆西部和夏季），其增值最大。
• 在海洋区域的表现仍然较优，Ri_new 在这些区域也提供了最佳的总体区分能力。
• 该方法在物理上自洽且统计上稳健地改善了颠簸诊断，具有对航空预测和气候影响评估的潜在益处。

Figure 2: ROC curves for TI1 index (blue), the classical Richardson number (Ri old , black), and the optimal Ri new formulation (red) for turbulence intensity thresholds of (a) EDR $=$ 0.10, (b) EDR $=$ 0.20, and (c) EDR $=$ 0.30 $\mathrm{m}^{2/3}\,\mathrm{s}^{-1}$ . Gray curves show Ri new for diff