For 104 years, the Richardson number has told pilots where turbulence lives. It's the ratio of buoyancy to shear — stable stratification versus destabilizing wind gradients. When Ri drops below about 0.25, turbulence wins. Simple, elegant, and wrong in exactly the way that simplicity tends to be wrong: it ignores a dimension.
Foudad, Teixeira, Williams, and Kaluza (arXiv:2602.21770) introduce Ri_new, a generalized Richardson number that adds horizontal shear — deformation and divergence — to the classical formulation. They validate it against 247 million automated turbulence reports from commercial aircraft, spanning 2017 to 2024. Not hundreds. Not thousands. Two hundred and forty-seven million. And Ri_new wins.
The classical Richardson number considers only vertical wind shear: how fast the wind changes with altitude. This captures the dominant turbulence-generating mechanism in the stratified atmosphere, where vertical mixing against buoyancy forces is the energetically expensive process. But near jet streams — where clear-air turbulence actually injures flight attendants and terrifies passengers — horizontal shear matters too. The jet core creates lateral velocity gradients that the classical formulation entirely ignores.
The fix is derived from the turbulent kinetic energy budget. Instead of asking only “does vertical shear overcome buoyancy?”, Ri_new asks “does total shear — vertical and horizontal — overcome buoyancy?” The horizontal contribution is weighted by the ratio of horizontal to vertical eddy viscosities, Kmh/Kmv. This ratio is uncertain and hard to measure directly, but the authors find optimal predictive performance when it falls between 10^3 and 10^4, peaking near 5000. Horizontal eddies are thousands of times more viscous than vertical ones — which makes sense, because the atmosphere is thin. Horizontal scales dominate.
The dataset is remarkable in itself. 247 million turbulence reports from commercial aircraft over seven years is not a research dataset — it's an industrial census. Every bump, jolt, and smooth patch recorded by automated systems on every commercial flight. The result isn't a marginal academic improvement. It's a measurable gain in probability of detection at operationally relevant false-alarm rates.
What took so long? The classical Richardson number was introduced by Lewis Fry Richardson in 1920. Its one-dimensional character has been known from the beginning. But the simplicity was useful — vertical profiles are what radiosondes measure, and the approximation worked well enough for most operational forecasting. The computational infrastructure to incorporate three-dimensional wind fields at forecast resolution is relatively recent, and the validation dataset of 247 million reports is only possible in the era of automated aircraft sensors.
The broader lesson: when a diagnostic works well, its failures hide in the places where the simplifying assumption breaks down. Ri works well in the open stratosphere where vertical shear dominates. It fails near jet streams where horizontal shear is strong. The fix doesn't replace the old diagnostic — it generalizes it. The classical Richardson number is a special case of Ri_new when horizontal shear vanishes. Generalization preserves what works and extends it to where it doesn't.
Sometimes the thing the instrument can't measure is the thing that matters most.