# Bulk richardson number

From AMS Glossary

## bulk Richardson number

- An approximation to the gradient Richardson number formed by approximating local gradients by finite difference across layers.

The bulk Richardson number R_{B}iswhere*g*is gravitational acceleration,*T*_{v}is absolute virtual temperature, Δθ_{v}is the virtual potential temperature difference across a layer of thickness Δ*z*, and Δ*U*and Δ*V*are the changes in horizontal wind components across that same layer. In the limit of layer thickness becoming small, the bulk Richardson number approaches the gradient Richardson number, for which a critical Richardson number is roughly Ri_{c}= 0.25. Gradient Richardson numbers less than this critical value are dynamically unstable and likely to become or remain turbulent. Unfortunately, a critical value is not well defined for the bulk Richardson number, leading to uncertainty in turbulence likelihood for values near the critical value.*See*Richardson number.

- In the context of convective storm forecasting, a nondimensional ratio of the convective available potential energy (CAPE) to a measure of the vertical wind shear, used to characterize convective-storm types for various environments.

The vertical wind shear is one-half the square of the difference between the 6-km density- weighted mean wind speed and a 500-m mean surface layer wind speed. Generally, values of the bulk Richardson number less than 45 support supercell convection, while values greater than 45 support multicell or ordinary cell convection.

Weisman, M. L., and J. B. Klemp 1986. Characteristics of isolated convective storms. Mesoscale Meteorology and Forecasting. P. Ray, Ed., Amer. Meteor. Soc., ch. 15, . 504–520.