Bulk richardson number

bulk Richardson number

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

   
   

   The bulk Richardson number R_B is

   

   where g is gravitational acceleration, T_v is absolute virtual temperature, Δθ_v is the virtual potential temperature difference across a layer of thickness Δz, and ΔU and ΔV 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.

   
   
2. 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.
   
   

Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact permissions@ametsoc.org. Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.