# Bulk Richardson number

The Bulk Richardson Number (BRN) is a dimensionless number in meteorology relating vertical stability and vertical shear (generally, stability divided by shear). It represents the ratio of thermally produced turbulence and turbulence generated by vertical shear.

Practically, its value determines whether convection is free or forced. High values indicate unstable and/or weakly sheared environments; low values indicate weak instability and/or strong vertical shear. Generally, values in the range of around 10 to 45 suggest environmental conditions favorable for supercell development. See also: Monin-Obukhov Length.

## Formula

Below is the formula for the BRN.[1]

$Ri = \frac{g\Delta \theta _{v}/\theta _{v}}{[(\Delta U)^2 + (\Delta V)^{2}]/\Delta Z}$

## Critical values and interpretation

There is no exact interpretation of BRN values but, in general, for a BRN less than 10, vertical shear dominates over buoyancy and the storm will likely be eviscerated by the shear. For BRN values between 10 and 45, the shear tends to balance the buoyancy favoring strong convective supercells. A BRN larger than 40 supports ordinary cell or multicell convective storms but due to updraft tilt stemming from the lack of shear, supercells are not likely to be observed.

## Difficulties in interpretation

Different combinations of convective available potential energy (CAPE) and shear can lead to identical BRN values so the same BRN can represent a myriad of convective situations. Another source of difficulty in forecasting convective storm potential with BRN is that the BRN does not include important assessment parameters like wind direction or air moisture. Insignificant levels of CAPE and shear can also produce significant BRN so it is important that CAPE or the lifted index (LI) are used as a primary measure of atmospheric instability first. Since CAPE is difficult to compute by hand, a computer program is often used to calculate and report BRN given a vertical temperature profile.

## References

1. ^ Lackmann, Gary (2012). <Midlatitude Synoptic Meteorology: Dynamics, Analysis, & Forecasting>. 45 Beacon Street, Boston, Massachusetts 02108: American Meteorological Society. pp. 193–215. 978-1878220103.