The Bulk Richardson Number (BRN) is an approximation of the Gradient Richardson number.
Formula
Below is the formula for the BRN, where g is gravitational acceleration, T<sub>v</sub> is absolute virtual temperature, Δθ<sub>v</sub> is the virtual potential temperature difference across a layer of thickness, Δz is vertical depth, and ΔU and ΔV are the changes in horizontal wind components across that same layer.
::<math>
R_{B} = \frac{(g/T_{v})\Delta\theta_{v}\Delta z}{(\Delta U)^2 + (\Delta V)^{2
</math>
Critical values and interpretation
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 50 suggest environmental conditions favorable for supercell development.
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<sub>c</sub>= 0.25. Numbers less than this critical value are dynamically unstable and likely to become or remain turbulent.