Convective Instability and CAPE
The energy available for convection is:
\[\text{CAPE} = \int_{\text{LFC}}^{\text{EL}} g\,\frac{T_{v,p} - T_{v,e}}{T_{v,e}}\,dz\]and Convective Inhibition (CIN) is the negative area that must be overcome for parcels to reach the LFC:
\[\text{CIN} = -\int_{\text{surface}}^{\text{LFC}} g\,\frac{T_{v,p} - T_{v,e}}{T_{v,e}}\,dz\]Typical severe-weather environments have CAPE $> 2000\ \text{J kg}^{-1}$ and CIN $< 50\ \text{J kg}^{-1}$.
Wind Shear and Storm Mode
Bulk wind shear over the 0–6 km layer governs storm organisation:
| Shear (m s$^{-1}$) | Typical mode |
|---|---|
| $< 10$ | Ordinary pulse storms |
| $10–20$ | Multicell clusters |
| $> 20$ | Supercells, organised MCS |
The storm-relative helicity (SRH) quantifies the rotation potential available to updrafts: $\text{SRH} = -\int_0^h (\mathbf{V} - \mathbf{c}) \times \frac{\partial\mathbf{V}}{\partial z}\cdot\hat{k}\,dz$.
Cold Pool Dynamics
Evaporative cooling beneath convective precipitation generates a surface cold pool that spreads outward as a density current. The cold pool propagation speed scales as:
\[C \approx \sqrt{2\,\frac{\Delta\theta_v}{\bar{\theta}_v}\,g\,H}\]where $H$ is cold pool depth and $\Delta\theta_v$ is the virtual potential temperature deficit. When $C$ matches the low-level shear, the cold pool lifts ambient air optimally and the MCS reaches a steady, long-lived state.