[1] In this discussion, winds associated with tornadoes and tropical cyclones are excluded from consideration.

[2] In the demonstration, the contribution to the density from pressure perturbation is ignored. Note that buoyancy represents an unbalanced pressure gradient force.

[3] The presence of condensed water particles in the parcel is felt via viscous forces but these are on a scale that is not represented easily. Hence, the effect is treated as if it reduces buoyancy.