Beyond Parcel Theory: Accounting for Entrainment and Perturbation Pressure Effects on the Vertical Velocity Structure of Convective Storms

Strong vertical motion within updrafts is one of the defining features of convective storms. It is critical for driving many basic elements of severe convective weather, including large hail and frequent lightning. A basic meteorological concept is that updraft vertical velocities are closely related to CAPE, the convective available potential energy. From the vertical momentum equation, one can directly calculate the maximum vertical velocity of a rising parcel as (2CAPE)^1/2, neglecting entrainment and pressure effects. This is often referred to as the “thermodynamic maximum” vertical velocity, and it is well-known to substantially over-predict the actual vertical velocity under most conditions; a rule of thumb is about a factor of two over-prediction. This presentation includes recent work that has gained insight into critical factors that influence the vertical velocity structure, including pressure perturbations and entrainment. A simple theoretical analytic model is derived for the updraft buoyancy and vertical velocity that includes these effects. This analytic model quantifies the detrimental effects of entrainment and dilution for narrow updrafts and buoyant perturbation pressure for wide updrafts, and explains the typical factor of two over-estimation by the thermodynamic maximum vertical velocity. This model is used to show that updraft aspect ratio (radius divided by height) and environmental relative humidity are critical factors affecting the vertical velocity, in addition to the CAPE and environmental shear. The model gives results that are similar to high-resolution numerical simulations using the Bryan Cloud Model CM1 over a wide range of conditions. Additional insights provided by theory will also be discussed, including why moist updrafts tend to occur as a succession of rising thermals.