Shear Available Potential Energy (SHAPE): A Quantitative Measure of the Effect of Wind Shear on Convective Updraft Potential

The frequency and intensity of convection in high-shear, low-CAPE (HSLC) environments has been a growing topic of discussion in recent years. It is accepted that dynamic pressure perturbations, induced by the interaction of wind shear with updrafts, affect supercell thunderstorms. However, the role of these pressure perturbations on potential quasi-linear convective systems (QLCS) is not well-known, nor quantified. Often, intense updrafts and severe thunderstorms can develop in environments with CAPE less than 500 J/kg, when enough shear is present.

We have developed a new diagnostic parameter known as Shear Available Potential Energy (SHAPE) that uses thermodynamic and wind profiles (available in observed or model soundings) to estimate the maximum updraft potential for an idealized QLCS, including the effects of buoyancy and dynamic pressure perturbations (p’) due to wind shear. Through the conversion of this calculated updraft kinetic energy back to potential energy, the available potential energy due to buoyancy and shear, or SHAPE, is calculated. Given that it has the same units (J/kg) and the same basic meaning as CAPE (lift for convective parcels), yet includes dynamic pressure perturbations in addition to buoyancy, it should be readily understood and applied by operational forecasters.

In this paper, we will present the methodology in calculating SHAPE. The thermodynamic profile is combined with the wind profile. Assuming an infinitely long, linear QLCS, we then simplify the dot product of the shear vector and the gradient in updraft. Numerical integration of the linear dynamic pressure perturbation equation shown in many texts (e.g., Houze 1993; Markowski and Richardson 2010) is performed, given the updraft due to buoyancy only, and assuming a constant horizontal updraft gradient. This allows for computation of p’ due to wind shear as a function of height. The vertical gradient of p’ may then be converted to a vertical acceleration, and maximum updraft due to buoyancy and shear induced pressure perturbations is calculated and converted to potential energy, known as SHAPE.

We will present case studies, using single- and dual-Doppler analysis, that show that the SHAPE provides far more accurate estimates of updraft intensity than CAPE alone in high-shear, low-CAPE QLCS’s. In one typical HSLC QLCS, the vertical gradient of the dynamic p’, represented in SHAPE, was responsible for approximately 76% of the upward acceleration in a QLCS updraft. In a low-topped but severe weather-producing QLCS examined using synthetic dual-Doppler analysis, when observed precipitation loading was included, updraft errors at 2 km AGL decreased from 16 m/s (using only buoyancy, or CAPE) to 7 m/s using SHAPE, a 56% improvement.

Statistical analysis, including null cases, will also be examined. The possible extension to non-linear storms will be analyzed. Implications for operational forecasting will be discussed.