March 31st was an intense day for severe weather across much of the Midwest and southeast United States. The Storm Prediction Center issued a level 5 of 5 risk of severe weather for two separate portions of the Midwest. On a synoptic scale, the strengthening of the system was supported by increased vorticity advection with height over the surface low, warm air advection, and favorable jet stream dynamics. The traditional QG-omega equation will be used to analyze the forcing from advection of vorticity as well as from the Laplacian of geostrophic temperature advection.
First, there was a notable amount of differential absolute geostrophic vorticity advection by the geostrophic wind. At the center of the low at the surface, there is no geostrophic wind so there is no vorticity advection at the surface. However, as shown in Fig. 1, there is significant absolute geostrophic vorticity advection by the geostrophic wind. The vorticity map shows a clear maximum at the base of the trough at 500mb and there are wind barbs showing where a component of the flow is geostrophic, advecting vorticity downstream of the trough over Iowa, southern Minnesota, and Wisconsin. This is exactly where the surface low is located, meaning that the vorticity advection increases with height over the center of the low. When this is the case, the first term on the right-hand side of the QG-omega equation, -fo ∂/∂p [-Vg∙∇(ζg+f)], is positive because there is increasing absolute geographic vorticity advection with increasing height. If the second term on the right-hand side is ignored, then the left-hand side term, the 3D Laplacian of omega, is also positive which would minimize omega, promoting upward vertical motion and a deepening of the low.
The second half of the QG-omega equation, the Laplacian of geostrophic temperature advection, also played a role in strengthening the surface midlatitude cyclone, though its role looked to be less significant than the forcing from differential absolute vorticity advection over the low. Fig. 2 shows that warm air advection, shaded in red, along where the warm front was stretching from Minnesota to the Atlantic coast. Where there is warm air advection, the temperature advection term is positive in those locations, making the 3D Laplacian term positive, also minimizing omega promoting upward vertical motion. The location of maximum of warm air advection did not overlap considerably with where there was positive forcing from the differential vorticity advection term past 18z March 31. Fig. 2 shows that there was an area of notable warm air advection just north of the location of the surface cyclone. This lent itself to deepening the low, but contributed less positive forcing for upward vertical motion as time progressed and the regions of warm air advection propagated eastward further from the low. The total positive forcing from the traditional form of the QG-omega equation is shown in Fig. 3 which is when both terms lend themselves to strengthening the surface cyclone the most as they are aligned with its position over Iowa.
The upper-level jet was also responsible for strengthening the surface low. As seen in Fig. 4, the low was positioned directly in the left jet exit region. In this region, we expect to see upward vertical motion because there is divergence of ageostrophic wind aloft. This is because ageostrophic wind is equal to k/f × (dVg)/dt. The wind decelerates as it moves eastward away from the jet streak where maximum speeds are shown in figure 4. This means that the acceleration of the wind is pointed in the opposite direction of its northeastward flow and k hat is perpendicular to that pointing upward. This means the ageostrophic wind will point into the right jet exit region. This means there is convergence aloft at this location, and divergence aloft as a result in the left jet exit region, driving upward vertical motion due to mass continuity.
