The event of interest here is a mid-latitude cyclone off the northwest Pacific coast of the U.S.. Instead of examining the strengthening of this event, we will instead examine the maturation and death of this strong cyclone as it reaches land. At 00Z March 28th, the system reached a low of 987mb and its’ occluded front wrapped around its eastern sector. The system is supported by an upper-level shortwave trough associated with the jet stream (Figure 1). This trough is highly positively oriented, facing mostly eastward rather than the typical northward. At this point, the system is located downstream of the trough and is in the vicinity of a jet streak its base. The different components of a jet streak have varying directions of vertical motion associated with them. At the entrance of a jet streak, the acceleration of wind is pointing towards the center of the jet streak and crossing the acceleration with the k-hat vector, we get that ageostrophic wind is directed northward. This means that ageostrophic divergence is south of the ageostrophic wind vector, implying that there is upward vertical motion here by mass continuity. At the exit region of the jet streak, the roles are reversed. The wind is decelerating eastward, or accelerating westward, so therefore the ageostrophic wind vector is pointing southwards. This implies that there is upward vertical motion north of the vector, or at the left jet exit region. Upward vertical motion is a key strengthening factor to low pressure systems. From Figure 1, we can see that the system is slightly north of a jet streak, and close to the left exit region. This will initially strengthen the system, due to the rising air.
As we step forward 36 hours into the forecast, we can see that the upper-level winds corresponding to the jet stream are much faster than the movement of the system (Figure 2). This places the center of low pressure within the vicinity of the left entrance region of the jet, which implies downward vertical motion and thus weakening the system. Although the center of low pressure is not exactly located where the left entrance region is, it will propagate towards it because the system will move in the direction of thermal wind, as proven by the Sutcliffe Development Theorem. Thermal wind moves parallel to the thickness contours with lower values of thickness to the left of the flow. At this point, the thermal wind is directed towards the southeast, where the jet streak is located relative to the cyclone. The fact that the system is no longer strongly associated with the jet streak either could also be a contributing factor to its weakening.
Another synoptic development that can be observed relative to this system is quasi-geostrophic forcing. The two parts of the traditional Quasi-Geostrophic Omega Equation are the vertical derivative of absolute geostrophic vorticity advection by geostrophic wind (referred to as Term B) and the Laplacian of geostrophic temperature advection (referred to as Term C). When these are positive, it means that omega, which represents vertical motion of air, is minimized and therefore air is rising. In this scenario, we will focus on Term B, because Term C is minimal. Although there are changes in temperature advection due to the cold front pushing warm air into the center of the cyclone, it is not at all strong, and Term B has much more influence over the forcing. Term B is influenced by both shear and curvature vorticity, seen in the expression below (Figure 3 slide 13).
ζ = V/Rs – ∂V/∂n
The curvature vorticity at the center of the cyclone is positive due to the winds becoming more southerly as the radius of curvature increases. The shear vorticity located on the northern coast of California and Oregon is also positive, due to a decrease in wind speed in the direction of the n-hat vector. This initially makes the omega term positive, and implies rising air and strengthening of the system. As we march forward in time though, the strength of cyclonic vorticity decreases (Figure 4, slide 14). This decreases the strength of the quasi-geostrophic forcing and thus weakens the cyclone. It can be caused by multiple reasons, including the aforementioned left jet entrance region as well as some counteraction by Term C, as it becomes negative when the cyclone matures. These factors, along with terrain features not discussed in this post, weakened the cyclone to the point of nonexistence as it arrived at the coast of southern California.
