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The week starting on April 17^th was a rather event week of severe weather. There was a total of 274 hail reports, 68 wind reports, and 20 tornado reports in the two-day span between April 19^th and April 20^th. This is however not the end of the severe weather streak. A high amplitude long-wave trough is currently positioned over the central US is expected to propagate eastward over the Appalachian Mountain range and produce more extreme weather along the east coast states. The 4/21 12Z HRRR model run (Figure 2) shows the trough becoming negatively tilted at 4/23 0Z as the jet streak at the base of the trough intensifies. Those are synoptic features that are often associated with severe weather. The Storm Prediction Center (SPC) has a slight risk outlook for 4/22 Saturday (Figure 1) spanning from Maryland to the to South Carolina. The primary severe weather risk is expected to be damaging winds and hail. Although the Tornado risk was marginal, it is not out of the question.

As the shortwave energy of the trough intensifies, a surface low is projected to form near Kentucky around 12Z of 4/22 and intensify downstream of the trough. This is the result of a combination of trough/ridge and jet streak dynamics.  At the base of the trough, vorticity is maximized due to the curvature of the thermal wind. Therefore, the region downstream of the trough experiences positive vorticity advection and UVM forcing according to Term A of the QG Omega equation. Upward vertical motion promotes divergence aloft and surface convergence due to the mass continuity principle. Moreover, the presence of a strong jet streak at the base of the trough dynamics promotes ageostrophic divergence and upward vertical motion in the left exit region of the jet.

In the 4/21 12Z HRRR model run, the surface low is expected to intensify to 997 mbr by 0Z of 4/23. The center will move NE parallel to the 500 mbr height contours. As the surface low intensifies, a cold front form and advects cooler air from the NW. By using the 1D frontogenesis equation, the vertical forcing along the cold front can be diagnosed primarily with term B, A, and C. Although sign analysis of HRRR surface temperature at 18Z of 4/22 (Figure 3) reveals the shearing term (A) to be negative (-*+), the confluence term (B) is positive (-*-) and likely at a much larger magnitude. The diabatic term is inconclusive due to extensive cloud cover on both sides of the front during a time of day time heating. And overall positive sum of the 1D frontogenesis equation implies that frontogenesis is occurring at that point in time. This is associated with upward vertical motion ahead of the cold front which promotes convective activity ahead of the cold front.  

Figure 3: 12Z 4/21 HRRR run, valid for 18Z 4/22. 2m Temperature (f, colors)and surface winds (kt). Source: Pivotal Weather.

This particular synoptic set up is conducive of extreme weather, because the presence of a strong jet streak at 500 mbr is usually associated with strong 0-6km wind shear. The wind shear values in Virginia in particular are up to 70 knots, which is sufficient for supercell development if given sufficient instability. The strong southerly flow ahead of the cold front also increases 0-1 km wind shear. Despite the strong southerly flow, the moisture and instability from the Atlantic Ocean is inadequate compared to the Gulf of Mexico. CAPE values are forecasted to be around 500 J/kg, which is barely enough to fuel convection. However, tornadic supercells should not discounted due to the potential for a much different outcome if diurnal heating generates more instability than originally anticipated. The convective storms forecasted on Saturday is expected to form a squall line with embedded supercells according to the 4/21 12Z HRRR run. Damaging wind gusts and hail are likely with some chance of weak QLCS tornadoes.

On Tuesday, April 18th, 2023, a weak area of low pressure moved over the Rocky Mountains. The motion of the associated air column over the mountain range created increased potential vorticity. When an air column is over mountains, it is squished or flattened, and will spin slower – much like a figure skater with their arms out; when an air column clears the mountains, it is stretched and will spin faster – much like a figure skater with their arms tucked in.

One day later, at 12Z on Wednesday, April 19th, 2023, two 1004mb areas of low pressure formed east of the Rockies (Figure 1). Both centers of low pressure were roughly positioned between a trough to the west and a ridge to the east, an optimal spot for ageostrophic divergence. At the base of a trough, the acceleration vector points into the axis of rotation. Crossing the acceleration vector and k-hat, yields an ageostrophic wind vector pointing west. At the crest of a ridge, the acceleration vector points into the axis of rotation. Crossing the acceleration vector and k-hat, yields an ageostrophic wind vector pointing east. Given that these ageostrophic wind vectors are pointed opposite, it can be determined that there is ageostrophic divergence and upward vertical motion by mass continuity. Since the season is transitioning from spring to summer, the jet stream is weakening and there is not much in the way of jet streak dynamics.

The Traditional form of the QG Omega equation can be used to further diagnose upward vertical motions in the vicinity of the surface lows. Since the severe weather occurred late on April 19th, April 20th maps will now be used for analysis. Specifically, maps from April 20th at 0Z will be used. Figure 2 shows the forcing of Term A or the vertical derivative of absolute vorticity advection by the geostrophic wind (-(f₀/σ)[∂(-v_g·∇η_g)/∂p]). Since the magnitude of geostrophic wind at the center of the surface cyclone is zero, geostrophic vorticity advection is also zero. Therefore, it can be inferred that positive absolute vorticity advection is increasing with height (shown by the yellow and orange shading). Neglecting Term B, a positive term A means that omega is being minimized and there is upward vertical motion. However, the positive absolute vorticity advection with height contributes much less forcing than the geostrophic temperature advection (Figure 3; -(R/σp)[∇²(-v_g·∇T)]). Areas with positive term B, neglecting Term A, imply that omega is being minimized and there is upward vertical motion. In other words, the warm sector is getting warmer, and the cold sector is getting colder. Both vorticity advection and temperature advection contributed to significant upward vertical motion in the vicinity of the surface lows.

Fig. 1 – NOAA Storm Prediction Center Filtered Storm Reports for 15 April 2023 as of 1510Z 18 April 2023 (NOAA SPC Archive). Red circles indicate tornado reports, blue circles indicate wind reports, green circles indicate hail reports, black squares indicate large hail (≥ 2” diameter) reports, and black circles indicate high wind reports (≥ 65 knots).

This past weekend, a low-pressure system (LPS) moved through the continental US, bringing with it significant hail, straight-line winds, and 13 tornadoes, with one EF-2 in Maries, Missouri. Hail larger than 2” was common with this storm system, across Missouri down to Texas, and high winds were experienced around the Gulf of Mexico from the outflow of these storm systems. The magnitude of hail reports suggests the presence of strong and concurrent updrafts for these systems in addition to cool, dry air aloft. The magnitude of high wind reports suggests strong straight-line winds associated with a strong outflow boundary. Both require significant upward vertical motion (UVM) in the region over our LPS. In order to diagnose the synoptic forcings at play for this event, we first turn to the 250 hPa jet.

Fig. 2 – 250 hPa jet map plotted for 00 Z 16 April 2023 (Alicia Bentley Real-time GFS Maps). 250 hPa windspeed (shaded, color bar, m/s), mean sea level pressure (solid black isobars),1000-500mb (dashed red and blue lines, blue = below freezing), blue arrows indicate centripetal acceleration, red arrows indicate the ageostrophic wind vectors, orange circles indicate areas of ageostrophic divergence aloft, red “L” indicates surface low-pressure system

The high-amplitude trough within the polar jet stream is just west of our surface LPS (red L), indicating that this system is a westward tilt with height. We also have a strong setup for divergence aloft, with the downstream trough and upstream ridge for both the polar and subtropical jet. The subtropical jet pattern displayed this pattern nearly directly underneath the polar jet, possibly slightly ahead of the polar jet. We can see the ageostrophic wind vectors (red arrow) oriented to the west for the troughs and to the east for the ridges. This creates an area of ageostrophic divergence aloft in the yellow-circled regions. The area of our surface LPS straddles both of these divergence areas, which is likely responsible for the magnitude of the upward vertical motion and rapid development of these storm systems. To confirm the hypothesis that the upper trough-ridge dynamics were the dominant factor in the development of this system, we turn to the traditional form of the Quasi-Geostrophic (QG) omega equation.
We will break down the QG forcing into two main terms. Term A, -(f₀/σ)[∂(-Vg·∇η_g)/∂p], is defined as the vertical derivative of the absolute geostrophic vorticity advection by the geostrophic winds. Term B, -(R/σp)[∇²(-V_g·∇T)], is the Laplacian of horizontal geostrophic temperature advection.

Fig. 3 – QG Omega Plots (Thomas Galarneau Real-time QG Diagnostics)

Top: 700 hPa Z, Temperature, Differential Vorticity Advection Term (A) from 00 Z 16 April 2023, 700 hPa geopotential heights (black, every 3 hPa), forcing from differential vorticity advection (shaded, 10^-12 Pam^-2s^-1)

Bottom: 700 hPa Z, Temperature, Thermal Advection Term (B) from 00 Z 16 April 2023, 700 hPa geopotential heights (black, every 3 hPa), isotherms (dashed black contours, every 6 K) forcing from the Laplacian of geostrophic temperature advection (shaded, 10^-12 Pam^-2s^-1)

From the analysis, we can see that term A, the differential vorticity advection term is the dominant forcing for upward vertical motion in our QG analysis, as indicated by the significant region of warmer (yellow-orange) colors in the top image. This indicates that there is positive differential vorticity advection and thus the left-hand side (LHS) of the QG equation would be positive, so omega is minimized and there would be UVM. Under the traditional QG equation, our term B, the thermal advection term, indicates a significant amount of cold air advection or a local maximum, which makes the LHS term negative so omega is maximized, and downward vertical motion would occur in the region of the blue. This term does display the significance of the cold air advection brought by this frontal passage, but it fails to accurately account for the impressive upward vertical motion, which is indicated by term A. It is likely the differential vorticity advection that is driving the upward vertical motion over our LPS.  To better understand why term B might be misrepresenting the UVM, let’s take a look at the frontal dynamics at play.

Fig. 4 – GFS 850 hPa frontogenesis map for 18 Z 15 April 2023 (Tropical Tidbits Analysis), temperature (isotherms, °C, red is above freezing, blue is freezing and below freezing) , temperature advection (shaded, color bar, K/hr, red colors indicates warm air advection, blue colors indicate cold air advection), wind barbs (knots), frontogenesis (purple contours, K/100km/3hr)

Here we can see a nice shearing pattern as indicated by the circled areas, with a strong northwesterly wind on the west to a strong southwesterly wind on the east, which will act to tighten the temperature gradient and strengthen this front. Additionally, we see a significant amount of cold air advection (CAA) on the cold side of this frontal passage and some warm air advection (WAA) on the warm side, which will lead to frontogenesis. However, the CAA is much more significant than the WAA here, which is consistent with what we saw in the QG term B plots. While the magnitude of WAA might be less, the CAA provided enough of a strong frontal passage and lifting mechanism to generate initiation. This initiation was then aided by jet stream dynamics and differential vorticity advection to create massive divergence aloft and thus upward vertical motion. While warm air advection might have been weaker, the cool, dry air brought southeastward by this frontal passage was contrast enough to provide explosive initiation. While these synoptic features are only part of the picture, this venting of our LPS allowed it to maintain its strength while providing the strong updrafts and downdrafts we saw with this system.

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, -f_o ∂/∂p [-V_g∙∇(ζ_g+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 × (dV_g)/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.

Atlanta will become victim to a cold air damming event during the weekend of April 8th, 2023, where precipitation, high winds, and cold temperatures will plague our region. In this case, I will detail the synoptic environment regarding jet streak dynamics, trough ridge dynamics and QG-theory. In Fig. 1, an initialized GFS-model run on April 6th, 2023, at 1800 UTC shows a strong upper-level jet streak positioned over the northeastern states with winds reaching up to 90 knots on April 8th, 2023, at 12 UTC. To the northwest of the jet streak, a surface anticyclone (blue H) is positioned just north of the Great Lakes with a pressure of ~ 1036 mb. Through time, the surface anticyclone will head to a region of maximum ageostrophic convergence by following 1000-500 hPa thickness contours with lower values to the left. A four-quadrant figure is provided to show the different quadrants of the jet streak where the left jet-entrance region is the top-left quadrant where ageostrophic convergence will provide continual support to maintain the strength of the surface anticyclone through subsidence (downward vertical motion). The surface anticyclone will propagate towards this region. Regarding trough ridge dynamics, a weak upper level is positioned over central CONUS. To the right of the base of the trough, ageostrophic divergence will promote upward vertical motion due to mass continuity where there is surface convergence between the base of a trough and the crest of a ridge. This will in turn support lifting for possible storms in our area as the jet propagates eastward.

Fig 2. Shows 500 hPa ascent (blue) and cyclonic relative vorticity in 10^-5 s^-1 where blue ascent depicting upward vertical motions on is seen over Alabama due to ageostrophic divergence associated with the trough, ridge dynamics discussed in the previous paragraph. A longwave ridge is also shown barreling up from the upper Midwest into northern Canada. At the crest of this ridge, this is an area of relative vorticity minima due to super-geostrophic winds in relation to trough, ridge dynamics. By following the 900-500 hPa thickness contours on Fig. 3, as thermal wind flows parallel to thickness contours with lower values to the left, the direction of thermal wind will be northwesterly and westerly towards our region of interest. By the Trenberth form of the QG-omega equation known as the “absolute geostrophic vorticity by the thermal wind.” calculated by the equation: σ(Δ²+f₀/σ ∂²/(∂p²) = 2f₀ [-V_T∙∇(ζ_g+f), areas of positive omega (upward vertical motion) and negative omega (downward vertical motion) can be plotted. When the right hand of the equation is < 0, there will be negative absolute geostrophic advection by the thermal wind due to the thermal wind advecting more values of negative vorticity from the vorticity minima over northern Canada into northeast CONUS and subsequently maximize omega creating downward vertical motion. This can be seen in Fig. 3 where there are blue colors in the vicinity of the surface anticyclone denoting downward vertical motion (positive omega). The Trenberth form of the QG-omega equation will, in addition to the left jet entrance region discussed above, will aid in the maintenance of the surface anticyclone strength of ~ 1036 mb.

As the surface anticyclone moves towards New York State, Fig. 4 shows a forecast run for 1800 UTC 8 April 2023. The anticyclone has now progressed towards a region favorable for continual maintenance discussed in Fig. 1 with the left-jet entrance region and Fig. 3’s negative absolute geostrophic advection by the thermal wind supporting downward vertical motion. The now 1032 forecast mb surface anticyclone’s flow (clockwise) will provide northeasterly and easterly winds from the Atlantic Ocean that will begin to be blocked by the Appalachian Mountains and deflected parallel to the Appalachian Mountains. The air approaching the Appalachian Mountains from the Atlantic Ocean is less dense and warmer than the surrounding air, so it will begin funneling denser, cooler air downstream (southwest) where Atlanta and surrounding areas will experience rainfall amounts ranging between an inch or two, gusty winds reaching up to 30 mph, and what could very well be the last “cold-air outbreak” of this Spring with maximum and minimum 24-hour temperatures in the low 40s for April 8th, 2023! This is known as cold air damming where the “C” shaped MSLP pressure contours in the southeast is a clear signature of this event.

Figure 4: A MLSP GFS-model map initialized at 1800 UTC 6 April 2023 where MSLP is plotted in the solid black contours every 4 hPa, precipitation shaded in the fill pattern along the x-axis in mm/6h, 850 hPa temperature in the dashed contours with at or below freezing values in blue and above freezing values in red every 5℃, and 10-m winds in the black barbs in knots at 1800 UTC 8 April 2023. The blue ‘H’ represents the surface anticyclone positioned over New York, moderate precipitation plagues the southeast, and the ‘C’ shape of the MLSP contours depicts a cold air damming event. (Alicia Bentley)

This year has started with a bang for severe weather season, with a rare double high-risk being issued on the last day of March. We’re going to look at a case that almost mirrored the setup of March 31, 2023, only a few days later on April 5, 2023. The defining feature of this event was a strong NE-SW jet streak (Figure 1) that helped to sustain a surface cyclone of 985mb across most of the US. The surface low for this cyclone is positioned near the southeasternmost tip of Minnesota (Figure 2) at 06 UTC on April 5, right in the left jet exit region (a known promoter of upward motion due to ageostrophic divergence). We’re going to focus on the Trenberth form of the QG-Omega equation today, using it to diagnose upward vertical motion as a result of the advection of vorticity.

Taking a look at Figure 3, we see a large strip of positive relative vorticity extending from the panhandle of Oklahoma to the western edge of Minnesota, and that is what we are going to focus on. First, we must introduce the Trenberth form of the QG-Omega equation. Simplified so it is easier to diagnose operationally, this is given by σ(∇^2+f₀/σ ∂²/∂p² )=2f₀ [-V_T∙∇(ζ_g+f)], where we care the most about the right-hand side. This is the absolute geostrophic vorticity advection by the thermal wind. The nice thing about the Trenberth term is we only need one component of it since it neglects the deformation terms found for the traditional form. We can look at our region of high vorticity in Figure 3 and compare it to the flow of the thermal wind in Figure 1. Thermal wind (-V_T) flows parallel to thickness contours with lower values to the left of the direction of the flow. Analyzing this in Figure 1, we can assess that the thermal wind is southwesterly. Since the thermal wind is pushing areas of relatively high vorticity to areas with little to no vorticity, there will be positive vorticity advection.

So, what does this mean in terms of synoptic forcing and the life cycle of this system? Because we are maximizing absolute geostrophic relative vorticity advection by the thermal wind, we also maximize the left-hand side of the equation. This, due to the second derivative test, will minimize omega and force upward vertical motion. We can see this in Figure 4, where there is a solid red blob over Minnesota, indicating the analysis is correct. Figure 3 also has a tool to analyze upward motion, the ascent at 500mb in blue contours. There is a healthy amount of blue contours over the overlapping region of red in Figure 4, so it is safe to say that there will be upward motion as a result of vorticity advection. What does this mean for the surface cyclone? It was forecasted to be supported below a 990mb pressure level across the entire US and up into Canada by this synoptic forcing. The surface low also stayed in the left jet exit region throughout it’s travel across North America. It is expected that this storm will create strong severe weather in a wake similar to that of the outbreak of March 31, 2023.

California has been getting significant precipitation this winter from the slew of atmospheric rivers that have battering the coast. Fox 5 San Diego reported on March 16 that the state has been directly hit by 14 of these since December, only two were considered “relatively weak”. Unfortunately, a cyclone off the coast on Sunday, March 20, 2023, accompanied yet another atmospheric river into the Bay Area (see figure 1). Orographic uplift during the “landfall” of an atmospheric river will be a consistent contributor for precipitation. In this region, when tropical moisture held within the airmass is advected eastwards with the geostrophic wind it makes its way onto land and is intercepted by California’s Coastal range where it is mechanically forced upwards and the moisture precipitates out of the airmass. The difference here is that the synoptic environment exasperated the terrestrial downpour that occurred in Cali through the early part of the week into Wednesday.

The synoptic environment during the onset of precipitation included several text-book qualities which led to strengthening of the low-pressure system as it was seen over the eastern Pacific Ocean at 0600 UTC on March 21, 2023, in figure 2. The second term in the QG-omega equation will be used to summarize a diagnostic tool that meteorologists use to track cyclones such as this one. The QG-omega equation aims to identify regions of airmass uplift (the Laplacian of omega, known as Term A) due to both differential geostrophic absolute vorticity advection by the geostrophic wind (known as term B), and the Laplacian of temperature advection (known as term C). Each of these terms can be evaluated independently to diagnose vertical motions. To focus only term B’s influence on vertical motions and the intensity of this cyclone over time a 500 mb map showing geopotential heights, ascent and cyclonic relative vorticity are used (figure 2) as well as a surface map with Mean Sea Level Pressure (figure 3) to show the atmospheric conditions at 0600 UTC 21 March. From figure 2, the warmer shaded fill at the base of cutoff low exhibits a strong region of positive relative vorticity. Since this cyclone is in the Northern Hemisphere, planetary vorticity is positive which indicates that absolute vorticity is also positive. Because the wind at this level is geostrophic, we can infer that the positive absolute vorticity values will travel parallel to the geopotential height contours as this cyclone moves Eastward. This is positive absolute vorticity advection by the geostrophic wind. From figure 3, the surface center of this cyclone is further to the east than the center is aloft. Because there is a vorticity maximum at the center of the surface low, absolute vorticity advection by the geostrophic wind here is zero. Because the value of absolute vorticity advection by the geostrophic wind increases with increasing height, term B in the QG-omega equation is positive which makes term A positive if we do not consider the effect from term C.

Using the values from term B, we can plot the magnitude of the differential absolute geostrophic vorticity advection by the geostrophic wind. This is shown in figure 4 below where the warm colors represent that positive values of differential absolute vorticity advection by the geostrophic wind will lead to upwards vertical motions within the vicinity of the cyclone. This upward motion of air from the surface helps intensify the cyclonic flow as time progresses and the storm moves eastward, closer to the California coast. This was seen throughout the day as the cyclone’s surface pressure dropped on March 21. Off the coast of Monterey Bay, CA an ocean buoy recorded a pressure drop of 24mb in just 17 hours, bottoming out just after 1900 UTC on March 21 (2:00 pm PDT).

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 28^th, 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/R_s – ∂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.

On March 24th, 2023 at 12Z, a longwave trough persists over continental United States, with its axis digging into the north-northwest edge of Mexico (Figure 1). A straight jet streak exists east of the axis over New England with wind speeds of over 200 knots. The placement of the jet streak aids in the dissipation of the trough by March 25th and may have lead to instability within the upper atmosphere that aided the strengthening of the 997 hPa surface cyclone situated at the intersection of Arkansas, Tennessee, and Mississippi.

Following the traditional four-cell model of straight jet streaks in the Northern Hemisphere, upward vertical motion is expected in the right jet entrance and left jet exit regions due to the divergence of ageostrophic winds (k/f × dv/dt) and mass continuity (∂p/∂t+▽⋅(ρu)). By March 25th, significant ageostrophic divergence can be seen in both regions, as denoted by the irrotational wind vectors within the vicinity of the surface cyclone (Figure 2). Instability within the region was also encouraged by the lifting of south winds by the cold frontal passage due west of the surface low. Both of these factors contributed to strengthening the surface low in Arkansas.

Implementing the Trenberth (1978) version of the quasi-geostrophic equation, which is given by σ(▽²+f₀²/σ ∂²/∂p²)ω=2f₀ [-(v_T) ⋅▽(ζ_g+f)], there is positive absolute geostrophic vorticity advection by the thermal wind. Evaluating the right-hand side of the equation, the thermal wind can be found using a 1000-500 hPa thickness map initialized at the same time. Because there is no absolute geostrophic vorticity at the surface and the Coriolis parameter f is positive in the Northern Hemisphere, the 500 hPa map of relative vorticity can be used directly to determine the sign of the equation. In Figure 3, it is shown that the southwesterly thermal wind is advecting positive values of absolute geostrophic vorticity within the vicinity of the surface cyclone. This makes the overall sign of the left-hand side of the equation positive, and this indicates upward vertical motion, which strengthens the surface cyclone to 989 hPa by March 25, 2023 21Z (Figure 4).