# NCHurricane2009's Blog

Extratropical to Tropical Transition Part 1
 Posted by: NCHurricane2009, 8:49 AM GMT on November 29, 2009 +0
I have been meaning to post this blog for a few weeks now, but had some difficulties with my laptop crashing and then my school work ramping up on me. I know it has been a while since this year's Tropical Storm Grace, but here is part 1 of my technical discussion on extratropical (non-tropical) cyclone transition to tropical cyclone transition (such as what happened with Grace). Part 2, coming soon, will talk about how this process can happen over waters colder than 26 deg C.

I would like as much feedback as you can give as to understanding the technical discussion in this entry. If you liked the idea, I can make technical posts on other weather topics in the future. My hope is to be able to with satisfaction explain weather phenomenon to the average blog viewer.

Introduction
This year’s Tropical Storm Grace and 2005’s Hurricane Vince show that tropical cyclone formation is possible over cool Sea Surface Temperatures (SSTs). We’ve always been taught that 26 deg C was the threshold for tropical cyclone formation, but there is an emerging theory on how tropical cyclones can develop over cooler waters. Usually, the tropical cyclones that indeed do develop over cool waters develop from a parent extratropical (non-tropical) system. The environment of these parent extratropical systems provides unique features that allow for the formation of a small tropical cyclone at its core. In order to understand how this process happens, we need to go over a crash course in some meteorological fundamentals first.

Section 1: The Hydrostatic Equation
The hydrostatic equation can provide an understanding of the vertical (up and down) forces in our atmosphere. It can be used to approximate the vertical dynamics in weather systems, but is inaccurate for vigorous small-scale systems such as squall lines and tornadoes [1]. Since we are studying large scale hurricanes in this discussion which features negligible vertical accelerations, we can use the hydrostatic equation.

Imagine a vertical column of air, Figure 1. In that column, we define z as the upward direction. In that air column, imagine that we are studying a thin layer of it. The layer of air has three forces acting on it:
1. The force of gravity due to its mass. This force is equal to mass m times acceleration due to gravity g, or mg.
2. The force of atmospheric pressure acting on the top side of the thin air layer
3. The force of atmospheric pressure acting on the bottom side of the thin air layer

Figure 1: Geometry of a vertical air column used to develop the hydrostatic equation

Recall that as you go up in the atmosphere, the air pressure P reduces (because there are fewer and fewer air particles above you pressing down on you as you go up). Let us say that the bottom side of our thin air layer is under atmospheric pressure P. Now, on the top side of the air layer, the air pressure is lower than on the bottom. If we define the change in air pressure from the bottom side of the layer to the top as dP, where dP is a negative value since the pressure on top is less than the bottom, then the pressure on the top of the air layer is P + dP.

If you remember in physics that pressure = force divided by area. Thus, force is equal to pressure times area. So, in conclusion, our three forces on our thin air layer become:
1. The force due to gravity mg
2. The force due to atmospheric pressure acting on the top side of the thin air layer (P + dP)A
3. The force due to atmospheric pressure acting on the bottom side of the layer PA.

Now, recall Newton’s Second Law of Motion from physics, force is equal to mass times acceleration. If we apply this to our vertical z direction we see in Figure 1, we can write Newton’s second law as:

Sum (Fz) = ma (Equation 1a)

Now, it’s a good time to say why they call it the hydrostatic equation. That’s because the assumption is that acceleration a = 0. In large scale systems such as hurricanes, vertical accelerations are generally negligible (yes there are updrafts, but are not accelerating (changing their velocity) rapidly). That’s why with tornadoes and squall lines the equation does not work, we see more rapid vertical accelerations in those systems. So now, Equation 1a becomes (forces mg and (P+dP)A have minus signs because they act in the opposite direction of the z direction defined in Figure 1):

Sum (Fz) = 0
PA – (P + dP)A – mg = 0
PA – PA – dPA – mg = 0
– dPA – mg = 0
– dPA = mg
dPA = - mg (Equation 1b)

Now, lets do some additional magic to the equation. Remember from physics that density D is mass divided by volume. Thus, it is true that mass is density D times volume V, or…

dPA = - DVg (Equation 1c)

Looking at Figure 1 more closely, we see that the rectangular shaped thin air layer has dimensions dx by dy by dz. We define the dimensions this way becuase as we travel across the air layer for instance in the x direction, your position changes by amount dx (i.e. dx means change in x direction). The same meaning is behind dy and dz in the y and z directions. If the lengths of the air layer’s sides are dx, dy, and dz, then we know from geometry that if we multiply the lengths of the sides together, we get the volume of the air layer. Likewise, if we multiply dx and dy, we get area A which we defined in Figure 1:

dPdxdy = - Ddxdydzg
dP = - Ddzg
dP/dz = - Dg (Equation 1d)

Equation 1d is the famous hydrostatic equation. The fraction dP/dz represents how much the pressure changes (dP) as you change your height z in the atmosphere (dz). The equation tells us that the rate at which pressure drops during your go up in the atmosphere is equal to density D times acceleration due to gravity g (the minus sign indicates that as you go up in the atmosphere, the pressure is decreasing).

Section 2: The Ideal Gas Law
When studying gases, scientists were able to summarize its behavior under different conditions using the following formula:

PV = mRT (Equation 2)

Where R is the ideal gas constant. Many gases, including air, have an R value. Lets say I have a finite mass m of air in a balloon. Somehow, lets say that I am able to heat up the temperature T of the air in the balloon. That means that the right side of Equation 2 increases, which means that the left side of Equation 2 must also increase (that means pressure P or volume V of the air in the balloon must increase). Well, if the balloon is free to expand, the pressure in the balloon stays constant while the volume of the balloon grows larger. However, if I constrain the balloon walls so that the balloon cannot expand, the volume stays constant but the pressure in the balloon increases (until it pops!). Thus, Equation 2 tells us how a gas behaves, which matches or intuition and observations on how we see gases behave.

Section 3: The Hypsometric Equation
In meteorology, we define what we call geopotential, which we will define as G* in this discussion. We also define geopotential per unit mass as G = G*/m. Recall from physics that the amount of work done is how much force you apply to an object over a certain distance, which we make into a mathematical value as force times distance. Geopotential is defined as the amount of work spent traveling up from SEA-LEVEL to the CURRENT LEVEL in the atmosphere you are at against gravitational force mg. So, lets say you traveled from sea-level to height h1 in the atmosphere, your geopotential is:

G* at h1 = (Gravity Force)*(Distance from sea-level) = (mg)(h1)
G at h1 = (g)(h1)

Now lets say that you traveled to height h2 in the atmosphere, which is higher than height h1:

G at h2 = (g)(h2)

Recall the z coordinate in Figure 1. Lets say that I travel from h1 to h2, which means that I changed my z coordinate, which means that I traveled by distance dz (change in vertical coordinate z):

(G at h2) – (G at h1) = (g)(h2-h1)
dG = gdz (Equation 3a)

Now, lets do some rearranging with Equation 2:

PV = mRT
P = (m/V)RT
P = DRT
D = P/(RT) (Equation 3b)

Substituting Equation 3b into Equation 1d:

dP/dz = - Pg/(RT)
dP = - (Pgdz)/(RT)
- (RT/P)dP = gdz
gdz = - (RT/P)dP

…and then substitute Equation 3a into the above:

dG = - (RT/P)dP (Equation 3c)

As you climb from h1 to h2, the pressure changes from P1 to P2. But, pressure P2 is less than P1 as pressure drops as you climb up, and thus dP (the change in pressure as you go from h1 to h2) is a negative value. Thus, dG in Equation 3c will still be a positive number despite their being a negative sign in the right side of the equation (negative sign multiplied by negative dP leads a to positive value). The fact that dG (the change in geopotential) remains positive makes sense since it takes more work to go from sea-level to h2 than it does to go from sea-level to h1. In our original definition of geopotential in Equation 3a, as we climbed from h1 to h2, dG was also positive. So, we have made a quick check to see that Equation 3c is valid because it matches the trend in our original definition of geopotential.

We know that as we climb up in the atmosphere, temperature decreases as well. To simplify Equation 3c, we define average temperature T*, the average temperature as we climb from h1 to h2:

T* = - TdP/P (Equation 3d)

…and thus Equation 3c becomes:

dG = RT* (Equation 3e)

Now, we define geopotential height Z (not to be confused with the regular vertical coordinate, which is lowercase z) as:

Z = G/g (Equation 3f)

…and we manipulate Equation 3e further while incorporating Equation 3f:

(G at h2) – (G at h1) = RT*
g(Z2 – Z1) = RT*
Z2 – Z1 = RT*/g (Equation 3g)

Equation 3g is known as the hypsometric equation.

Section 4: Warm Air is “Thick,” Cold Air is “Thin”
At this point, we have combined the hydrostatic equation, the ideal gas law, and geopotential into a single equation known as the hypsometric equation. It actually has significant implications in relating the temperature of an air mass to its vertical structure in the atmosphere. If the average temperature T* is high, the “thickness” between geopotential heights Z1 and Z2 increases, and vice versa for a low average temperature T*. This is why we can say warm air masses are vertically “thick,” and cold air masses are vertically “thin.” But, we need to really understand what exactly geopotential height is physically to really see the significance of this statement.

We defined geopotential height in Equation 3f, which is geopotential per mass G divided by acceleration due to gravity g. Recall from physics that geopotential is a unit of work, which is force times distance, or Newtons N times meters m (or simply a Newton meter N*m). Geopotential per mass is thus N*m/kg. An unbalanced single Newton N of force is equal to accelerating 1 kg of mass by 1 m/s^2. So, the units of geopotential per mass is actually…

N*m/kg = [(kg*m/s^2)*m]/kg = m^2/s^2

Acceleration due to gravity g is in units of m/s^2. Thus as Equation 3f tells us to do, if we divide the units of geopotential by g, we end up with the following as the unit of geopotential height Z:

[m^2/s^2] / [m/s^2] = m

Thus, we see that like regular height lowercase z, geopotential height (capital Z) also has units of meters m. Acceleration due to gravity g, technically, varies with how far away you are from the Earth’s surface (when you are far away from Earth in space for instance, Earth’s gravity doesn’t pull you down). Even within our own atmosphere, especially above the troposphere, g begins to drop off in value. Notice carefully when we defined geopotential G* = mgh in Section 3 (where h is height above sea-level), we assumed that g = 9.81 m/s2, and thus we assumed g WAS CONSTANT even as we climbed up. We even assumed that if h was so large that you were in outer space, that Earth’s acceleration due to gravity would still work against you as you climbed (which is not true!). Thus, if we climbed from Earth’s surface to outer space and calculated geopotential work as mgh, we severely overestimated how much actual work it takes to climb into outer space from sea-level. Now lets say you wanted to calculate your height above Earth’s surface based on how much work you spent climbing up against Earth’s gravity. Lets say you climbed really really high, and your “work-o-meter” reads 100,000 N*m/kg. Now, you say to yourself “I am going to use the geopotential height equation to calculate how high I am above Earth’s surface”:

Z = G/g (Equation 3f)
Z = [100,000 N*m/kg]/[9.81 m/s^2] = 10,194 m

So you say, hmmm, I have climbed 10,194 m above Earth’s surface. You didn’t use a ruler, you used the reading off of your “work-o-meter.” But if you used a ruler instead of the geopotential height equation, you would be surprised to find that you actually climbed even higher than 10,194 m! What went wrong? In Equation 3f, you assumed that g was constant as you climbed up; but in reality, g was dropping off because Earth’s gravitation weakens with height. So, if you really did climb and spent 100,000 N*m/kg of work, you went higher than 10,194 m. So, why do meteorologists use geopotential height Z instead of actual height measured with a ruler z? Because….

Pretty much you’ll find that z = Z in the tropopause
z > Z above the tropopause

…and the tropopause is where weather occurs. Geopotential height is an estimating calculation of how high you are above Earth’s surface based on how much work (measured in N*m/kg) you did to climb, all while assuming that Earth’s gravitational field is constant (g = 9.81 m/s^2). This estimating calculation falls apart above the tropopause. Using geopotential height instead of actual height also makes our meteorology math easier, if we did take into account that g was variable with height, Equation 3g for instance would be a lot more complicated. Since geopotential height is pretty much actual height in the tropopause, we will now swap out z with Z as our vertical coordinate, and analyze the consequences of the hypsometric equation (equation 3g) in a vertical air column, Figure 2.

Figure 2: Relating the hypsometric equation to the thermal vertical structure of the atmosphere

In Figure 2, we are drawing horizontal constant pressure surfaces (pressure is meteorology is measured in millibars mb, also equal to hectopascals hPa). Lets say that we have air parcel 1 (an air parcel is an infinitely small particle of air to help us visualize what’s happening in the atmosphere) at geopotential height Z1 which is located on the 1000 mb pressure surface. Now lets say you have an air parcel 2 at geopotential height Z2 which is located on the 850 mb pressure surface. And also, we define the average temperature T* of the air layer between 1000 mb and 850 mb. If we heat up the column of air, T* increases, and Equation 3g tells us that thus the vertical distance between the air parcels Z2-Z1 MUST ALSO increase. Now watch the magic: because the vertical distance between the two air parcels increases, so does the vertical distance between the 1000 mb and 850 mb pressure surface (the air column gets vertically thicker!). Now, we understand that warm air column is “thick” and cold air columns are “thin.”

The hypsometric equation is a highly-mathematical way of explaining why warm air is “thick” and cold air is “thin.” For those that don’t like rearranging equations to explain things, recall that the hypsometric equation has in it embedded the ideal gas law, and we discussed our ideal gas air balloon earlier in Section 2. We talked about heating air up the balloon, which causes air inside it to expand. Think now if you heated up an air column, it will expand upward (or thicken). If you cool down an air column, it will contract downward (or thin).

In Figure 3, we put the cold and warm air columns together side-by-side and watch what happens: we get a cold-core upper low/trough, a warm-core upper high/ridge (this is why we hear upper lows are cold core and upper highs are warm core. Upper lows are often referred to as cold lows, and upper highs are referred to as warm highs. Upper troughs are referred to as cold waves, and upper ridges are referred to as warm waves). What’s happening at the surface in Figure 3? The upper-level air is being pushed outward from the upper-level high/ridge, and is blowing into the upper low/trough. Because air is escaping from the top in the upper ridge, the air pressure reduces at the surface as less air is pushing down on you from above, and thus there is a surface low below the upper-level high. In the upper low, air is accumulating from above, so at the surface more and more air is pushing on you from the top. Thus, a surface high forms below the upper low.

Figure 3: Vertical structures of warm core and cold-core circulations, and horizontal maps of the sea-level and 500 mb structures of the warm-core and cold-core circulations

In Figure 3, we also define two types of meteorological pressure maps. Our sea-level analysis is a map of constant pressure lines while analyzing at sea-level. The lines on a sea-level pressure map are called isobars in units of mb. Our upper-level analysis can be done at varying pressure surfaces. In Figure 3, we chose to do a 500 mb upper-level map, which is a map of the 500 mb pressure surface with lines of constant geopotential height. The lines on an upper-level map are thus called isoheights in units of meters.

Section 5: Latent Heat Model of Extratropical to Tropical Transition
Currently, we explain that extratropical cyclones thrive on horizontal air temperature contrasts (baroclinic instability) and that tropical cyclones thrive on latent heat release from condensing clouds. What we will explain here is the traditional way we explain how the complex process of extratropical to tropical transition happens.

Figure 4 is a time-scale evolution of how we can go from a weak upper-level cold wave with surface cold front to a vigorous hurricane. As we go in time in Figure 4, the left column of illustrations shows the vertical structure of our storm, and the center column shows a horizontal map complete with surface wind vectors in black arrows, surface fronts and surface lows in color, and 200 mb upper-level analysis in green. Orange shading is surface warm air, and blue shading is surface cold air. The right column shows a corresponding satellite image of the different phases of Atlantic Hurricane Michael, which occurred in October 2000 [2].

Our example storm, like any extratropical cyclone, begins with an upper-level cold wave (i.e. upper trough). How do these cold waves form? Well in the mid-latitudes, the prevailing wind direction is from west to east (westerly) in both hemispheres. If the surface of the Earth was perfectly uniform (made of all ocean or of all flat land of the same material), the prevailing westerly mid-latitude surface flow will be generally in a straight line, and cold air would stay poleward and warm air equatorward. However, there are obstacles like mountains and valleys (topographic obstacles). Plus oceans have higher heat capacities than land masses; so in the winter, oceans are warmer and land is colder, and vice-versa is true in the summer. Thus, we can have not only north-to-south temperature differences, we can also have east-to-west temperature differences. East-to-west temperature differences create baroclinic instability, and trigger extratropical cyclones. In the topographic case, a mountain chain can cause cold air pooling for example to the east and warm air pooling to the west. Or like off of the east United States coast in the early winter, the warm Gulf Stream waters with leftover summer heat create warm maritime air to the east that is in contrast to cold air masses over land to the west, and is thus a frequent source of baroclinic instability for the famed coastal extratropical nor’easter cyclones.

Now, lets break down the different phases in Figure 4 (Northern Hemisphere Case):
a. Frontal Boundary: Cold air has pooled off to the northwest on the horizontal map. Because as we learned in Section 4 that cold air is “thin,” the green 200 mb isoheight lines are dropping southward in association with the cold air. This creates a slight v-shaped cold wave in the 200 mb lines on the horizontal map (a 200 mb upper trough forms). Because of the balance of upper-level pressure gradient, coriolis, and centrifugal forces (force balances are not discussed in this post, but I may make another post on this later), the upper-level 200 mb flow also resembles a v-shape. On the west side of the 200 mb wave, the upper flow is northwesterly (traveling from northwest to southeast). On the east side of the 200 mb wave, the upper flow is southwesterly (traveling from southwest to northeast). Moreover, the flow on the east side of the 200 mb wave is accelerating (is decelerating on the west side of the wave). When air parcels arrive to the east side of the wave, they are accelerating away from each other. As the air parcels at 200 mb spread apart, the surface pressure below drops along a band at the surface (leading to the formation of a band of surface low pressure, which is a cold front/surface trough beneath the east side of the 200 mb wave). The flow around this surface cold front (as shown by the black arrows) also resembles a v-shape due to the balance of surface friction, pressure gradient, coriolis, and centrifugal forces. Notice carefully that the surface wind direction (black arrows) causes the cold air to be pushed further southeastward, and warm air to be pushed northeastward. As the cold air gets pushed southward, we see with time that the 200 mb wave becomes sharper (remember that cold air is thin).

b. Frontal Wave: The increasingly sharpening (strengthening) 200 mb wave (upper trough) features increasingly strong upper air acceleration on its east side. Increasing upper air acceleration intensifies the cold front further (remember that the cold front is a band of low surface pressure, and surface pressures continue to fall as the upper air acceleration strengthens). A local maximum of upper air acceleration on the east side of the upper trough causes a local maximum of surface low pressure (a low pressure center forms along the front). This new surface low pressure center is called many things (a frontal wave, frontal depression, frontal low, extratropical (non-tropical) low, extratropical (non-tropical) cyclone). The balance of surface friction, pressure gradient, and coriolis forces causes the familiar counter-clockwise northern hemisphere surface flow around the low pressure center (notice the black arrows are now spinning counter-clockwise around the low pressure center). Because of the counter-clockwise surface flow, the surface low pushes the frontal segment to its east northward (a warm front form east of the low pressure center), the remaining segment stays a cold front as the counter-clockwise flow drives cold air southward to the west of center. Because cold air continues to dive southward by the surface wind flow, the 200 mb wave (upper trough) continues to sharpen (remember that cold air is thin). The vicious cycle continues as the sharpening upper trough with increasingly stronger upper air acceleration supports a strengthening surface frontal low, and the strengthening surface frontal low in turn continues to pull cold air southward which causes the upper trough to continue to sharpen.

c. Start of Occlusion: It is well observed that cold fronts move faster than warm fronts as they make their counter-clockwise rotation around the surface low pressure center. This is because cold air is denser than warm air. On the east side of our surface low, the warm front struggles to push northward as the less dense warm air has a difficult time pushing out the more dense cold air to its north. On the west side of the surface low, the cold front easily moves south as the more dense cold air has an easier time pushing out the less dense warm air to its south. Occlusion begins as the faster moving cold front hits the slower moving warm front at the surface low pressure center. Notice how far south the cold air has traveled, which by this time has caused the 200 mb upper trough to now be really sharp. The vicious cycle still continues (the sharpening upper trough with increasingly stronger upper air acceleration supports a strengthening surface frontal low, and the strengthening surface frontal low in turn continues to pull cold air southward which causes the upper trough to continue to sharpen).

d. Deep Occlusion: This is the mature phase of our extratropical cyclone, featuring a long occluded front attached to our surface low pressure center. What is this occluded front? Recall that occlusion is the process of the cold front hitting the warm front. Ahead of our cold front and behind our warm front is a wedge of warm air, which has now become a narrow band of warm air (the occluded front is a narrow band of surface warm air, and notice a low-level warm core of sorts has formed right at the low pressure center from the occlusion). Also note that cold air has now pooled off to the southwest of the surface low pressure center, leading to a cold core 200 mb upper low due to the “thin” nature of our cold air (as discussed in Section 4). Note that the surface wind arrows (black arrows) no longer can push the cold air southward, and thus the cold core upper trough/low will no longer strengthen. Also notice carefully that the surface low pressure center is no longer underneath the east side of the upper trough/low, which means that the surface low can no longer strengthen underneath the upper air acceleration on the east side of the upper trough/low (finally, the vicious cycle ends). At this point, the extratropical deeply-occluded surface low is at peak strength, and begins weakening at this point while suffering from a lack of upper-level acceleration underneath the upper low. In fact, the upper low will continue to steer the surface low into its center (the surface low actually whirls into a position directly underneath the upper low). As air parcels getting sucked into the upper low accumulate above the surface low, the surface low weakens as surface pressures tend to rise beneath an upper low (recall Figure 3, where a surface high tends to form beneath an upper low).

e. Subtropical Cyclone: Typically, extratropical surface cyclones do not make it past the deep-occlusion stage (they very slowly dissipate beneath the upper low). However, the current explanation is that in some cases a deeply-occluded surface extratropical cyclone over sufficiently warm waters can gradually acquire tropical characteristics. Warm, moist air above the warm ocean spirals counter-clockwise into the surface low pressure center. As the moist air collides at the center of surface low pressure, the air parcels cannot go down into the ocean. Instead, the air parcels are forced to rise. The rising, moist air parcels get colder (remember air temperature cools as you climb up). The moist air contains in it water vapor (water in its gas state). As the water vapor gets colder, the water molecules are less excited (they slow down, they bounce around and vibrate less). It gets to the point where water molecules slow down in relation to each other such that they can bond with each other into a liquid phase, and clouds form (clouds are composed of tiny water molecules that have bonded into small liquid water droplets. The droplets do not fall as they are very tiny and float in the air. Eventually, rain forms as droplets continue to grow). As the water vapor condenses into water droplets (i.e. clouds), a very important reaction is happening:

H2O (gas) = H2O (liquid) + Heat (Equation 5)

As we go from water vapor (gas) in the left side of Equation 5 to water droplets (liquid), HEAT is being released into the atmosphere (this heat is called latent heat). Imagine two water molecules having a chemical bond in the liquid phase. In order for the two molecules to break their bond so they each become water vapor molecules (gas), the two molecules need to absorb energy from the surroundings. Because energy is neither created nor destroyed, if the two molecules rejoin into a liquid phase, that energy is released back into the surroundings. The form of energy we are talking about is heat (which is molecular level energy of motion). So, liquid water absorbs heat to become vapor, and releases heat when returning to a liquid phase. An intense thunderstorm cloud with plenty of condensation releases large amounts of heat into the atmosphere. As the atmosphere warms around the surface low pressure center, a low-level warm core matures. The low-level warm core that was once due to occlusion is now sustaining itself through latent heat from cloud formation. In addition, the surface low at this stage is no longer attached to any fronts. The system on satellite imagery would appear as a tropically organizing core of swirling clouds at the low pressure center, and above there is still a leftover cold-core upper low. We are now at a subtropical cyclone phase (subtropical depression/subtropical storm).

f. Shallow Tropical Cyclone: Continued concentrated latent heat release at the surface low pressure center causes the warm core to vertically grow. Because we learned warm air is “thick” in Section 4, we know that air pressure above is rising as a warm-core upper ridge starts to form (recall warm-core upper ridges in Figure 3). In this stage of Figure 4 (in the vertical structure), a warm core upper ridge has formed at 500 mb. Air parcels above the surface low are pushed outward by the upper ridge, which maintains the low pressure at the surface (now the system is a tropical cyclone). In the case of a strengthening tropical cyclone, there is a net accumulation of condensation latent heat, see Figure 6 [5]. Meteorologists tend to look for cirrus outflow clouds blowing away from the storm top, this indicates that the warm core upper ridge (also called an upper anticyclone because winds spin opposite to cyclonic around an upper ridge) has formed, and that the subtropical cyclone is now a tropical cyclone (tropical storm, hurricane, etc.), see Figure 7. The tropical cyclone at this stage is somewhat shallow (because its entire vertical warm core structure is still beneath a decaying 200 mb cold core upper low).

g. Well-Developed Tropical Cyclone: Very well-developed tropical cyclones have impressive upper anticyclones (upper warm core ridges) that reach into 200 mb. A shallow tropical cyclone can continue to become well-developed as long as concentrated storm clouds continue firing at the center (more latent heat=a more developed warm core). At this point, the leftover 200 mb upper low has become replaced by a warm core 200 mb upper ridge. Often, this is referred to as the 200 mb upper low becoming “punched out.” The vertical structure of the well-developed and well-organized tropical cyclone resembles that of the warm-core circulation shown in Figure 3 (a surface low pressure center that is supported by a warm-core upper ridge).

Figure 5 is the same as Figure 4, but now shows a southern hemisphere case (rare south Atlantic Hurricane Catarina is the example storm in Figure 5). Because of the coriolis force, winds around the surface low pressure center are now clockwise instead of counter-clockwise.

Section 6: Why 26 deg C?
In the late 1940s to late 1960s, papers on tropical cyclones trended toward establishing 26 deg C as a necessary condition for development, for example references [5] and [6]. The 26 deg C sea surface temperature (SST) “limit” was determined by combining SST data with the typical temperature of the upper atmosphere during summer. It was found that in the region of SST warmer than 26 deg C (which effectively becomes the temperature of the lower atmosphere), the upper to lower atmospheric air temperature contrast was high enough such that the atmosphere was generally unstable, allowing for towering thunderstorm clouds (and hence latent heat release) to develop. The opposite trend was noted for regions of colder than 26 deg C SST.

In order to understand the stability of the atmosphere, meteorologists tend to look at skew-T Diagrams. Part 2 of this discussion (Extratropical to Tropical Transition) will cover atmospheric stability and looking at skew-T diagrams, which will help us understand the theories on how it is possible for extratropical to tropical transition over cooler waters. Part 2 will be later posted on my blog. Until then, I hope you enjoyed and understood this discussion…

Figure 4: Time-scale evolution of an extratropical cyclone transitioning into a tropical cyclone with Hurricane Michael in October 2000 as an example [2].

Figure 5: Same as Figure 4, but for the southern hemisphere case with the example storm Cyclone Catarina of March 2004 [3]. Catarina was a rare south Atlantic hurricane that barreled into Brazil.

Figure 6: Tropical cyclone intensification from a finite amount of latent heat accumulation [5]. A cloud burst in column b causes a finite amount of latent heat accumulation. In column c, the accumulated latent heat results in the formation of a warm core upper ridge at around 100 to 200 mb due to atmospheric thickening (as shown in Figure 2). Air at 100 to 200 mb spreads outward from the ridge, and column d represents what happens once the upper ridge has finished evacuating its high pressure and dissipated (notice the 100 to 200 mb pressure surfaces are flat). Because the air column is heated, the vertical distance between the pressure surfaces must remain high (thick) even though the 100/200 mb surfaces have flattened, and this results in the pressure surfaces below dipping downward (surface pressures fall, and the tropical cyclone strengthens).

Figure 7: Visible satellite image of impressive Atlantic Hurricane Isabel in September 2003 [4]. At the storm top, there are thin, wispy cirrus outflow clouds blowing away. The green arrows represent the upper-level wind direction based on the cirrus outflow cloud appearance, and notice that they are anticyclonic (opposite to cyclonic) about the storm center, indicating a warm core upper ridge represented by the green H (signature of a tropical cyclone). The red arrows are the surface cyclonic flow about the surface low pressure center. In a tropical cyclone, the upper anticyclone spreads away air parcels above the surface low, which is key to maintaining the low pressure at the surface.

References
[1] Holton, James R. An introduction to Dynamic Meteorology 4th Edition. Elseiver Academic Press: Burlington, MA. 2004.
[2] ftp://eclipse.ncdc.noaa.gov/pub/isccp/b1/.D2790P/images/2000
[3] ftp://eclipse.ncdc.noaa.gov/pub/isccp/b1/.D2790P/images/2004
[4] http://earthobservatory.nasa.gov/images/imagerecords/12000/12124/Isabel_trmm2003254_lrg.jpg
[5] Gray, William M. Global View of the Origin of Tropical Disturbances and Storms. Monthly Weather Review. Vol 96. No 10. October 1968
[6] Palmen, E. On the Formation and Structure of Tropical Hurricanes. 1948.
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