More Thermal Winds in Hurricanes

So I know that I said that I was going to move on and compare the thermal wind structure surrounding a hurricane with the thermal wind structure surrounding an extratropical cyclone next.  Unfortunately for that aspect of the discussion, our current weather conditions in the US lack a well-defined extratropical cyclone right now.

Fig 1 -- GOES E Water Vapor image from 1045Z, Nov 7, 2010.  From the HOOT website.

And until we have a better-defined extratropical cyclone, I would rather wait on moving that part of the discussion forward.

Instead I want to take a closer look at some other things we can glean from the thermal wind construction around the hurricane.  Some discussions I had about that last blog post with a few colleagues of mine piqued my interest and led me to thinking about what exactly was being implied by that thermal wind relationship in a new way.  Below is a copy of my thermal wind diagram from the last blog post with one additional arrow added:

Fig 2 -- Thermal wind diagram around a warm-core system with the mean wind throughout the layer added.

I've added a purple arrow which represents the mean wind in the layer between the upper- and lower-level winds.  Basically, you take the average of the components of the two vectors representing the upper- and lower-level winds and the resulting vector is plotted as such.  The magnitude may or may not be exactly correct, but what is more important is its direction.  This implies that in the layer between the upper- and lower-level winds, there is a mean wind blowing across the direction of the thermal wind from the warm side to the cold size.  You can see here that the purple arrow is generally directed from the "warm" to the "cold" region, or down the temperature gradient.  This means that warm-air advection is going on in that layer.

Since a hurricane has no fronts (another feature of a warm-core system!), we can generally assume that a hurricane is loosely axisymmetric and therefore this same thermal wind orientation with warmer temperatures in the center of the hurricane would be found all the way around the hurricane. (For a very brief (two pages!) paper about the frequency of "perfectly" symmetrical hurricanes, see Knaff et al. 2003).  Since the hurricane is roughly axisymmetric, we can also infer that there would be a similar wind structure all the way around the hurricane and therefore a net warm-air advection outward from the center of the storm.  Does this make sense?

Fig 3 -- A generalized schematic drawing of a cross-section through a hurricane.  From Introduction to Tropical Meteorology, 1st Edition, Version 1.4.1, Produced by the COMET^® Program. Copyright 2007-2010

Above is a schematic of a cross-section through a hurricane showing the generalized flow patterns.  Note that near the surface we see an inflow region, whereas aloft we see outflow.  The thermal wind argument from before would lead us to conclude two things:

1. As a warm-core system, the center of the hurricane is warmer than the surrounding environment.
2. There is a net warm-air advection outward from the center of the storm through the depth of the hurricane.

How does this reconcile with the inflow region of the storm?  In the lower levels (i.e., the boundary layer), air is flowing inward toward the center of the hurricane.  But, if the center of the storm is warmer than its surroundings, wouldn't this imply cold-air advection into the interior of the storm?  By a very generalized view of the conservations of mass and energy, it could be argued that the mass and energy of air entering the storm must equal the mass and energy of air leaving the storm.  So how do we reconcile that there should be a net warm-air advection leaving the storm with the fact that there should be an "equal" amount of "cold-air advection" (cold is a relative term here) entering the storm in the inflow?

The answer (I believe) comes from latent heat.  (I know many people frown upon the term "latent heat" and right here, right now I am recognizing the fact that yes, arguing about things in terms of "latent" and "sensible" heat is up to some debate.  I'm still going to use it...). We have to start thinking about our temperature advections in terms of potential temperature advection if we are going to start comparing advection aloft (at lower pressures) to advection at low levels (at higher pressures).  So lets consider what happens as a parcel of air at potential temperature theta enters the hurricane.

There are competing theories (CISK and WISHE, for example) about how a hurricane gains its energy, particularly in the inflow region.  To avoid choosing one theory over another, we're going to look at a parcel with some potential temperature theta that has just reached the center of the storm (the eyewall).  Remember this is a hurricane, so that inflow air is going to be nearly saturated, if not already saturated.  As soon as it enters the eyewall and begins rising, that parcel will begin to cool.  But since it is nearly saturated, the parcel will cool moist adiabatically, not dry adiabatically.  All of that water vapor will begin to condense, releasing latent heat and warming the parcel, so it cools at a much slower rate than it would have f it were dry.  Since a parcel would have to cool dry adiabatically to conserve its potential temperature, the added heat from the latent heat release contributes to an increase in the parcel's potential temperature as it rises.  Just look at how the potential temperature changes with height on our sounding from Friday, which was roughly moist adiabatic.

Fig 4 -- Sounding from Kingston, Jamaica, from 12Z, Nov. 5th, 2010.  Annotated by the author to show potential temperatures at various levels.  From the HOOT website.

Therefore, by the time the parcel exits the storm in the upper levels, the potential temperature is well above the potential temperature that the parcel started with near the surface.  In fact, assuming the parcel is saturated right as it begins its ascent, the potential temperature of the parcel will always be greater than its initial potential temperature at any point along its ascent.  As such, any outflowing parcel will have a higher potential temperature than it did at its inflow, due to the latent heat release of condensing water vapor.  This confirms caveat two of our thermal wind consequences--

There is a net warm-air advection outward from the center of the storm through the depth of the hurricane.

The exiting parcels will be warmer than the entering parcels.  The first caveat is trickier to contend with, since as I mentioned before there are different theories (Craig and Gray, 1996) about how moisture and heat are handled in the inflow of a hurricane.  But that's a debate for another time.  I just wanted to address the question of how this warm-air advection outward from the hurricane implied by the thermal wind relationship makes sense.

By the way, please, please, please feel free to comment on any of these blog posts, send me an email, send me a text message, talk to me in person or anything regarding what I say here.   In fact, thoughts surrounding an in-person discussion I had about yesterday's post led to today's post. I tend to be wrong a fair amount of the time and would really appreciate corrections as well.  If people have alternate explanations for things, I'd be glad to have a "guest columnist" post, too.  And thanks for reading!