Re: [FRIAM] Comparing negative numbers

[Nicholas Thompson]

Hi, everybody (anybody),

 

Many thanks to Russ, Frank, Stephen, and Steve S and others who got in touch 
with me off line. I try not to bother you guys unless I am pretty desperate, so 
I guess I was pretty desperate. 

 

A little history: I have been a weather-nerd ever since my early teens when the 
Worcester Tornado and two substantial hurricanes tracked through Massachusetts 
in  the early  I am also a gardener, so during the 80's I wrote The 
Weather-Wise Gardener 

 . Most of my knowledge comes from obsessive reading of forecaster discussions 
and recently I began to notice terminology creeping in that I did not 
understand and I began to wonder if I might update the book.  So I began 
reading weather texts and the numerous wonderful publications of NOAA and the 
AWS, and sat down to read Mid-latitude Atmospheric Dynamics with a friend from 
LANL. 

 

I have learned two lessons from this review, one happy, one sad.  The happy one 
is that my book holds up remarkably well, given its author and its longevity. 
It not only lays out the basic theory of the time pretty faithfully, but 
anticipates some ideas that weren’t all that current at the time.  I only 
detected a few colossal blunders, eg., a failure to honor the difference 
between centrifugal and Coriolis forces.   

The sad discovery was that meteorology is a cesspit of counter intuitive 
relations.  As altitude goes up, pressure goes down, temperature goes down, 
potential temperature goes up, potential vorticity (mostly) goes up. As 
temperatures go down, stability goes down, and clouds go up.  The more moist 
air is, the lighter air is, but precipitation releases latent heatand makes air 
lighter.  Both sun angle and daylength contribute to heating but in the winter 
hemisphere those es work together where as in the summer they work against one 
another. 

 

Most weather people when dealing with the public obfuscate these problems 
hideously.  For instance, a TV forecaster will speak about warm air advection 
aloft.   The air that is advecting is usually pretty cold by human standards, 
but its potential temperature is warm by the standards of that altitude.  75 
degree air in Santa Fe would be 110 degree air in Houston!  Santa Fe air, when 
it floats out over the plains, produces the temporary capping inversions that 
allow thunderstorm explosions during Oklahoma afternoons.  In the summer, one 
can see little pockets of Santa Fe air aloft almost anywhere in the country, 
and where they occur over pockets of cooler, moister air, the normal venting of 
diurnal heating to the upper atmosphere is temporarily inhibited with 
potentially explosive results. 

 

If I do rewrite this book, I will have to explain all of this to the layish 
(layer?) reader, and this is how I got thinking about my poor cats, Dee and 
Ess.  What words do I use to explain these dynamics when the signs are going 
every which way.  I suspect that you-guys learned something crucial while I was 
engaged in a fruitless struggle to become interested in Chaucer, something 
about how to make words and numbers work together, something that perhaps one 
cannot learn in one’s 80’s.  

 

Ah Well, 

  Frank and Russ, thanks for working through basic 5th grade 
mathematics with me and reminding my that if I want to compare two numbers, 
subtraction is the way and that the order of the subtraction can be manipulated 
to get any result like, positive or negative.  (Duh!) That’s how desperate I 
was.  

 

Thanks to Stephen and Steve for honoring  my childlike wonder and my faith that 
with enough help, even I can learn it.

 

NIck 

 

 

 

 

 

On Fri, Apr 12, 2024 at 12:00 PM Nicholas Thompson mailto:thompnicks...@gmail.com> > wrote:




My Dear Phellow Phriammers, 

Over the years I have asked you some doozies.  Still, I am pretty sure this the 
stupidest question I have ever asked this forum, so I am at your mercy.

I am in one of those situations where language and mathematics are rubbing 
together and driving crazy.  

Let say that my patio is ten steps down from my back door.  I have two cats,  
Dee and Ess, and  Dee is dominant to Ess.  So, if I go out to let them in, and 
I find  Ess on step -2   and  Dee on step -8,  I know I have an unstable 
situation. I fear that I will have a cat fight as Dee rushes past Ess to claim 
his rightful position by the preferred cat bowl.  Intuitively, I would  rate 
the degree of instability as a positive 6.  How would I compare the two numbers 
mathematically to get +6? 

But let’s say that for theoretical reasons I now want to conceive of the 
situation as a degree of stability, with negative stability corresponding  to 
instability.   Now, according  to my index, the situation is a minus 6.  How 
would I compare the two numbers mathematically to get  a -6?

The situation I am trying to model here is the origin of the 

Re: [FRIAM] Potential Vorticity and the Dynamic Tropopause

[Stephen Guerin]

Dan GuPTa had this response when asked to relate your .PDF to Bernard cells
and other prompting:

Here’s a integration of potential vorticity (PV), atmospheric stability,
and their relationship to Bénard cells, emphasizing isentropic layering in
both meteorological and experimental fluid dynamics contexts.

### Connecting Bénard Cells and Atmospheric Dynamics

In Bénard cells, fluid heated from below shows a critical transition from
conductive to convective heat transfer, forming cellular patterns.
Similarly, in the atmosphere, when the vertical temperature gradient
becomes unstable—akin to the Bénard cell transition—convection can
initiate, influenced by factors like the earth's rotation and potential
vorticity.

### Potential Vorticity and Stability

- **PV on Isentropic Surfaces:** Potential vorticity combines fluid
rotation and atmospheric stratification. In meteorology, PV is mapped on
isentropic surfaces (constant potential temperature layers), where it
highlights regions prone to atmospheric instability and potential
convection, akin to early instability in Bénard cells.

- **Dynamic Tropopause:** Acting like the fluid surface in a Bénard cell,
the dynamic tropopause is flexible, responding to distortions from jet
streams. These distortions can lead to convective activity by modifying
local stability and vorticity, driving weather patterns similarly to
temperature gradients in Bénard convection.

### PV Anomalies and Convective Cells

- **Weather Forecasting:** Monitoring PV anomalies helps predict convective
weather events, similar to observing Bénard cells to anticipate pattern
formation. For example, sharp PV changes can indicate regions ripe for
convective storms if conditions like moisture and surface temperature align.

- **Role of Isentropic Layering:** Both in Bénard cells and weather
systems, the spacing between isentropic layers indicates stability. Closer
layers suggest a steep gradient and instability, potentially leading to
convective movements. In the atmosphere, this translates to dynamic
interactions where lower stability near the surface can trigger or enhance
convective processes.

### Conclusion

Understanding the parallels between Bénard cell dynamics and atmospheric
conditions through potential vorticity and isentropic surfaces not only
illustrates universal fluid dynamics principles but also enhances
meteorological predictions of convective weather events, demonstrating how
small-scale changes in stability can lead to significant atmospheric
phenomena.

On Thu, Apr 11, 2024, 2:04 PM Nicholas Thompson 
wrote:

>
>
> Hi, Phellow Phriammers,  Nick, here.
>
>
>
>
>
>
> I have been lost in the weather.  This publication,
>
>
>
> https://acrobat.adobe.com/id/urn:aaid:sc:us:d481610b-e5d5-4a03-879c-6db6ec1d5e4a
>
>
> with its glorious eye-candy, is an example of what seems to be a new
> perspective in meteorology, the DT-PV perspective.  PV refers to a
> parameter, potential vorticity, which seems to be a measure of how liable
> the atmosphere is to churn; DT refers to the DYNAMIC tropopause.  The
> tropopause is the transition zone between the stratosphere and our own
> layer, the troposphere, through which gas exchange is limited because the
> lapse rate of the troposphere  -- its decline in temperature with fall of
> pressure -- is reversed in the stratosphere.   In the Bad Old Days, we
> were taught that the tropopause was like a ceiling, tilted upward from the
> poles to the tropics.  Now we have begun to think of it as more like a
> tent fly, still tilted up equator-ward, but loose and floppy and buffeted
> up and down by the jetstreams’ winds. These floppings up and down have the
> power to destabilize the lower atmosphere and lead to bad weather, if
> conditions there are ripe.
>
>
>
> This is not one of my usual cries for help.  I have some good tutors.
> However, I would love to hear from others whom this paper interests.  In
> particular I am struggling with the notion of potential vorticity, whose
> formula seems to take many odd forms.
>
>
>
> Best,
>
>
>
> Nick
>
>
>
>
>
> Nicholas S. Thompson
>
> Emeritus Professor of Psychology and Ethology
>
> Clark University,
>
> nthomp...@clarku.edu
>
>
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