[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 <https://www.amazon.com/Weather-Wise-Gardener-Understanding-Predicting-Working/dp/087857428X> . 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 <thompnickson2 at gmail.com <mailto:thompnickson2 at 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 notion of static stability in meteorology.  Static Stability has a lot to do with differential lapse rates, the degree to which temperature declines with increasing altitude.  Lapse rates are minus numbers.  So a parcel is unstable if it has a lower lapse rate (a less minus lapse rate?) than surrounding parcels, and the greater the absolute value the difference between them, the greater the instability.

I asked “George” (GPT) to help me with this, but he (?) suggested I just take absolute values and give them whatever sign I want.  However, somebody told me, way back when, that taking absolute values was not kosher in mathematics.  (Why else would the variance be the mean SQUARED deviation about  the mean?).   

So there it is. 

Yeah.  I know. 

 

Nick 

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