From: men@bjerknes.colorado.edu (Matthew Newman)
Subject: Re: NEW Casio Alto Watch...
Organization: NOAA Climate Research Division
Date: Fri, 28 Aug 1992 19:46:00 GMT

In article <1992Aug28.082800.19948@sol.UVic.CA> dmanke@caliban.UVic.CA (Dennis  Manke) writes:
>
>Firstly, I must point out that I have the original Casio Watch and have found
>it to be very acurate, dispite any wild temp changes. I do however keep it
>on my wrist and in very cold conditions it's under a glove or something.
>Staff at MEC have also tested them and claim they find the Casio watch
>reports an alt within 5m of a top of the line, temp compensated aneroid
>altimiter. In one of the more recent (maybe 6 months back) IEEE journals
>(possibly the spectrum) they had a article on semiconducter pressure sensors.
>I skimmed it & I think they typically had a wide temp operating range,
>but I didn't skim it too closely.
>
>Well, since nobody has an answer, I thought I'd point out my other
>question again. The equations used to predict altitudes depend on pressure,
>temp, humidity, latitude, etc., and I found no quick and simple blurb on how
>important each parameter is. I can't find my photocopy of the article & I have
>no time to try and find the reference again, but I believe that humidity looked
>about as important as temp.
>
>===============
>Can anyone out there share shed some light on how important these
>parameters are and especially in a semiconducter based altimeter ? ? ? ? ? ?
>
>Dennis        dmanke@sanjuan.uvic.ca

Well, you asked for it:

The relationship between altitude, pressure, and temperature in
the atmosphere is given by the hydrostatic equation:

dp   -pg
-- = ----
dz    RT

where p=pressure, z=altitude, T=temperature, g=constant (due to gravity)
and R=gas constant of the atmosphere.  Variations in R due to
changing humidity are pretty small, and this is the only place
humidity can enter.

Altimeters work by *assuming* a relationship between temperature and
height called the standard atmosphere, in which temperature decreases
with altitude by about 6.5 degrees (Celsius) per kilometer.  Thus, the above
equation changes to:

	        T0     (    (  p )**(R*(dT/dz)/g) )
       z=z0 +  ----- * | 1- (----)                |
               dT/dz   (    ( p0 )                )

        where dT/dz= 6.50deg/km
              z0=height altimeter is calibrated (i.e., where you
                 enter the known altitude
              p0=pressure at height z0
              T0=temperature at height z0

In reality, some of the parameters are somewhat variable.  
Changes due to variations in g and R are extremely small.
Changes due to dT/dz, T0 and p0 are more substantial, depending on
local and largescale atmosphere dynamics.    However, typically
in midlatitudes (where most people on the net do their climbing) the
temperatures tend to change with height fairly evenly.  (This is not
necessarily the case in low latitudes, which is why these altimeters
are latitude dependent.)

The main effect of temperature variation is that if the air is warmer than
the watch thinks it should be at that altitude (i.e., warmer than the
'standard' atmosphere temperature), it will cause the
displayed altitude to be too high, and vice versa.  This effect gets worse 
with decreasing pressure (i.e., increasing altitude, so that altimeter
errors can get larger as you go upward).  Also, these errors accumulate
as you change altitude, so a 'true' temperature-corrected altimeter
would have to constantly keep track of temperature and altitude 
(of course, these new Casio watches might have a large enough computer 
to do this).

(Or, for those who can't get enough math,

dz'    - R    
--- = ----- * (T-Ts)
dp      pg     

where z' is the error in altitude, and Ts=the temperature the 
watch is assuming for that altitude.)

To get the most accurate results from any altimeter, it should be reset 
whenever the elevation is known.  Note that an approaching low that would cause
a barometer to drop 8 mb would correspond to an elevation increase of about
64m (1mb==~8m).  This would not be corrected for by a temperature
compensated altimeter.

I find that my watch-altimeter is accurate to within the limits 
that Casio mentioned in the manual.  The error due to temperature and
pressure variation is pretty small, especially when I recalibrate my
watch at known altitudes.

Actually, there are two other sources of error that I haven't seen mentioned, 
which I think might also be important:

1) Bernoulli effect -- as wind blows across the surface of the watch
(particularly, the pressure sensor), it will reduce the pressure there.
I observe this all the time--in high winds, it can fluctuate 15 m--so
when I read my altimeter in these conditions, I try to shield it with
my other hand (not that this is too effective).

2) As the sun warms the mountain, it also warms the air right next to
the surface.  This produces a reduction in pressure relative to the same
altitude in the atmosphere (hopefully, the picture below makes this clear)

         /\
        /  \ low(er) p             high(er) p
       /    \
      /      \
     /        \ 
----/  mtn     \------------------------------

The effect is to fool the altimeter into thinking that it must be higher 
than it really is (since it correctly reads a lower pressure).
I don't know if this is a large effect, but I do know that I invariably
seem to be a little lower than my altimeter thinks as I go up a peak.
(Of course, this could also partly be due to the error from temperature 
mentioned above.)
At night, this would be reversed, since the mountain cools strongly;
but I don't go hiking then.  I would be interested if anyone who has
an altimeter notices if the nighttime errors are invariably to register
altitudes that are too *low*.

(Crossposted to sci.geo.meteorology for anyone who wants to show me right
or wrong).

Matt Newman
men@noaacrd.colorado.edu



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