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    Re: Refraction and dip
    From: Marcel Tschudin
    Date: 2005 Oct 13, 10:37 +0300

    > Marcel you wrote:
    > "After downloading millions  of balloon data of stations at different
    > latitudes, I calculated in a first  test run refraction and dip for
    > latitude
    > 60N."
    
    Frank questions:
    > May I ask, who's your  intended "market" or "user base" for your
    > calculations? I know you mentioned at  one point that you were trying to
    > calculate the
    > positions of stars etc. as  accurately as possible. If this is strictly
    > for
    > astronomical use, an interesting  issue arises.
    
    Referring to the intended "market" or "user base":
    For my application I require (astronomical) refraction values near the
    horizon, this also for observers at heights above sea level. This was the
    reason for searching refraction values for negative altitudes. Since stars
    are not visible at such low altitudes (extinction), the application is well
    comparable to Andy Young's "Sunset science". After finding that no such
    (decent) refraction data are available, I decided to derive them on the
    basis of actual measurements done (balloon soundings).
    
    > Shouldn't you limit your balloon
    > data to days/nights when the sky  was clear or mostly so? It's important
    > because
    > certain types of temperature  inversions arise because clouds are forming
    > or
    > have formed at the altitude of  the inversion. Also, there are big
    > day/night
    > variations which may be much more  important astronomically than some of
    > the
    > latitudinal variation which has been  the traditional "averaging" bin for
    > these
    > sorts of data.
    
    There always will be somewhere a sort of averaging if one tries to provide
    certain "general" results. The analysis itself provides the limits of what
    is for the bin and what not.
    
    I agree with you that one should also consider whether there are clouds or
    not. A possibility would have been to drop all profiles with 100 percent
    relative humidity. I realised this after all the data were already
    downloaded, without this information. This means that my data are for
    average weather conditions.
    
    Regarding the daily variations: The data represent a "sort of" daily
    averages since the soundings are done at 00Z and 12Z. However, for locations
    at different longitudes these daily averages are for different times. Note
    that the daily variations are only important very close to the surface as
    may be seen from Fig. 3 in this document
    http://www.phys.unsw.edu.au/jacara/Papers/pdf/Toulouse2004_Aristidi1.pdf
    
    Comparing these daily variations with the latitudinal and seasonal
    variations indicate that the two latter one seem to be more important. This
    is due to the seasonal varying inversions which are already apparent at 35
    deg from the equator. I did hope to find sufficient latitudinal symmetry to
    reduce the amount of analyses, unfortunately the profiles indicate that the
    data from the northern and southern latitudes have to be analysed
    separately.
    
    
    
    > And:
    > " The  results showed that the refraction and the dip vary with the
    > seasons and that  the values are generally higher than the published
    > values
    > which seem to have  been calculated on the basis of a standard atmosphere.
    > The lowest  (unrealistic?) values are those new ones published by USNO.
    > The
    > results  showed also that the Bowditch formula for calculating the dip
    > (the
    > factor  1.76 in the metric version) should be at 60N during January around
    > 1.65 and  during July around 1.73 (the other months can be interpolated
    > using
    > a cosine  function). This might also be (one of) the reason(s) why Bill
    > encounters  these differences with the Chicago buildings or for Asbjorn's
    > differences who  is living somewhere around 60N. "
    >
    > I don't think very much of it would  come from differences in the
    > *average*
    > lapse rate. It's really a very small  difference. You have to be a hundred
    > feet
    > above the ground before a 10%  difference in the dip constant yields even
    > a 1
    > minute of arc difference in the  calculated dip. That said, we can expect
    > very large differences in the dip when  there is a really large variance
    > from the
    > standard atmospheric lapse rate (even  at low observer heights above sea
    > level). For example, if the atmospheric lapse  rate is -34.1deg Celsius
    > per km (as
    > opposed to the average rates of -6.5 for  moist air and -9.75 for dry
    > air),
    > there is no refraction at all. That is, a pure  geometric calculation of
    > dip
    > will work and the equation sqrt(2*height/R_Earth)  will match observations
    > of
    > actual dip. One can go beyond this and calculate dip  as a function of
    > lapse
    > rate and temperature (dip DOES depend on temperature but  only weakly).
    
    The indicated dip value was a value averaged over 9 different locations for
    an observer at 10m above sea level. Depending the selected location along
    60N and the month, the factor varies between 1.55 and 1.84. Why then
    Bowditch publishes 1.76 if only 1.8 or even only 2 would be sufficient?
    
    The standard atmosphere does not take into account any inversions. This is
    more or less only the case at the equator. From there the values increase up
    to e.g. an average of over 80K/km in the first 50m height above the south
    pole.
    
    > By the way, when considering the refraction tables and dip  tables
    > published
    > in the Nautical Almanac, it's worth remembering that these are
    > specifically
    > designed to be useful for observers AT SEA. If you look at weather
    > balloon
    > sounding data from places like Bermuda, Jamaica, Pago Pago, etc, the
    > patterns
    > are different from inland sites at similar latitudes. So a direct
    > comparison
    > between the Nautical Almanac tables and your intended use may not  work
    > out very
    > well.
    
    BUT, there are also differences even at sea level depending on the latitude
    and, from what it looks like, they have not been considered in those
    published values.
    
    >
    > And:
    > "A main problem arose by realising that  the
    > lapse rate distributions within a height layer are  distributed
    > asymmetrically, meaning that taking the average or the median of  these
    > values is not good enough. At the moment I try to derive a  calculation
    > procedure in order to find an estimate for the most likely value  (mode)
    > of
    > lapse rate within a height layer. "
    >
    > Why would you want that  mode value? What I mean is, what purpose would
    > that
    > serve (it doesn't  necessarily have to serve any purpose at all --I'm just
    > curious to know how you  would use this mode result)?
    
    By using only average values one underestimates the most likely lapse rates.
    The average value is mostly off the highest populated area in the histogram,
    thus indicating a less probable value. This difference is especially
    important for the inversions: Using the average underestimates the
    inversions.
    
    Marcel
    
    
    

       
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