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Re: (meteorobs) The formulae of ZHR
Hello Huan Meng,
> ZHR=HR/[r^(Lm-6.5)*cos(z)^1.47] (in the calendar, and it was said it's from
> IMO)
>
> or
>
> ZHR=(1+sum n)/sum(Teff/C)
> C=r^(6.5-Lm)*F/sin(h) (in nearly all the IMO shower circular)
both formulaes are in a sense "correct", even though there are two
differences that require some explanation.
First of all, cos (z) = sin (h).
z is the zenith distance, h is the altitude. So z = Pi - h, and
cos (-x) = cos (x) = sin (x+Pi)
You are right the the field obstruction factor F was left out in the
first formula, you in general you should try to avoid obstruction, anyway.
The first real difference is the so-called zenith correction exponent,
which is assumed to be gamma=1.47 in the first formula (cos(z)^1.47) and
gamma=1.0 in the second (sin(h)^1.0=sin(h)). This exponent gamma has been
discussed for many years in a number of publications. Some people favour a
value of 1.47, whereas other investigations came up with a value close to
one. This is why in all IMO Shower Reports the old "standard value" 1.0 is
used. When publishing ZHR figures you should always state which gamma you
applied, as the difference in the computed ZHR will usually be quite
large.
The second difference comes from the statistics of small numbers. In the
upper formula there is simply written HR, which is HR=(sum n)/sum(Teff).
However, statistics teaches us that the correct expectation value for HR
is (1+sum n)/sum(Teff). There was an article by Janko Richter in WGN a
few years ago (?) which pointed to this little inconsistency in the
standard ZHR formula(*), and since then the correct formula (with +1) has
been used in all shower reports. The impact on the computed ZHR is
neglectible for major showers, but noticable for minor showers with ZHRs
well below 10.
So for your own calculations I suggest you use the second formula.
Best wishes,
Sirko
PS: I explained the stuff above to the best of my knowledge - don't
hesitate to correct me if I'm wrong in some point! :-)
(*) It may look strange that the expected HR value is >0 when you
observed 0 meteors in a given time interval, but consinder the extreme
case that you observed only one minute. Even when watching in August you
will probably have seen no meteor in that minute, but the expected HR
value is certainly not zero during the Perseids. If you add 1 as tough by
statistics this does not happen. The expectation value for HR will be 1,
for example, if you watch for a full hour but see no meteor, and will
converge to zero the longer you observe without success.
--
**************************************************************************
* Dipl.-Inform. Sirko Molau * *
* RWTH Aachen, Lehrstuhl fuer Informatik VI * __ *
* Ahornstr. 55, D-52056 Aachen, Germany * " 2B v 2B " *
* * *
* phone: +49-241-8021615 * Shakespeare *
* fax : +49-241-8888219 * *
* email: molau@informatik.rwth-aachendot de * *
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* www : http://www-i6.informatik.rwth-aachendot de/Colleagues/molau *
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