[SQM] Function to approximately predict variation of sky brightness with cloudiness

Christopher Kyba christopher.kyba at wew.fu-berlin.de
Mon Feb 13 13:26:37 UTC 2012


Please excuse me for needing to send a correction to the last message.
 I noticed a small error in the formulas I sent.  The value of "C" is
the difference between the SQM value measured during clear skies and
22.6.  That is:

C=22.6-(clear sky SQM value)

C tells you the degree to which the sky is polluted relative to an
assumed "perfect" value of 22.6.

Christopher Kyba
Institute for Space Sciences
Freie Universität Berlin
http://userpage.fu-berlin.de/~kyba/



On Mon, Feb 13, 2012 at 1:56 PM, Christopher Kyba
<christopher.kyba at wew.fu-berlin.de> wrote:
> Hello LPResearch list and Unihedron SQM list,
>
> I just wanted to let you know that I've found an equation that
> approximately describes the relationship between sky luminance (as
> measured by the SQM) and degree of cloudiness.  I "fitted" the
> parameters by hand using data we have measured
> (http://dx.plos.org/10.1371/journal.pone.0017307), and compared it to
> my estimates of the SQM values observed at CESAR
> (http://www.rivm.nl/bibliotheek/rapporten/680151002.html).  You can
> see the curves in the attached plot.  Red points are for SQMs without
> a lens, black points for SQMs with a lens.  The x and o represent our
> measurement location inside of Berlin, the crosses are CESAR, and the
> stars are a rural location outside of Berlin.
>
> The curves I've plotted are:
>
> mag/arcsec^2=22.6-C*(1+0.8*F^2)     (SQM with lens)
> mag/arcsec^2=22.6-C*(1+0.7*F^2)     (SQM without lens)
>
> Where C is the SQM value measured for clear skies, and F is the
> fraction of sky that is covered (clear=0, cloudy=1).
>
>
> I will be testing/refining this equation based on data from
> international sites this spring, but I thought that some of you might
> be interested in seeing this functional form.  In principle, it could
> be used to very roughly predict "circadian dose" over a long time
> period using weather reports and a single SQM reading on a clear
> night.  Note that this equation probably only works for locations with
> light pollution - if you have clear/cloudy SQM data from a pristine
> location I would be very interested if you could send me the values
> you have observed.
>
> Best wishes from Berlin,
>
> Christopher Kyba
> Institute for Space Sciences
> Freie Universität Berlin
> http://userpage.fu-berlin.de/~kyba/


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