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

Christopher Kyba christopher.kyba at wew.fu-berlin.de
Mon Feb 13 12:56:18 UTC 2012


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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