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

Constance Walker cwalker at noao.edu
Mon Feb 13 13:55:43 UTC 2012

Hi, Chris,


The plots make sense in that there should be a larger difference  
between measurements without a lens than with a lens when comparing  
city vs rural area.

Thank-you for sharing the results.

On Feb 13, 2012, at 5:56 AM, Christopher Kyba 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/
> <sqm_cloudiness.pdf>_______________________________________________
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Constance E. Walker, Ph.D.
director, GLOBE at Night campaign (www.globeatnight.org)
member, Astronomical Society of the Pacific Board of Directors
member, International Dark-Sky Association Board of Directors
chair, International Dark-Sky Association Education Committee
chair, 2012 Global Astronomy Month's Dark Skies Awareness Program
co-chair, International Astronomical Union 2012 Special Session on  
light pollution
associate scientist & senior science education specialist, NOAO

National Optical Astronomy Observatory (NOAO)
950 N. Cherry Avenue
Tucson, AZ 85719 USA
cwalker at noao.edu

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