Converting World Atlas floating point values into sky brightness predictions

Updated January 9, 2020.

Over the past several years, I was involved in the team that published the "The new world atlas of artificial night sky brightness" last summer. My main role in the project was in calibrating the map based on sky brightness observations. The two main sources of observations were the all-sky brightness surveys of the US National Parks Service Natural Sounds and Night Skies Division and observations with hand-held or vehicle mounted Sky Quality Meters (SQMs). In the end, we chose to do the main calibration with the SQM dataset, because thanks to the participation of citizen scientists, it covered locations on all 6 inhabited continents, including many more urban locations than were otherwise available. The NPS surveys, some additional telescopic data, and data from permanently mounted SQMs were then used to verify the result from the SQMs.

Now that the Atlas is published, many researchers are interested in using the map to understand their area. For most people, and also for many researchers, the colorized version of the map that we've made freely available is sufficient. For example, if you're looking for a good place to go stargazing, you'll do fine with the colored map. You can either view the Atlas with from within your web browser, or you can  download a set of tiles for Google Earth.

The rest of this post is technical, and will only interest a small subset of blog readers.

Some researchers will want to use the floating point dataset for further analyses*. The data is now openly available, and can be requested via a form from this page. The form sends an email to Fabio Falchi and Christopher Kyba, so that we are aware of who is using the data and can follow up if necessary.

The floating point data are stored in a single GeoTIFF file covering nearly the entire world's extent (arctic latitudes excluded). The map reports simulated artificial zenith luminance in mcd/m². If you want to use the data to estimate how bright a real sky is, you need to add in the natural portion manually. Natural light at night is quite variable, mainly due to the position of the Milky Way and the amount of airglow that is present.

When we calibrated the World Atlas, Dan Duriscoe from the US NPS provided me with estimates of the natural sky brightness for the specific date and time the observations were taken at each of the tens of thousands of locations worldwide. These observations were taken from 2007-2015, with the largest number of observations taken in 2013 and 2012. Over this time period, the predictions for the natural sky brightness ranged from 21.01 to 22.11 mag/arcsec². The most typical value was 21.65 mag/arcsec² (or about 0.236 mcd/m²). The average value changed over the years (due to changing solar activity), from faintest values of 21.88 mag/arcsec² in 2007 to brightest values of 21.58 mag/arcsec² in 2014.

Once you choose a natural sky brightness**, you should add that value (in mcd/m²) to the artificial sky brightness from the Atlas. Let's call this value "X". To convert this value into a prediction of what an SQM would see, use this equation:

SQM_pred = -2.5 log₁₀(X/ (10.8 x 10⁷))

I'd like to thank to Salvador Bará for sending me a question that prompted me to write this blog post.

* For researchers using the data in publications, please note that the data DOI is separate from the World Atlas publication. If you write a manuscript using the data, you should separately cite both the World Atlas publication and the data DOI.

** Note that in the model we also included an additional free parameter "S", which is a linear scaling factor for the natural sky component. We put it in to account for the fact that the SQM band does not match the V band. The best fit for this value was 1.15, meaning that the average natural sky brightness was increased from 21.65 mag/arcsec² (0.236 mcd/m²) to 21.50 mag_SQM/arcsec² (0.271 mcd/m²).