Measurement device and units

The SQM measures sky radiance in a cone of about 20° (full width at half maximum) in a spectral band that is similar, but not identical to, the visual band for which luminance is defined49,50. Measurements are taken in the logarithmic astronomical units of mag/arcsec2. The mag/arcsec2 scale is constructed so that a decrease of 5 in mag/arcsec2 corresponds to a factor of 100 increase in radiance. We follow the convention of Biggs32 and other authors and report all measurements in terms of the SQM spectral band mag SQM /arcsec2. An approximate conversion to luminance is possible using the formula cd/m2 = 10.8 × 104 × 10−0.4x, where x is the radiance in mag SQM /arcsec2. However, at artificially lit locations, the sky becomes redder with increasing cloud cover33,42 and this conversion would likely overestimate the luminance.

Since the mag/arcsec2 scale is not familiar to most readers, in many places the results are reported in “natural sky units” (NSU). A value in NSU indicates how much brighter or darker the sky is compared to a typical historic clear night sky. It is defined here as NSU = 100.4Δ, where Δ is 21.6 minus the observed value in mag SQM /arcsec2.

Observation locations

Sky radiance data were collected by professional researchers and citizen scientists using 54 SQMs at 50 locations (in some cases the SQM was swapped or used in multiple locations). The observing sites were located in the USA (12), Netherlands (9), Germany (8), Italy (5), Canada (4), UK (3), Australia (2), Austria (2), Spain (2), Japan (1), Mexico (1) and Norway (1) (Tab. S1, Tab. S2). Data contributors classified their site as “urban”, “suburban”, “rural” (within 100 km of a city of 50,000 or more), or “pristine” (far from cities and almost no lighting within 50 km). While the locations sample a wide variety of artificial light regimes, from the entirely natural to the entirely urban, they are neither a random nor a representative sample of locations on Earth and are almost exclusively located in developed countries.

Data were collected primarily in two periods, from 1 May 2011 to 30 September 2011 and 1 May 2012 to 30 September 2012, to avoid the influence of reduced foliage and frost or snow on the observations. Some SQMs were installed or de-installed during the measurement period (e.g. to avoid monsoon seasons) and uptime was sometimes reduced due to problems such as readout computer or power failures (Tab. S2). Data from two sites in Australia were taken between 21 and 29 November 2011 (Alice Springs) and from 15 March to 29 April 2012 and 21 May to 1 October 2012 (Adelaide). Some subsamples of these data have been reported previously29,30,33,35,37,38, but this is the first time the datasets have been systematically contrasted with each other.

All devices were installed in a weatherproof housing and aimed at zenith. Results were corrected for the extinction coefficient; two sites are excluded from the analyses because it was unknown (Tab. S3). The manufacturer reports that unit-to-unit differences between SQMs result in a systematic uncertainty of 0.1 mag SQM /arcsec2 (~10% in luminance), consistent with the differences observed in field campaigns51. Data were taken using SQM-LE, SQM-LU and SQM-LU-DL devices. The devices are optically identical and differ in how they are read out. The Ethernet connector of the SQM-LE produces some internal heating, but the light sensor has a known temperature dependence that is internally corrected before readout52.

Data processing

Data were taken using a variety of different file formats, with different time references (e.g. UTC, local and unix time). These were converted to a uniform format and each group verified that the time was properly encoded for their site. To improve future data exchange, a standard format for reporting skyglow measurement was developed in consultation with skyglow researchers worldwide. The standard was officially adopted on 15 September 2012 at the 12th European Symposium for the Protection of the Night Sky53.

The sampling rate at the sites ranged from a minimum of 1 observation every 15 minutes to a maximum of 1 observation per second. To simplify the analysis, data from sites with sampling rates greater than one observation per minute were averaged to produce a minute-by-minute dataset. Two locations were affected by a software thresholding problem, in which data were not recorded when the sky was darker than 20 mag SQM /arcsec2 (Tab. S3) and were not used in the analyses. Four additional locations were rejected from the analysis because they experienced SQM or setup failures that resulted in inconsistent data (Tab. S3). As a result, the total number of observing sites was reduced from 50 to 44.

The total amount of data from each site varied due to the sampling rate, the period over which the SQM was installed and working and latitude. Data were rejected if the sun was not more than 18° below the horizon (astronomical night). With the exception of the moonlight cloudy night analysis, periods during which the moon was above the horizon were also rejected. To separate the effects of clouds and temporal changes in skyglow, some analyses restrict data to periods near to “midnight”. Here, midnight is defined as the hour that falls closest to the time when the sun reaches its deepest point below the horizon for each individual site. Depending on the observation's location relative to a time zone boundary and whether a community uses daylight savings time, “midnight” could be 23:00, 00:00, 01:00, or 02:00 in local time (e.g. in Berlin, “midnight” occurs at 01:00 local time).

Cloud coverage analysis

The analysis follows a method similar to that used by Kyba et al.29,33. Cloud coverage was obtained from SYNOP reports downloaded from the ogimet website for the SYNOP station nearest to the site (www.ogimet.com). This distance ranged from 3 to 112 km. SYNOP reports describe fractional cloud coverage in oktas and only completely overcast (8 oktas) and completely clear (0 okta) conditions are considered. The clear and overcast sky radiances are defined as the median radiance observed within ±15 minutes of midnight under the given cloud condition.

Approximately half of the SYNOP stations did not provide hourly reports, so the cloud coverage analysis was not possible for these sites. To extend this analysis to include data from all sites, the relationship between brightness percentile and clear sky radiance at sites with SYNOP data was investigated. The 28th percentile was found to match the clear sky radiances the best and the 81st percentile was found to match overcast sky radiances best. We also compared the 5th percentile in observed sky radiance (darkest nights) to the 95th percentile. For urban sites the 5th percentile occurs on clear nights, whereas for pristine locations, the 5th percentile likely occurs on overcast nights.

Comparison to World Atlas

The median sky radiance observed on cloud free nights was compared to the predictions of the “First World Atlas of Artificial Night Sky Brightness”20 for sites in Europe and North America. The georeferencing of the Atlas was known to be off by about a pixel, so it was newly georeferenced. Whereas the Atlas was calculated for nights with a fairly transparent atmosphere, nights with clear skies but high humidity or aerosol content would be included in our analysis. Additionally, the estimates in the World Atlas are for the Johnson V band, which is not the same as V SQM . Finally, the satellite data for some of the Northern latitude sites was mainly taken during winter periods.

Temporal radiance change analysis

Temporal change was studied in two ways. First, contour plots showing all of the moon-free night data were produced for each site (this technique was first published in Ref. 37 and was also independently presented earlier at workshops by den Outer.) Contours were calculated using Gaussian kernel estimation and can be visually inspected for trends. Second, the sites found to be primarily artificially lit (20.85 mag SQM /arcsec2 or brighter) were studied to find the rate of change in the artificial light component. The median observed clear sky radiance was found for these sites at intervals of ±15 minutes around each of 22:00, 00:00 and 02:00 (where 00:00 is “midnight” as described above). Radiances were converted to NSU and the assumed natural background of 1 NSU was subtracted. The rate of change over each two hour interval was then calculated.

Overcast moonlit night analysis

The SQM is designed to measure a relatively uniformly lit field and point-like sources such as the moon do not match this assumption. However, on completely overcast nights, the radiance of moonlight leaving the cloud base can be assumed to have little zenith dependence (similar to the overcast sky in daytime, see e.g. Ref. 54.) Contour plots of overcast sky radiance against moon elevation were produced for sites with SYNOP data (Fig. S6). To minimize any effect from temporal changes, only data taken within 15 minutes of midnight were considered. Note that this timing restriction introduces a relationship between lunar elevation and phase. Plots were only produced for sites with at least 40 data points and at least one observation taken on a moonlit night.