The Nachtlichter app was developed within a project called Nachtlicht-BüHNE (Citizen-Helmholtz Network for research on night light phenomena)⁵, using a co-design process in which academic and citizen scientists met regularly over a several year period. Our co-design process, app methodology, site selection, systematic variability of the observations, data pre-processing and data structure have already been described in detail⁵. This section therefore briefly covers the data and validation and focuses mainly on the methods unique to the analyses presented here.

Nachtlichter data and validation

In a Nachtlichter observation, participants conducted a ‘survey’ while walking along a ‘transect’, which typically extended from one street corner to the next. The participants used the app to classify and count all of the light sources that they could see. A total of 18 light categories were used for the 2021 experiment (Fig. 2). Depending on the light type selected, participants provided additional information about the size, emission direction (that is, shielding), color and subjective brightness. Transects were pre-defined in most cases and selected and arranged to completely survey the publicly accessible areas covered by a reprojected DNB satellite pixel. We therefore somewhat undercount the total number of installed lights because we did not record lights installed in areas not visible from public spaces (for example, backyards, courtyards and rooftops; Supplementary Fig. 5).

The observation time (of night) was not constrained, but the main experiment took place from 23 August to 14 November 2021, usually over a period of weeks for each pixel⁵¹. Additional smaller data-taking campaigns were conducted in the spring and autumn of 2022 to develop a correction for certain lighting types that were found to frequently turn off. The campaign in autumn of 2022 took place immediately after a German law requiring switch offs of some signs was passed²². However, as our statistics were not sufficient to observe a difference to the data taken in 2021, all of the available data were combined for determining the correction factors. The app and training materials were updated in 2023 to perform an experiment directly investigating lighting changes; data from that campaign is not included in the analyses reported here.

Observations were collected mainly in Germany from city centers, suburbs and villages (Extended Data Fig. 7). Region selection was based partly on where citizen scientists were present and able to count, and areas without sharp changes between land use near the boundaries were preferred⁵. Brighter areas in cities are therefore overrepresented compared to their relative frequency by area, but this means we cover nearly the full range of radiance observed for German communities¹³. Areas with high-rise buildings were generally avoided because of the difficulty in counting windows, but there were a few cases in which buildings of approximately ten stories were located along the transect. For most of the counting areas, buildings were one to four stories tall. The raw data may be downloaded from within the app itself (https://lichter.nachtlicht-buehne.de), and a processed dataset more suitable for analysis is available from GFZ Data Services⁵².

Observations were validated by comparing our total counts of streetlights to the numbers reported in public databases⁵. The values agreed to better than 7% for our areas in Berlin, Cologne and Dresden. In Fulda and Leipzig, the Nachtlichter counts were 40% and 90% larger, respectively. This was due to the presence of streetlights on private roads in these two measurement areas and exemplifies how Nachtlichter data are more complete than existing public lighting databases. Observations were additionally validated by comparing the counts of different participants to each other on the same transect. This was complicated by the fact that participants did not count at identical times, and later observations had fewer lights. The standard deviation for the total number of lights on the two most frequently observed streets was 15% for observations during 19:30–21:30. The counts were more consistent for streetlights than for other types of light, such as signs and windows, for which participants estimated sizes.

Time of night correction

As mentioned above, some light source types turn off during the course of the night⁵. Different satellite pixels were sampled at different dates of the campaign, and the earliest (by date) observations were acquired later at night, due to the late sunset. We therefore developed an approximate temporal correction to account for the changes and tested a few strategies using a Monte Carlo simulation of counting data. We found that the dataset size limitation would prevent fitting a general function. We therefore decided to model the switch off with a logistic function:

where p is the probability that a light is on at time t (in hours relative to midnight), f is the fraction of lights that turn off, s is a parameter that describes how quickly the lights turn off and h is the time (relative to midnight) at which half of the lights that will turn off have done so (Extended Data Fig. 8).

This function was motivated by published curves for private window illumination in Manhattan, New York, USA⁵³, and for its simple interpretation (for example, for private windows, h is effectively the average bedtime and s is related to the variability in bedtimes across the population). For most light source types, we do not have sufficient data to detect a change in lighting, or the returned fits did not describe the data well (for example, streetlights in Extended Data Fig. 8). For these sources, we do not apply a correction. The function is based on the assumption that all transects in Germany behave identically. While this is not the case, we found the fit for five of the light source types to be plausible and use it to extrapolate (or in some cases interpolate) the observations from each street to an estimate for what would have been observed at 19:00 and 00:00 (Extended Data Fig. 8 and Supplementary Table 1). The category ‘signs’ is based on the sum of illuminated signs, self-luminous signs and video screens. The same correction is applied to all three.

The fit parameters were found by minimizing the sum of errors over all surveys on transects with multiple observations. The individual survey error is defined by a least-squares-like function (Supplementary Fig. 6):

where N_c is the reported (counted) number of lights and N_e is the expected number of lights based on our fit. N_e is calculated via N_e(t) = N_t × p(t), where N_t is the estimated number of total lights on the transect in the early evening. N_t is found by minimizing E_surv for the current fit parameters. This minimization causes the red dots and yellow stars in Extended Data Fig. 8 to be distributed equally above and below the fit line as N_t is estimated separately for each transect.

The left term of equation (2) is similar to the usual weighted least-squares term for normally distributed data, but we have effectively increased the standard deviation to account for participant counting errors and the (frequently) small number of lights counted. However, our errors are not actually normal (or Poisson) distributed; large differences can occur if a set of lights is controlled by the same switch and turned off in unison, if a participant makes a dramatic counting error, or if the lights on the transect do not behave like the ‘average German street’. The right-hand term, therefore, minimizes the contribution of information from transects that do not behave in a typical fashion (that is, the difference compared to what we expected is larger than 3σ). In our tests based on Monte Carlo data, this procedure successfully returned fit parameters that reasonably match the inputs used in the simulation, even when we included the possibility of counting errors and correlated lights.

When a single Nachtlichter observation was made for a transect, the extrapolation process to obtain an estimate of the number of lights at an alternative time is straightforward. If N_c lights were observed (counted) at time t₀, then the estimated (maximum) total number of lights that would be turned on in the early evening for this transect is N_t = N_c/ p(t₀). The number of lights we would expect to be observed at a different given time t is then N_e = N_t × p(t). When a transect was surveyed multiple times, then N_t is estimated by finding the value of N_t that minimizes the sum of E_surv for all observations on the transect. The estimate at a given time t is then N_e = N_t × p(t) as before. For the light types for which no corrections are applied, multiple observations were simply averaged. These procedures lead to fractional values for the total number of lights.

Satellite data

The DNB⁵⁴ observes the Earth nightly at an equatorial crossing time of 1:30, with a consistent resolution of 750 meters across the scan. The detector is sensitive to electromagnetic radiation in the wavelength range 500 nm to 900 nm (for convenience referred to here as ‘light’). The combined light emissions from all sources within the ~0.56 km² is integrated into a single observed radiance value for the pixel. The nightly observations are combined into monthly and annual composite products by the Earth Observation Group²⁵, which uses a 15-arcsecond global raster. The pixel size therefore depends on latitude and is roughly 470 by 300 meters in central Germany (Fig. 1). Because the reprojected pixel is smaller than the intrinsic resolution, the radiance reported for a single pixel includes light from surrounding pixels. To the greatest extent possible, we therefore aimed to have Nachtlichter study sites located in areas surrounded by areas of similar character⁵. Nevertheless, the satellite radiance is biased downwards for lit areas near the city limits, and the radiance observed by adjacent DNB pixels is correlated.

We estimated the radiance of the Nachtlichter study areas using DNB observations taken during September through November during 2019 to 2021 (September 2021 was excluded because of considerable areas of Germany with no data, due to stray light on the sensor). We also calculated the total radiance from the mainland of Germany using airglow corrected data^55,56 for the months of October and November of 2015–2023 (a longer time series was used to better estimate uncertainties). The standard deviation of the sum of Germany’s lights was 7%, and the standard error was 1.7%. For Berlin, these numbers were 9% and 2.0%, and for our selection of DNB pixels (below), 12% and 4%.

Satellite and total lights analyses

We defined 181 analysis areas, usually associated with single DNB pixels (Fig. 1). In 12 cases, we joined multiple DNB pixels and Nachtlichter counts into a combined analysis area, as we felt it was more appropriate based on the relative positioning of the transects and pixel boundaries (for example, in the case of a single very long rural street segment that runs through multiple pixels and that was created directly by a participant rather than pre-defined by the main team). These were mainly in rural sites; the group of 12 had a median DNB radiance of 2.3 nW cm⁻²sr⁻¹.

We calculated the fraction of each transect that lay inside of a pixel boundary and multiplied this by the individual light type counts to obtain an estimate of how many of the transect’s lights are located inside of the pixel. These results were then summed to obtain a total number of counted lights within the pixel. The median relationship for all 181 analysis areas was 317 counted lights per km² per nW cm⁻²sr⁻¹. This is shown as a straight line in Fig. 3, and similar medians are shown in Extended Data Figs. 1 and 2 and Supplementary Figs. 1 and 2.

Graphing the median relationship is useful for showing when light types do or do not have a proportional relationship to satellite radiance, but it means pixels are weighted equally, rather than by the number of counted lights. As an alternative that assigns equal weight to counted lights and radiance, we divided the sum of counted lights over all pixels by the sum of the product of radiance and area for each individual pixel. This effectively treats all of our observations as if they were one single contiguous analysis area. When done for the German pixels only, and for the estimated light counts at midnight, we find a conversion factor of 219 ± 11 (standard error) lights per km² per nW cm⁻²sr⁻¹ (Supplementary Table 1 provides other selections). This factor was then multiplied by the product of mean radiance and total area to obtain the estimated number of lights that would be observed if all of Germany or all of Berlin were sampled using our methodology at midnight.

The Spearman rank correlation coefficient was calculated for each of the individual light types separately (Extended Data Figs. 1 and 2). In all cases, the (two-sided) null hypothesis of no correlation between satellite radiance and light type was rejected. The null hypothesis was least strongly rejected for garden decoration lights (p < 0.04) and house numbers and doorbells (p < 0.0002).

Uncertainty estimation

The estimation of the number of lights on at midnight is affected by three sources of uncertainty: person-to-person variability in the number of lights counted, uncertainty on the fit to the time-of-night light extinction curve and the uncertainty on the ‘sum of light’ from the DNB (reported above). The uncertainty on person-to-person variability was estimated via Monte Carlo. In a series of simulations, the sum of lights count (N_c) of each participant was adjusted according to N_sim = N_c/ v, where ‘v’ is an individual variability factor randomly chosen from a normal distribution with a standard deviation of 15%. We then calculated N_total = ∑N for each simulation and measured a standard deviation of 2.1%.

The uncertainty on both the fit parameters and the total lights at midnight were estimated using bootstrap with replacement⁵⁷. Each survey with N > 1 observations was assigned a statistical weight of N − 1 (because one degree of freedom is used for each transect to estimate the total number of lights). A total of 1,000 replacement samples were then randomly assembled with an equivalent statistical weight to the full sample, and the extinction curve was fit for each light type for this sample. For the uncertainty on the fit parameters, we report the confidence interval covering the 15.715th to 84.285th percentile (corresponding to 1σ; Supplementary Table 3). For each bootstrap dataset and fit, we then calculated the sum of lights for the five fit light categories and its standard deviation. We find that the fit introduces a standard error of 3.2% for the estimate of the total lights (all 18 categories) at midnight (Supplementary Table 4). The three uncertainties were then added in quadrature to yield a total standard error of 4.1% for Germany and 4.3% for Berlin.

Land-cover analysis

Our land-cover analysis makes use of the most recent CORINE (Coordination of Information on the Environment) Land Cover (CLC) classification from 2018⁵⁸. The CLC includes 44 different types of land cover, but 94% of our transects were located in one of just three land-cover classes: continuous urban fabric (typically city or town centers, with >80% of the land surface covered by impermeable features), discontinuous urban fabric (built-up areas with 30 to 80% of the surface covered by impermeable features) and industrial and commercial areas (Extended Data Figs. 9 and 10). Only 2% of transects were associated with the next most frequent land-cover class: urban green areas. Because our observations were made primarily in cities, the ‘industrial and commercial’ areas within this analysis are mainly commercial areas.

The minimal mapping unit of CLC is 25 ha. Because our transects are rarely longer than 200 meters, they are typically entirely within a single CLC class. (A higher-resolution land-cover dataset, such as the Copernicus Urban Atlas, would introduce additional complications, because transects would be more frequently split between land-cover types. It would also not be available for our rural sites.) We calculated the midpoint of each transect and assigned the transect to the land-cover category at that point. We then summed the light counts for all of the selected transects within the land-cover type, using the 19:00 and 00:00 projection for the overall comparison (Fig. 4) and the actually counted data (using the mean in case of multiple surveys) for the examination of the shielding, color and brightness properties (Extended Data Figs. 4 and 5 and Supplementary Figs. 3 and 4). For our examination of the prevalence of motion control detection (Extended Data Fig. 6), we treat each transect separately and show the maximal value reported. This is because in the early evening, observers may not notice that lights are activated based on presence detection, due to the higher number of people present on the street.

Light contribution analysis

Light is additive, so each light source located within a radiometer’s pixel increases the overall radiance measured by the instrument for that pixel proportional to its flux at the sensor. We attempted to find ‘weighting factors’ that would return radiance estimates based on the lights counted on the ground:

Here L_pred is the predicted radiance observed for a given pixel, w_i is a weighting factor for one of the 370 combinations of light and associated characteristics (for example, ‘video screen, small, medium brightness, white’), C_i is the total number of lights of that type observed within the pixel and the sum is over all of the different individual light types counted within the pixel. The values of w_i can be estimated by minimizing the value of a cost function that depends on them, such as:

Because we observed fewer than 370 DNB pixels, it was necessary to reduce the number of parameters. By assuming four variables representing the contribution of different sizes, emission directions, colors and brightnesses are constant across all lighting types, the number of variables could be reduced to 22. We attempted such minimizations with DNB, SDGSat and aerial photography data, with several different cost functions (the value of 0.2 above was motivated by the observation that the standard deviation of pixels in monthly DNB data is proportional to its radiance²⁴). Regardless of what we tried, the procedure never returned physically meaningful results.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.