Philippa Kaur

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Description of PTEsThe descriptive statistics of the contents of soil PTEs in the study area were shown in Table 1. From Table 1, the mean contents of As and Ni in the oil-affected soils exceeded their corresponding risk screening values33, which may damage the soil ecological environment and affect crop growth. Compared with the secondary standard of soil environmental quality34, the mean contents of As, Cu and Zn were all lower than their corresponding Grade II standard values, but the mean contents of Cd, Cr, Ni and Pb in the oil-affected soils were 1.07, 7.46, 7.14 and 1.36 times of their standard values. In contrast with the background value of Hubei province35, except Mn, the mean contents of As, Cd, Cr, Cu, Ni, Pb, Zn and Ba in the oil-affected soils all exceeded their background values. Meanwhile, the variation coefficient of Cr (1.41) was greater than 1. In general, the soil Cd concentration in the study area was higher than that around Gudao Town, a typical oil-producing region of the Shengli Oilfield in the Yellow River Delta, China12, and from Yellow River Delta, a traditional oil field in China9, but was lower than that around two crude oil flow stations in the Niger Delta, Nigeria36. The concentrations of other PTEs were higher than the corresponding element concentrations, detected in the soil around Gudao Town, a typical oil-producing region of the Shengli Oilfield in the Yellow River Delta, China12, from Yellow River Delta, a traditional oil field in China9, and around two crude oil flow stations in the Niger Delta, Nigeria36. The above analysis exhibited that PTEs in the oil-affected soils had a certain degree of accumulation and may be affected by human activities.Table 1 Statistical characteristics for potential toxic elements in in the study area (mg·kg−1).Full size tableLevels of PTEs enrichment and pollutionThe EF and PLI of soil PTEs in the study area were calculated to evaluate the pollution degree of soil PTEs. The calculation results of EF and PLI were shown in Fig. 2 and Table S4. From Fig. 2, the mean EF values of PTEs were showed as Pb  > Cr  > Ni  > As  > Cd  > Zn  > Cu  > Ba. The mean EFs of all PTEs were greater than 1. Among them, the average EF of Cu, Zn and Ba was between 1 and 2, which was slightly enriched. And As (2.18) and Cd (2.12) were moderately enriched. In particular, the average EF values of Cr, Ni and Pb were 14.23, 8.69 and 15.45, respectively, reaching a significant enrichment level, and all samples of Cr, Ni and Pb were at moderate or above enrichment, of which 10% of the Cr samples were extreme pollution, 85% of Cr samples, 95% of Ni and 5% of Pb (Table S4) were significantly enriched. These proved that these PTEs were generally enriched in the study area, especially Cr, Ni and Pb.Figure 2The map of enrichment factor and contamination factor of PTEs in the study area.Full size imageExcept Mn, the average CF values of other PTEs were all  > 1 (Fig. 2), indicating that the accumulation of Mn in the study area was relatively light, and there was no obvious Mn pollution. The CF values of all samples of As, Cr, Ni and Pb, 80% of Cd samples, 75% of Cu samples, 30% of Mn samples, 65% of Zn samples and 75% of Ba samples (Table S4) were higher than 1. And the mean CF values of Cr, Ni and Pb were 14.21, 7.58 and 12.73, respectively, certifying that the pollution of Cr, Ni and Pb in the study area was considerably serious. PLI was calculated based on the CF value of PTEs, and the results were shown in Fig. 2. The average value of PLI was 2.62, indicating that the soil PTEs in the study area were seriously polluted.Spatial distribution of soil PTEs in the study areaGeostatistical analysis was utilized to do ordinary Kriging interpolation of the PTEs in the study area, the results were shown in Fig. 3. As shown in Fig. 3, the spatial distribution of As, Cr, Ni, Zn and Ba was relatively consistent, and their hot spots were concentrated in the southeast, northwest, and central and eastern parts of the study area where oil wells were distributed. The spatial distribution of Cr and Ni exhibited that there were large-scale hotspots near the oil wells, and the content of Cr and Ni in these hotspots was much higher than second-level environmental quality standards of China, which proved that the content of soil Cr and Ni was significantly affected by the oil production activities of the oil production plant. There were crude oil leaks in B and C, and the contents of Zn and Ba in the vicinity of these two oil wells were relatively high, indicating that soil Zn and Ba in this area may be affected by the crude oil leakage, resulting in a certain degree of accumulation in the soil. The area with the second highest As content mainly resided in the middle of the study area. According to the survey, the herbicides were sprayed every year around the H oil well in the middle of the study area, indicating that the accumulation of As in the soil was not only related to oil extraction activities, but also to the use of pesticides (contains copper arsenate, sodium arsenate, etc.)10, 14. In addition, the hot spots of spatial distribution of Pb, Cd and Mn were concentrated in the southeast, and Cu was mainly concentrated in the southeast and midwest. As analyzed above, in addition to Mn, the PTEs Pb, Cd and Cu all have a certain degree of accumulation. And the investigation found that there were many petroleum machinery manufacturing plants in the central and eastern part of the study area, therefore, the accumulation of Pb, Cd and Cu in the soil may be related to factors such as petroleum extraction, crude oil leakage and machinery manufacturing. The above analysis indicated that the influence of human activities is evident on the distribution of soil PTEs3, 23.Figure 3spatial distribution map of soil PTEs in the study area.Full size imagePotential ecological risk assessmentThe potential ecological risk assessment model after adjusting the threshold was used to evaluate the PER of the oil production plant. The individual potential ecological risk of PTEs was shown in Table 2. From Table 2, the average ({E}_{r}^{i}) values of PTEs were Cr  > Pb  > Cd  > Ni  > As  > Cu  > Zn  > Mn. The average ({E}_{r}^{i}) values of Cr and Pb were 79.62 and 63.64, respectively, reaching a relatively high level of potential ecological risk; the average ({E}_{r}^{i}) values of Cd and Ni were 55.95 and 37.91, respectively, which were at medium potential ecological risk level; the average ({E}_{r}^{i}) values of other PTEs were all lower than 30, with minor potential ecological risk. Specifically, all samples of Cu, Mn and Zn were at slight potential ecological risk level; 5% of As samples, 80% of Cd, 85% of Cr, 80% of Ni and 100% of Pb (Table S5) were at medium and above potential ecological risk. In particular, the potential ecological risks of 35% of Cd samples, 10% of Cr samples, 5% of Ni samples and 80% of Pb samples (Table S5) were relatively high, 10% Cd samples reached high potential ecological risk level, and 10% Cr samples had extremely high potential ecological risk. In summary, Geostatistical analysis shows that the hotspot distribution of all PTEs in the study area is almost related to the distribution of oil wells. In addition, the hotspot distribution of PTEs may also be related to factors such as agricultural and industrial activities3. The average value of PER in the study area was 265.08, and the proportions of the three risk levels of medium, slightly high and high were 5%, 75% and 20%, respectively (Table S5). It proved that the study area was at a higher potential ecological risk. Among them, the PER values of samples A, B, D, E, F, G, H, I and J (Table 2) were all greater than 280, reaching fairly high ecological risk.Table 2 Single ecological risk index and potential ecological risk of soil PTEs in study area.Full size tableHuman health risk assessmentThe non-carcinogenic risk assessment of As, Cd, Cr, Cu, Mn, Ni, Pb, Zn and Ba in the soils of the study area was carried out, and the assessment results were shown in Table 3. The THI values of children and adults under the three exposure routes of soil PTEs in the study area were 7.31 and 1.03, respectively, and the THI values were all  > 1, which indicated that soil PTEs around the oil production plants posed significant non-carcinogenic health risks to children and adults. The non-carcinogenic hazardous quotient (HQ) of children and adults in Table 3 revealed that the HQ of all PTEs for adults under each exposure route was less than 1, while the HQ of Cr and Pb for children under the oral intake route was greater than 1, which were 4.91 and 1.17, respectively. For HQ with different exposure routes of the same PTE, each soil PTE presented the risk of oral ingestion  > oral and nasal inhalation risk  > skin contact risk. The result was in agreement with the reports14, 37. Therefore, oral intake was the main exposure route of non-carcinogenic risk, and oral intake of Cr and Pb caused serious non-carcinogenic risk to children. Statistical analysis of HI for soil PTEs in the study area showed that the HI values of PTEs for children were significantly higher than those of adults, and the HI values of PTEs in children and adults were all Cr  > Pb  >   > As  > Ni  > Mn  > Ba  > Cu  > Zn  > Cd. Among them, the HI values of all PTEs for adults were less than 1, indicating that the non-carcinogenic risks caused by a single PTE did not have a significant impact on adults; while the HI values of Cr and Pb for children were 4.93 and 1.17 greater than 1, indicating that they have caused serious non-carcinogenic risk to local children. In addition, the HI values of As and Ni for children and the HI values of As, Cr and Pb for adults were all greater than 0.1, which requires attention. In summary, children suffered from significant non-carcinogenic risk, and adults suffered from minor non-carcinogenic risk in the study area; soil Cr and Pb were the most important non-carcinogenic risk factors for children and adults in the study area.Table 3 Non-cancer and cancer risk assessment of adults and children under different exposure routes.Full size tableIn this study, soil As, Cd, Cr, Ni and Pb from the study area were assessed for carcinogenic risk, and the results were shown in Table 3. The TCRI of children and adults under the three exposure routes of these five PTEs were 9.44E−04 and 5.75E−04, respectively, indicating that soil PTEs around the oil production plants have caused serious carcinogenic risk to local children and adults. The CR values of children and adults showed that the CR values of Cr (6.33E−04) and Ni (2.64E−04) for children, and Cr (3.87E−04) and Ni (1.49E−04) for adults were all greater than 10–4. In addition, As, Cr and Cd all presented oral intake risk  > oronasal inhalation risk  > skin contact risk. In conclusion, Cr and Ni caused serious carcinogenic risk for children and adults in the study area, and oral intake was also the primary way of carcinogenic risk. The CRI statistics of adults and children exhibited that the CRI values of all PTEs were lower than those of children. The CRI values of the PTEs in adults and children under the three exposure routes were Cr  > Ni  >   > As  > Pb  >   > Cd. Among them, the CRI values of Cr and Ni in children and adults by oral intake were both greater than 10–4, showing a strong carcinogenic risk. It is noteworthy that the assessment based on total concentrations of PTEs in soil might overestimate potential health risks38. The above analysis revealed that both children and adults in the study area suffered from serious carcinogenic risks, and Cr and Ni were the chiefly carcinogenic risk factors. More

Characteristics of LVD dataset and assembled vOTUsThe land use virome dataset LVD was derived from 2.6 billion paired clean reads of sequences across 50 viromes of 25 samples with five types of land uses (Supplementary Data 2). A total of 6,442,065 contigs ( >1500 bp) were yielded, of which 764,466 (11.8%) contigs were identified as putative viral genomes through VIBRANT. Subsequently, putative false positive viral genomes were removed (see Methods section), and 27,951 and 48,936 bona fide viral genomes were retained from the 25 intracellular VLPs (iVLPs) and 25 extracellular VLPs (eVLPs) viromes, respectively. These genomes were clustered into 25,941 and 45,152 vOTUs for iVLPs and eVLPs viromes, respectively, in which the iVLPs and eVLPs viromes shared 11,467 (19.2%) vOTUs. Subsequently, they were merged and dereplicated, resulting in 59,626 vOTUs (Supplementary Data 3) for the following analysis. A total of 8112 (13.6%) vOTUs genomes were classified as complete, in which the median length of all and circular vOTUs were 25,183 bp and 45,511 bp, respectively (Supplementary Fig. 4).To explore the taxonomic affiliation of vOTUs in family and genus-level, a gene-sharing network consist of 59,626 vOTUs genomes from this study and 3502 reference phage genomes (from NCBI Viral RefSeq version 201) revealed 6009 VCs comprising of 37,224 vOTUs, of which 34,417 vOTUs were from LVD, besides 2794 singletons (2653 from LVD dataset), 16,056 outliers (15,833 from LVD) and 8492 overlaps (8061 from LVD) were detected (Supplementary Data 4). Of these, only 157 VCs contained genomes from both the RefSeq and LVD dataset (1864 viral genomes) (Supplementary Data 4). Most of VCs (1837, 30.4%) included only two members.At the family level, most of vOTUs were classified into Siphoviridae (712 by vConTACT2 and 29,671 (50.9%) by Demovir, tailed dsDNA), Podoviridae (610 by vConTACT2 and 9923 (17.6 %) by Demovir, tailed dsDNA), Myoviridae (485 by vConTACT2 and 5445 (9.9%) by Demovir, tailed dsDNA), Tectiviridae (50 by vConTACT2 and 10 (0.10%) by Demovir, non-tailed dsDNA) (Fig. 1). Besides, the Eukaryotic viruses Herpesviridae (159 by Demovir, 0.26%, dsDNA), Phycodnaviridae (120 (0.20%) by Demovir, dsDNA); the Virophage Family Lavidaviridae (15 (0.03%) by Demovir) were detected as well, but a majority of vOTUs were unclassified in genus-level.Fig. 1: The taxonomic assignment of LVD.Pie charts showing the affiliation of 56,870 vOTUs at family level assigned by script Demovir (a). and the affiliation of 1864 vOTUs at family level assigned by package vConTACT2 (b). Source data are provided in the Source Data file.Full size imageViral community structures differ across land use typesBray–Curtis dissimilarity of viral communities (median 0.9951) showed strong heterogeneity of viral communities among different sites (Fig. 2a). While, the Bray–Curtis dissimilarity (median: 0.5109) between paired viral communities of iVLPs and eVLPs from each site have a significant lower heterogeneity than inter-sites (Wilcox.test, p  0.05; Fig. 2b). Therefore, the paired iVLPs and eVLPs viromes from each site were merged for subsequently viral community analysis.Fig. 2: The macrodiversity of soil viral communities.a Boxplot showing Bray–Curtis dissimilarity of viral communities of intra-sites (between the corresponding community of iVLPs and eVLPs, n = 25) and inter-sites (between different sample sites, n = 300). The minima, maxima, center, bounds of box and whiskers in boxplots from bottom to top represented percentile 0, 10, 25, 50, 75, 90, and 100, respectively, the difference between different zones was tested using the two-sided Wilcox.test, ****p  More

DefinitionWe present here a new statistical approach to measure and characterize light pollution. The objective is to define an indicator which is not limited to clear sky measurements and does not require a precise calibration of a photometer. The key attributes of the indicator are the following:

It requires the automated acquisition of a large number of zenithal NSB measures when the Sun is below (-18^{circ }) and the Moon below (-5^{circ });

The acquisitions must at least cover a period of 6 months in order to record a wide range of possible weather conditions from perfectly clear to totally overcast skies. The objective is to obtain a significant sample of every type of cloud conditions (e.g. cloud density and ceiling altitude) as well as a good characterization of the average clear sky ;

It is based on the analysis of the zenithal NSB measure dispersion which is directly linked to the level of light pollution a site experiences.

As presented above in Fig. 2, the NSB density histograms, which are assembled from a large number of NSB measures, display a higher density zone which denotes a characteristic clear sky level that we name nominal NSB in the scope of the indicator calculation. On both sides of the clear sky level (above and below), NSB measures are distributed in a way that reflect the zenithal night sky luminance in cloudy conditions: NSB measures above the clear sky level mean that the light pollution is amplified by clouds while those below the clear sky level indicate a darker environment where clouds mask light pollution from distant sources as well as natural light sources. The calculation of the indicator is based on the evaluation of the NSB measure dispersion on both sides of the nominal NSB (i.e. characteristic clear sky level). Since there can have strong variations of artificial light emitted into the environment at the beginning and end of the night (decrease then increase of human activity, extinction of public lighting, etc.), the range of NSB measures retained for calculating the indicator is restricted to a portion in the middle of the night, typically 2 h.Figure 8 shows a typical NSB density histogram for a site which is quite severely impacted by light pollution. It covers a 2 h time range between 23:00 UTC and 01:00 UTC and one can easily see that the zone above the nominal NSB is much higher and denser than the one below, i.e. cloud conditions create more often a brighter environment than a darker one and with a greater amplitude.Figure 8NSB density histogram where the nominal NSB that represents the most common clear sky conditions is identified. It delimits two areas, the NSB bright dispersion above the nominal NSB and the NSB dark dispersion below.Full size imageBased on the determination of the nominal NSB, a quantitative indicator, called NDR for NSB Dispersion Ratio, is calculated in the following way:$$begin{aligned} NDR = (N_b cdot MAD_b) / (N_d cdot MAD_d) end{aligned}$$where (N_b) is the number of measures above the nominal NSB (brighter sky), (N_d) is the number of measures below the nominal NSB (darker sky), (MAD_b) is the median absolute deviation of the measures in the bright dispersion zone (above the nominal NSB) and (MAD_d) is the median absolute deviation of the measures in the dark dispersion zone (below the nominal NSB). The median absolute deviation is a statistical tool used to measure the variability of a data set, which is exactly what we try to achieve with the two NSB extensions above and below the nominal NSB. It is formally defined as (MAD = median(|X_i – tilde{{mathbf {X}}}|)) where (X_i) in our case represents an NSB value and (tilde{{mathbf {X}}}) is (median(X_i)). The median absolute deviation is a better choice than the usual standard deviation to measure the spread of NSB measures since the data does not follow a normal distribution.In order to make the determination of the NSB Dispersion Ratio stronger from a statistical standpoint, we use a bootstrapping with replacement resampling method on the set of night portions used to compute the indicator. Assuming we have N night portions at our disposal, we randomly select a sample of N items in this set of night portions knowing that a given item can appear multiple times in the sample (hence the bootstrapping with replacement). The NDR value is then computed for the considered sample. This process is repeated 1000 times and the average NDR value if eventually computed. This average value represents the actual NDR indicator of the considered site.The NDR indicator takes into account both the number of NSB values on each side of the nominal NSB and the dispersion of these values. This is what makes it relevant as an indicator of light pollution which encompasses all kinds of meteorological conditions experienced at a particular site. On that aspect, it is therefore not an astronomical light pollution indicator since it is not focused on clear sky conditions. On the opposite, it requires to have a significant number of NSB measures in all sorts of cloudy conditions so that a valid NDR indicator can be derived.A key aspect of the NDR calculation methodology is to determine the level of the nominal NSB, i.e. the typical clear sky level, since it will be used to differentiate the NSB measures that go in each of the two sets to calculate the bright and dark dispersions. As we have seen earlier in the article, such a determination can be biased by natural light sources that raise or lower clear sky NSB at different times of the night. This can result into a “blurry” high density zone which makes the determination of the nominal NSB difficult or even impossible depending on the observation period. Based on the quantitative estimate of the different natural light sources presented above, the most important bias to address is the contribution of the Galactic plane. This contribution must be eliminated for all the NSB measures which are used to calculate the NDR indicator. In order to do that, Noxi, the Ninox processing software developed by DarkSkyLab, calculates for each NSB measure the corresponding Galactic plane and star fields contribution using the galactic coordinates of the zenith and integrating the combined flux of all stars in the field of view using the UCAC4 astrometry and photometry star catalogue. It is not possible to cancel the contribution of the airglow due to its unpredictable nature, but since it only appears in rare occasions, it is not seen as a problem and is ignored. Regarding the contribution of the zodiacal light, it is considered as minimal at the zenith and it is also ignored.As an example, Fig. 9 shows on the left an NSB density histogram where the Galactic plane bias has not been corrected in the data, and on the right the same data but with the Galactic plane bias corrected. It is easy to see that in the latter the nominal NSB is much easier to determine, providing a more accurate reference level to calculate the NDR indicator. Once the Galactic plane bias has been corrected, the nominal NSB is determined as the highest density zone of the NSB histogram. It must be noted that, as of today, all the NSB measures are corrected from the Galactic plane bias without regards to the presence of clouds or high levels of light pollution. This results into an additional source of inaccuracy that will be addressed in the future through the implementation of two heuristics within the Noxi software:

1.

A first heuristic will determine if a night portion is considered as having a clear sky or not so that the Galactic bias correction is applied only if the sky is clear. In order to do that, we have developed an indicator called the NSS (for Night Sky Stability). To determine the NSS for a full night of measures or just a night portion, we fit the NSB curve with a degree 10 polynomial and we then compute the difference between each NSB measure and it polynomial counterpart. As a result, we obtain a set of residuals. The variance of all the residuals defines the NSS for the considered NSB dataset. Below a given value, the sky is considered as clear knowing that the NSS indicator has been calibrated on several NSB data sets for which the corresponding weather conditions are known;

2.

A second heuristic will allow us to weight the Galactic bias correction to be applied to NSB measures according to their value. For non-polluted skies with high values of NSB, the full Galactic bias correction will be applied while below a certain NSB threshold (for instance 21 mag(_{mathrm{SQM}})/arcsec(^{2}) which corresponds roughly to the brightest parts of the Milky Way) no correction will be applied.

Figure 9NSB density histograms of the same data set with no correction of the Galactic plane bias applied on the left and a full correction applied on the right.Full size imageThe NDR indicator is unitless since it is the ratio of two quantities with the same unit (mag(_{mathrm{SQM}})/arcsec(^{2})). For the data set presented in Fig. 9, the NDR value which is obtained is 25 (which is justified by the fact that the bright extension in the density histogram is much higher and denser than the dark extension). This denotes a quite high level of light pollution despite the fact that the nominal NSB is at a level of 21.6 mag(_{mathrm{SQM}})/arcsec(^{2}). This highlights the fact that there is not always a strict correlation between the typical clear sky NSB obtained for a given site and its NDR indicator, i.e. the presence of clouds decreases the NSB more than we could have expected just by knowing the clear sky NSB. On that respect, the NDR ratio brings more information that the clear sky NSB alone.In addition to provide an indicator which is representative of light pollution in all possible atmospheric conditions, the NDR provides a tool to compare locations in a more meaningful way than just using a set of standalone NSB evaluations. First it is not dependent of an inter-calibration between different systems and second its statistical nature makes it more robust when it comes to perform comparisons.NDR into practiceThe NDR indicator has been calculated for several different sites by DarkSkyLab during various projects in France that involved NSB measuring sessions in the field. To demonstrate some of the results that have been obtained, Fig. 10 provides the density histograms of 4 different sites which have quite different light pollution profiles.Figure 10NSB density histograms of 4 different sites used to compute the NDR indicator. The nominal NSB (which corresponds to the most common clear sky conditions) is noted with a white tick mark next to the vertical axis. Relative levels of the bright and dark dispersion terms (((N_b cdot MAD_b)) and ((N_d cdot MAD_d))) are noted respectively with an orange tick mark and a green tick mark. The computed values of the NDR indicator and nominal NSB are provided in the top-left corner of each figure.Full size imageTo build these diagrams, only the measures acquired during a few hours in the middle of the nights have been used to ensure the maximum stability of the NSB curves and avoid lighting extinctions that create large gaps in NSB profiles. The Galactic plane bias is corrected on all plots and the same NSB scale is used in order to perform comparisons between the 4 sites. One can notice that the number of measures and nights for the 4 sites are quite different. However, they are all sufficient to derive a meaningful value of the NDR indicator using the bootstrapping with replacement resampling method described above, but it is clear that the more NSB measures used, the more accurate the NDR indicator.Table 2 summarizes the NDR indicators as well as the nominal NSB for the 4 sites which are sorted in the order of decreasing NDR indicator values.Table 2 Summary of the nominal NSB and NDR indicators of the 4 different sites.Full size tableOne can see that the NDR indicator values are not strictly correlated to the nominal NSB values, e.g. despite the fact that the nominal NSB of site (a) is slightly better than the one of site (b), the NDR indicator value is much larger for site (a) than for site (b). This can be explained if we consider the specificities of each site:

Cervières (a) is a small village in the Haut-Forez area, France, which is surrounded by large cities (Lyon, Saint-Etienne and Clermont-Ferrand at a distance between 50 to 80 km) and a closer mid-size city (Roanne at 30 km). At the top of that, the town of Noirétable and a large highway rest area are just 2 km away without any nocturnal extinction applied (as opposed to the village of Cervières itself for which public lighting is turned off from 23:00 to 05:00 local time). These conditions are favourable to the presence of a constant light pollution background which has a negative impact on the zenithal NSB measures in most cloudy conditions (distant large cities for high elevation clouds and Noirétable and the highway rest area for lower elevation clouds). Only rare cloud conditions actually protect the site from the effect of mid-distance light sources. In clear sky conditions, however, the fact that there is no close light sources provides reasonably good NSB levels;

The Copernic Association Observatory (b) is located 6 km from the large town of Gap in the mountain area of Hautes-Alpes in the south of France. There is no significant short distant light sources but in many cloud conditions the contribution of Gap has a very negative impact on the zenithal luminance. However, due to the fact that the observatory is at a higher altitude on the hills surrounding the city of Gap, there are cloud conditions that make the site darker. In clear sky conditions, the proximity of Gap does not permit a quality better than that of a rural sky;

The Astrièves Observatory (c) is located near the center of the small town of Gresse-en-Vercors in the Parc Naturel Régional du Vercors. There is a full nocturnal extinction of the village for a large part of the night resulting in a good sky quality in clear sky conditions. The large city of Grenoble is at a distance of 30 km in a valley at the north-east, and the two locations are separated by a few mountains which efficiently help masking the light pollution as soon as the cloud ceiling is below a certain altitude, resulting into a dark environment. On the opposite, high elevation clouds reflect the light from Grenoble and increase the zenithal luminance;

Eourres (d) is a small and isolated village located 20 km west of Sisteron in the department of Hautes-Alpes, France, which is surrounded by mountains. There is no significant light sources closer than those of Sisteron and this results into a very good night sky quality with, most of the times, a very dark environment in cloudy conditions.

Figure 11 provides a graphical representation of the NDR indicator values for the 4 sites. On the NDR scale, the value 1 indicates that the bright and dark dispersion terms (respectively ((N_b cdot MAD_b)) and ((N_d cdot MAD_d))) are equal, which means there is a balance between dark and bright conditions at the zenith on the considered site with reference to the most common clear sky level.Figure 11Summary of the NDR indicators obtained for the 4 sites. The diagram uses 1 as the pivotal value to delineate sites according to the two bright and dark dispersion terms ((N_b cdot MAD_b)) and ((N_d cdot MAD_d)).Full size imageThe NDR can theoretically vary between 0 (totally dark site) and several hundreds (extremely bright site) but in practice the best sites can reach NDR indicator values down to 0.3 in the best preserved locations and up to 200 for very large and polluted cities.Robustness of the NDR indicatorIt is important to evaluate how the NDR indicator is dependant on the number of measures used to compute it and to figure out what would be the minimum number of night sessions required to obtain a meaningful NDR indicator value at a given site. To achieve that, we have used the data from two of the four sites presented above (the two which have the largest number or recorded nights: Cervières with 424 nights and the Astrièves Observatory with 373 nights). The 1000-step bootstrapping procedure has been repeatedly executed on each data set with a regularly decreasing sample of nights: starting from the full number of nights, a decrement of 10 nights is applied at each step until only 20 nights are remaining. At every bootstrap step, each sample is composed of n nights randomly chosen among the N available ones knowing that any night can be selected several times.Figure 12 shows the NDR indicator values that have been obtained for each of the two sites as a function of the night sample considered. The 95% confidence interval is plotted against each NDR indicator value (it is preferred to the standard deviation since the NSB distribution in the data sets is not normal). In the right plot of Fig. 12, the last confidence interval for the 24 night sample is too wide to fit in the y-axis NDR range (the top value is 195).Figure 12Results of the NDR resampling on the two data sets of Cervières and Astrièves Observatory. The horizontal axis is the number of nights considered into the night sample and the vertical axis provides the NDR indicator obtained for each sampling set through a 1000-iteration bootstrapping with replacement calculation.Full size imageDiscussion on the required number of nightsWe can see in Fig. 12 that the NDR indicator and the confidence interval remain stable down to 200 nights. Below this threshold, the NDR starts to become unstable with growing confidence intervals. Based on this data, we can estimate that the minimum number of nights required to compute a robust NDR indicator is 200 (therefore between 7 and 8 months since there are periods around the full moons where there is no night portions recorded).However, depending on the measuring session objectives, the NDR indicator can be considered as accurate enough even when using a smaller number of nights. If the goal is simply to get a first estimate of the light pollution level at a given site, we can consider that 90 nights (a little more than 3 months of measures) are enough. On the opposite, if we want to perform a comparison between several sites for evaluating the impact of light pollution on a particular species, we might want to perform at least 200 nights of measurement to get a better accuracy for the NDR indicator. The experience from DarkSkyLab through many NSB measuring sessions is that 3 to 4 months of measures are required to get a meaningful density histogram, hence an accurate enough NDR indicator, so that a site can be sufficiently characterized from a light pollution perspective. Such a measuring period usually guarantees that the clear sky nominal NSB is well defined and that various cloud conditions have been observed. This estimate is sustained by the results obtained in Fig. 12.Value of the NDR indicator for ecological researchThe study of the impact of light pollution on biodiversity is currently in full expansion, amplifying a political and citizen demand for the reclamation of the night2,32,33.We identify three main contributions of the NDR indicator for ecological research. First, it overcomes the limits of an old problem of communication in terms of measurement units between disciplines and potentially limits the use of units without real meaning from a biodiversity point of view34,35. Secondly, the use of the NDR indicator limits the common biases linked to a characterization of the effects of anthropogenic light which is too limited in time and space35. Indeed, the life history traits of species are not only shaped by the intensity of light emitted into the nocturnal environment but also by its variation over time34,35,36. Currently, the characterization of light pollution is too often limited in time and space, which can lead to misinterpretation37. Thirdly, the NDR indicator provides ecological researchers with a unit of measurement that integrates a sufficiently long time step to study the impact of light pollution on the evolutionary processes at work in the life of species and particularly on population dynamics and animal behavior36,38,39.Limitations and future improvements of the NDR indicatorThe main limitation of the NDR indicator resides in the possible difficulty to identify a well defined value for the nominal NSB, i.e. the NSB value that represents the most common clear sky conditions of a given site. For the most part, this is due to the contribution of the Galactic plane to the zenithal sky brightness and, to a lower extent, to the contribution of other natural light sources (dense star fields, airglow and zodiacal light). The residual spread of NSB measures is due to changing atmospheric conditions at various time scales, but, for this particular contribution, we can expect a statistical compensation to eliminate a systematic associated bias.At the moment, the contribution of the Galactic plane and star fields is canceled into the NSB measures by calculating in the Noxi software the integrated flux of all the stars that belong to the field of view (using the UCAC4 star catalogue). However, this approach has proven some limitations, especially in the southern hemisphere where the Galactic center goes through the zenith and is particularly bright. A probable explanation for that lack of predictability is the fact that the Galactic plane contains diffuse sources such as nebulae which are not accounted for into the star catalogues and which actually cannot be ignored. To address this issue, DarkSkyLab has the project to create a brightness map of the Galactic plane with a square degree resolution or better so that the contribution of all sources can be correctly accounted for.In addition to better correcting the Galactic plane bias, an improvement must be made with regards to the NSB measures that need to be corrected. At the moment, all NSB measures are corrected from the Galactic plane bias without regards to the presence of clouds or high levels of light pollution. So a first heuristic must be implemented to only apply the bias correction to clear sky NSB measures. An other heuristic must also be developed to reduce the correction applied as a function of the NSB level.A third limitation of the NDR indicator is related to a possible lack of cloudy conditions at some sites (e.g. in the Atacama desert in Chile with more than 320 clear nights per year), the reason simply being that the NDR indicator requires the presence of clouds to differentiate the bright and dark extensions into the NSB density histograms. This means that the NDR indicator can hardly be used for such astronomy-oriented sites which experience rare cloudy conditions. More

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