Random forest regression exploring contributing factors to artificial night-time lights observed in VIIRS satellite imagery

ABSTRACT

Artificial night-time lights (ANTL) pose environmental, economic, and social problems. To effectively manage this issue, it is important to understand the sources that contribute to it. Previous research has presented conflicting views on the relative importance of streetlamps and spill-over light from buildings as contributors to ANTL. In this study, we used satellite images, ground surveys of streetlamps and buildings in the city of Hobart, Tasmania, Australia, to determine the major contributing sources of ANTL. Imagery from the Visible Infrared Imaging Radiometer Suite (VIIRS) satellite was used to map ANTL. We developed a predictive random forest regression (RFR) model and found that streetlamps were the major contributor, followed by the building footprint area. We also found that an increase in both the number of streetlamps and buildings leads to an increase in ANTL observable in VIIRS satellite data. The RFR model performed well with an R² of 0.94 and a median normalised root mean square error of 6.25%.

KEYWORDS:

• Artificial night-time lights
• streetlamps
• building footprint area
• Visible Infrared Imaging Radiometer Suite (VIIRS)
• random forest regression (RFR)

1. Introduction

Artificial night-time lights (ANTL) has long been considered a benefit for road safety, personal security against crime, and evening social and commercial activities. However, recent research has also identified ANTL as a potential risk factor for human health (Blask 2009; Cho et al. 2015; Davis and Mirick 2006; Kantermann and Roenneberg 2009; Stevens et al. 2014), the environment (Hölker et al. 2021; Hu, Hu, and Huang 2018; Meng et al. 2022; Silva et al. 2017; Škvareninová 2017; Torres et al. 2020; Van Doren et al. 2017; Voigt et al. 2017), and the economy (Zissis, Bertoldi, and Serrenho 2021).

Some countries have recognised the social, economic, and environmental impacts of ANTL and have taken steps to address it as a sustainability issue. For example, in the United States, the Congress passed the Energy Independence and Security Act in 2007 to introduce higher efficiency standards for light bulbs. The U.S. Department of Energy also launched the High-Performance Outdoor Lighting Accelerator program, which encourages the adoption of high-efficiency outdoor lighting at the municipal level. In the United Kingdom, the Environmental Protection Act 1990 (Section 79, amendment 06/04/2006) introduced artificial night lighting as a form of pollution that needs to be monitored and controlled (UK 1990). European and German environmental laws also address light pollution (Schroer et al. 2020). More recently, Australia has introduced national light pollution guidelines for wildlife. In response to national policies, some municipalities have identified ANTL as a form of pollution that needs to be addressed.

Several studies have attempted to identify and quantify the sources and contributions of both outdoor and indoor lighting (that leaks out of buildings) to overall ANTL (Bara et al. 2019; Hiscocks and Gudmundsson 2010; Kuechly et al. 2012; Kyba et al. 2021; Luginbuhl et al. 2009; Ściężor 2021). These studies have used a variety of instruments and methodologies and have been conducted at different spatial scales. The evidence on the contribution of streetlamps to total ANTL has shown a wide range of variation, with estimates ranging from a minimum of 12% to a maximum of 77% (as shown in Table 1). It is important to accurately identify and quantify the sources and contributions of different types of lighting to ANTL in order to understand the full extent of its impacts and to develop effective strategies for reducing ANTL and its associated negative consequences.

Table 1. Contribution of streetlamps to night-time lighting reported in the literature.

Estimated percentage	Measurement unit	Measurement methodology	Article	Study area
13%	Total Radiance	VIIRS satellite images	Kyba et al. (2021)	City of Tucson, USA
50%	Radiance	VIIRS satellite images	Ściężor (2021)	Cracow, Poland
12%	Million Lumens	Lighting Inventory	Luginbuhl et al. (2009)	Flagstaff, Arizona, USA
32%	Brightness factor	Aerial Photographs	Kuechly et al. (2012)	Berlin, Germany
45–60%	Lumens ration	Still Photographs from an elevation of 300 m above sea level	Hiscocks and Gudmundsson (2010)	Reykjavik, Iceland
55.5–77.3%	Luminance per metre square	Sky Quality Meter	Bara et al. (2019)	Galicia, Spain

Out of many instruments and methodologies, remote sensing technology offers numerous benefits for the study of ANTL. Publicly available remote sensing images provide cost-effective, non-invasive, and time-saving methods for collecting large-scale, daily data on ANTL, enabling comprehensive analysis of global and local patterns and impacts.

Remote sensing literature has long examined that ANTL satellite images represent the light illuminating in urban environments (Bhattarai et al. 2023; Chowdhury et al. 2019; Elvidge et al. 2017; Ju et al. 2017; Kamarajugedda, Acharya, and Lo 2017; Levin et al. 2020; Li and Zhou 2017; Xin et al. 2017; Zhang et al. 2017). However, the understanding of what urban factors contribute to the ANTL other than streetlamps is still limited.

Recently, few studies have used building area and height as proxies to estimate the contribution of indoor lighting from buildings to ANTL (Shi et al. 2019; Wang et al. 2019). Shi et al. (2019) found a strong positive relationship between the total radiance captured by the VIIRS satellite and both building area (R²= 0.94) and building volume (R²= 0.96). In contrast, Wang et al. (2019) found a weak positive relationship (R²= 0.48) between the total digital number value captured by the DMSP/OLS satellite and building height.

The above-mentioned studies used traditional regression methods to estimate the contribution of streetlamps and building attributes to ANTL. The use of machine learning techniques in remote sensing to estimate the contribution of different ANTL sources is also limited and is only applied to classify different types of streetlamps. For example, Cheng et al. (2020) utilised high-spatial resolution (1.5 m) commercial satellite imagery with three spectral bands and employed machine learning techniques to classify the streetlamp types from the images. In addition, Watson et al. (2023) applied the same satellite imagery and approach to classify and quantify the contribution of streetlamps in ANTL. However, both studies failed to leverage the true potential of machine learning techniques in identifying the contributing factors to ANTL. In this study, random forest regression (RFR) and its importance feature score is used to demonstrate the contributing factors of ANTL using publicly available low-resolution satellite data (500 m) along with ground surveys on streetlamps and building footprints. We use RFR features importance score as a statistical metric to estimate the influence of streetlamp and building attributes on predicting ANTL. This approach may provide more accurate and robust estimates of the contribution of these different sources to ANTL.

2. Methods

2.1. Study area

Hobart City Council (HCC), the capital city of Tasmania, Australia, was selected as the study area for this research. HCC has recognised light pollution as a key area that requires responsive and proactive actions and has developed a five-year action plan to reduce it (City of Hobart 2020). With a total area of 77.9 square kilometres, 55,077 residents, 13,525 families, and 24,748 private dwellings (Australian Bureau of Statistics 2021), HCC has invested around 16 million in improving the city’s outdoor lights between 2011 and 2021 (HCC 2011–2021).

2.2. Data

2.2.1. Satellite data

The emission of electromagnetic radiation in the range of 500–900 nm was captured in a 15 arc-sec lat/long grid by the Suomi NPP Visible Infrared Imaging Radiometer Suite (VIIRS) Day/Night Band (DNB) satellite sensor. This satellite orbits the Earth 14 times per day in a near-polar orbit with a 16-day repeat window, and the overpass time over Hobart is between 1:00 AM and 3:00 AM Australian Eastern Daylight Time (AEDT). Out of the many available VIIRS data sets, VNP46A2 was used as it provides the flexibility to apply quality masks according to the research needs, which is a daily moonlight and atmosphere-corrected night-time lights data set. VNP46A2 contains seven Science Data Sets (SDS), including the DNB BRDF-Corrected NTL, Gap-Filled DNB BRDF-Corrected NTL, DNB Lunar Irradiance, Latest High-Quality Retrieval, Mandatory Quality Flag, Cloud Mask Quality Flag, and Snow Flag.

Daily images from 1 January 2018 to 30 December 2018 were downloaded from the Level-1 and Atmosphere Archive & Distribution System (LAADS) Distributed Active Archive Centre (DAAC) (https://ladsweb.modaps.eosdis.nasa.gov) in a H5 file extension, using the Jupyter Notebook and GDAL python package. The H5 images were then transformed to the GeoTIFF format with the geographical coordinate system (EPSG:4326) using the GDAL package. The GEOTIFF images were then transferred to an array using the xarray python package.

First, the Mandatory Quality Flag was used to select high-quality (persistent night-time lights) pixels and discard high-quality ephemeral and poor-quality pixels. Second, the cloud mask quality flag was applied to select night, land and coastal, high-quality cloud mask pixels with clear sky, no shadow detected, no cirrus detected, and no snow surface. These quality and cloud mask criteria were applied to the ‘DNB BRDF-Corrected NTL’ band. After these steps, the pixels were clipped based on the study area extent.

2.2.2. Streetlamp

In 2018, the Hobart City Council (HCC) created a geocoded streetlamps inventory that included information on the coordinates, type of lamp, and rated power for each streetlamp. Based on the type of lamp and its rated power, in consultation with a lighting industry expert and the company brochure (Aldridge 2018; Sylvania 2023), which installed these lamps, the luminous flux for each lamp was determined. The inventory included nine different types of streetlamps (listed in Table 2), with the majority being LED lamps, followed by HPS lamps. Except for these two categories, the number of lamps in the other categories was relatively small, so we reclassified the nine categories into three categories as shown in Table 2. All the analyses in this study were based on these reclassified categories.

Table 2. Description of streetlamp categories.

Streetlamp type	Number of lamps	Reclassified categories
Light-emitting diode (LED)	2614	LED
High-pressure sodium lamp (HPS)	1770	HPS
Mercury vapour (MV)	679	Others
Compact fluorescent light lamp (CFL)	262
Others	256
Fluorescent lamp (FL)	33
Metal-halide lamp (MH)	9
Incandescent light lamp (INC)	9
Sodium-vapour lamp (SV)	6
Grand total	5638

The streetlamp point data were rasterised to VIIRS pixels using the ARCGIS Pro ‘summarize within’ function. This function summarised (counted) all the point data within each pixel (pixel polygon) and determined which group field value (in this case, streetlamp type) was the minority (least dominant) and the majority (most dominant). After the function was applied, each pixel was assigned to one of the following categories: LED, HPS, or others. Figure 1 illustrates this process and the resulting data.

Figure 1. Streetlamp point data rasterise to VIIRS pixels, the map (a) shows spatial distribution of streetlamps and their types. Lower map (b): using the ARCGIS Pro ‘summarise with’ function the points data are summarised (count by majority) to each VIIRS pixel. The category of streetlamp is reduced from nine different categories to just three. The number inside the parenthesis represents count of lights within each category.

In addition to categorising the streetlamps, the power rating of each streetlamp in watts and the luminous efficacy, which is the ratio of luminous flux (the light output of the streetlamp) to the power rating of the streetlamp, were considered. The summation of the power, luminous efficacy, and the total number of streetlamps per pixel was then calculated.

For LED lamps, the VIIRS sensor lacks sensitivity in the blue band. Consequently, the blue peak of the LED is not considered in satellite measurements. Therefore, it is necessary to correct the rated power consumption of LEDs to accommodate the spectral sensitivity of the VIIRS sensor. We calculated the fraction of the LED output that the VIIRS sensor is sensitive to base on the spectral output and response of the LED lamp and VIIRS sensor respectively (Figure 2). The fraction of the area under the curve that the VIIRS sensor can ‘see’ is 0.84. This value was then multiplied by the rated power of each LED lamp to correct for VIIRS spectral sensitivity.

Figure 2. Relative spectral power distribution of VIIRS DNB and LED neutral white streetlamps, 3700–5000 K CCT represent the LED streetlamps installed in Hobart City Council.

2.2.3. Spectral signature

In Australia, lighting for roads and public spaces is required to adhere to the AS/NZ 1158 series standards, which include five lighting categories: ‘P’ for pedestrian ways, ‘V’ for local roads with low to medium traffic volumes, ‘W’ for high traffic volumes such as highways, ‘C’ for high-speed roads with barriers to protect against collisions, and ‘S’ for special requirements. In Hobart, the two main categories are ‘V’ and ‘P’. For ‘V’, both HPS and LED lamps are used, while for ‘P’, MV and LED lamps are used. The correlated colour temperature (CCT) for both categories ranges from 3000 to 4000 K.

The spectral power distribution (SPD) of HPS lamps has several peaks and a broadened peak around 589 nm, which corresponds to the yellow/orange colour emitted by the lamp. In contrast, white LED lights are typically created by combining a blue LED chip with one or more phosphor coatings. These coatings convert some of the blue light into longer wavelengths, resulting in a broader spectrum of light (Nakamura, Mukai, and Senoh 1994).

The Tas Network institution responsible for purchasing, installing, and monitoring streetlamps has chosen to use CREE LED lights that are specifically designed to meet the AS/NZ 1158 standard. Figure 2 shows the relative SPD for the LED lamps with a colour temperature of 3700–5000 K, showing two peaks, one at around 450 nm and the other at 580 nm.

2.2.4. Building footprint

The building footprint data were downloaded from Land Information System Tasmania (https://www.thelist.tas.gov.au). This dataset includes polygons for all built structures and is regularly updated; the data used in this study was downloaded in December 2019 and includes the most recent updates for HCC.

The building footprint data included 18 different types of buildings, with the majority being residential buildings followed by commercial buildings. These categories were reclassified into five categories as listed in Table 3. The building footprint polygon data was rasterised to VIIRS pixels using the ARCGIS Pro ‘summarise within’ function. This function summarised (counted) all the polygon data within each pixel (pixel polygon) and determined which group field value (in this case, building type) was the minority (least dominant) and the majority (most dominant). After the function was applied, each pixel was assigned to one of the categories listed in Table 3. Figure 3 illustrates this process and the resulting data.

Figure 3. Building footprint data rasterised to VIIRS pixels, the map (a) shows the building footprints around Hobart. Lower map (b) using ARCGIS Pro summarise within majority function shows the pixels categorised based on the majority number of buildings per pixel.

Table 3. Description of building categories.

Building categories	Number	Reclassified categories
Residential building	16,802	Residential building
Commercial facility	618	Commercial facility
Education centre	169	Education centre
Industrial facility	107	Industrial facility
Administration facility	120	Others
Community venue	101
Shed	463
Care facility	78
Place of worship	46
Organisation	43
Structure	25
Health facility	22
Cultural centre	19
Amenity	18
Hospital	11
Emergency facility	7
Other	3
Ruin	1
Total	18,653

2.2.5. Target and predictor features

The radiance value in a 500 m spatial resolution pixel represents all the lights emitted from outdoor sources such as streetlamps and indoor spill-over lights from buildings. There is a large variability in the emitted radiance from streetlamps and buildings. Regarding streetlamps, variations in rated power, luminous efficacy of streetlamp, and lamp types are considered, as the illumination varies based on the combination of these factors. Similarly, to depict the heterogeneity of building spill-over, building area, the number of buildings, and the types of buildings are taken into account.

For 2018, the median radiance value (as the median is less sensitive to outlier values compared to the mean) was calculated for each pixel from the daily satellite images. In addition, the total streetlamp power in wattage, the total number of streetlamps, and the total streetlamp illumination flux per pixel were calculated. The total number of buildings and total building area within a pixel were also determined. For the analysis, the normalised building area per pixel was used, which was determined by dividing the total building area within a pixel by the area of the pixel itself (Table 4).

Table 4. Summary Statistics of features used as target and predictor for the random forest regression model.

	Features	Number of valid pixels	Mean	SD	Min	Max	Description
Target feature	Median radiance	495	5.825	12.02	0.200	95.40	Suomi NPP-VIIRS satellite captured, atmospheric and lunar corrected radiance.
Predictor feature	Number of buildings	300	67.04	69.16	1	257	Total number of buildings per pixel
	Normalised building area	300	0.08	0.097	1.23e-05	0.604	Sum of area of buildings within a pixel (meter square)
	Streetlamp power (wattage)	240	2617	3932	18	28,560	Sum of streetlamp’s rated power within a pixel (wattage). The rated power was corrected for the LED lamps to adjust the VIIRS sensor’s blue band blindness.
	Number of streetlamp	240	21.80	17.83	1	108	Total number of streetlamps per pixel
	LUM_WATT	240	110.50	28.75	22.5	152	Luminous efficacy is the ratio of luminous flux (the light output of the streetlamp) to the power rating of the streetlamp.
	BULD_CAT_Commercial Facility	234			0	1	1 = Pixels with the commercial facility, else 0
	BULD_CAT_Education Centre	234			0	1	1 = Pixels with the education centre, else 0
	BULD_CAT_Industrial Facility	234			0	1	1 = Pixels with the industrial facility, else 0
	BULD_CAT_Others	234			0	1	1 = Pixels with others category, else 0
	BULD_CAT_Residential Building	234			0	1	1 = Pixels with the residential building, else 0
	LAMP_CAT_HPS	234			0	1	1 = Pixels with the HPS streetlamp type, else 0
	LAMP_CAT_LED	234			0	1	1 = Pixels with the LED streetlamp type, else 0
	LAMP_CAT_Others	234			0	1	1 = Pixels with the Others type of streetlamps, else 0

2.3. Methodology

The estimation of ANTL using streetlamps and building attributes is often driven by bivariate (Hung et al. 2021; Kyba et al. 2021), multivariate regression models (Cheon and Kim 2020), and non-parametric models such as high-order polynomials (Bara et al. 2019). Since the distribution of most of the variables is skewed and does not meet the assumptions of normality and linearity, it was decided to explore machine learning techniques. The use of machine learning in remote sensing for feature extraction using VIIRS images (Liu et al. 2019; Liu, de Sherbinin, and Zhan 2019; Ma and Li 2018; Ruan et al. 2021; Sudalayandi, Srinivasan, and Kasaragod 2021; Wang et al. 2019; Wang and Shen 2021; Xu, Coco, and Gao 2020; Zhao et al. 2020) is increasing and has been found to be more accurate in estimation, although these techniques are criticised for their lack of transparency, commonly referred to as being a ‘black box’. However, Molnar (2022) argued that machine learning is no longer a black box. Among the many machine learning models, the Random Forest (Breiman 2001) is a widely acknowledged and used algorithm for non-linear multivariate regression (Zhang, Liu, and Shen 2022). Therefore, the Random Forest Regression model was selected to determine the confounding factors of ANTL.

2.3.1. Random forest regression model

The random forest regression (RFR) model in this study is tailored in terms of variable selection to capture the local conditions of Hobart. Since the VIIRS satellite overpass time is at 01:30 UTC every night, it was assumed that the buildings and streetlamps are the dominant ANTL throughout Hobart during this time.

However, in addition to the power of streetlamp and normalised building area, each pixel may also vary in types of streetlamps and buildings, as well as the number of streetlamps and buildings. To incorporate this heterogeneity, the categorical variables were transformed into logical numerical variables, where 1 represents ‘True’ and 0 represents ‘False’. Therefore, the predictor features encompass both continuous and categorical variables, showcasing the RFR model's capability to seamlessly utilise both types (Molnar 2022).

To estimate the contribution of streetlamps and buildings on ANTL, the Random Forest Regression (RFR) model in Python Jupyter Notebook using the Scikit-learn machine learning module was used (https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestRegressor.html). First, 70% of the total pixels were separated as training data and the remaining 30% as the testing data. Second, the optimal number of trees was determined by computing the number of trees from 20 to 1000 at intervals of 50, with 10 randomly selected train and test datasets for each tree. The Out of Bag (OOB) Score was compared to identify the number of trees until convergence was reached.

Third, the optimal number of features was determined iteratively by adjusting the number of features from 3 to 12 with an interval of 2, and 10 randomly selected train and test datasets for each feature. The OOB was again used to identify the optimal number of features.

To optimise the Random Forest Regression model, the number of trees and features was determined through an iterative process using the OOB score as a measure of model accuracy. The model parameters such as the maximum depth of the tree, minimum number of samples required to split an internal node, minimum number of samples required to be at a leaf node, and minimum weighted fraction of the sum of total weights required to be at a leaf node were set to their default values.

2.3.2. Contribution of individual feature

The impact of each feature on the model's performance was assessed using a metric called ‘permutation-based feature importance’. Permutation feature importance is defined as the decrease in a model score when a single feature value is randomly shuffled (Breiman 2001). This procedure disrupts the relationship between the feature and the target, and the drop in the model score indicates how much the model relies on the feature (Wei, Lu, and Song 2015). A feature with a higher importance score is more significant to the model. The importance score is normalised, with a maximum value of 1 indicating the most important feature.

It is important to note that the model's predictions are not affected even if the predictor features exhibit multicollinearity. However, the feature importance value is distributed among correlated features. To address this issue, Pearson's correlation coefficients were calculated for the features, and features with a correlation above 0.8 were clustered. From each cluster, one feature was selected.

2.3.3. Partial dependency plots

A partial dependence plot illustrates the marginal effect of one or two predictor features on the target feature while holding all other predictor constants. It provides a graphical representation of the relative importance and nonlinear relationships between predictor features and the target feature (Molnar 2022). In this study, the median ANTL extracted from the VIIRS images for 2018 was used as a target feature, and power rating of streetlamps, number of streetlamps, footprint area of buildings, number of buildings, type of streetlamps and type of buildings as predictor feature.

2.3.4. Model validation

To evaluate the accuracy of the RFR model, we used 30% of the total dataset for validation. We conducted this test using 1000 different testing datasets and calculated the variability of the model accuracy.

3. Result

This section presents the results of the Random Forest Regression (RFR) model, which includes details on the optimal number of trees and maximum number of predictor features, the computation of the RFR model using test and train samples, and the evaluation of predictor feature performance. The section also includes an assessment of the accuracy of the RFR model.

3.1. Features correlation

It is essential to check whether the features are correlated with each other. A Pearson’s correlation matrix was plotted to examine the correlation between the features. Figure 4 shows that the number of streetlamps has a positive correlation above 0.80 with the sum of corrected watts and the normalised building area. Since the sum of corrected watts and normalised building area are important features in this study relative to the number of streetlamps, the number of streetlamps feature was removed.

Figure 4. Correlation matrix of predictor features to check the collinearity.

3.2. Number of trees

The optimal number of trees for the best performance of the Random Forest Regression (RFR) model was determined by training the model with a range of values from 20 to 1000 trees, with 10 iterations for each RFR model and 100 different training and test datasets were randomly selected for each iteration. The maximum number of features was set to two different values: the square root of the total number of features. The results for the first feature option are shown in Figure 5. The RFR model converged relatively quickly in both cases. Therefore, it was decided to use 200 trees for the model's optimal performance.

Figure 5. Optimising number of trees in the RFR model. The bold blue line is the mean and transparent blue band is the result of 10 iterations for each RFR model with 20–1000 trees. The band indicates the maximum and minimum from 10 different iterations. The optimisation was conducted using the square root and auto as maximum number of features.

3.3. Maximum number of features

An iterative process was used to adjust the maximum number of features, which included 12 different features. The maximum number of features was set to 3 and the model was trained using 10 randomly selected training datasets. This same process was repeated with 1, 4, 7, and 10 features. The results of all the iterations are shown in Figure 6, which indicates that an RFR model with maximum features of 4 slightly outperformed the other models with low variability. As a result, we chose 4 as the maximum number of features.

Figure 6. Adjusting ‘max_features’ parameter for Random Forest Regression Model. Out of 12 features, the model was trained with 1–12 features with an interval of 3. The width of the violin plot represents the density, central box represents the interquartile range, and central white dot represent the median of the data.

3.4. Importance of predictor features

After adjusting the number of trees to 200 and the maximum number of features to 4, the RFR model was computed using 1000 randomly selected test and train samples. The normalised permutation-based feature importance was recorded for each iteration and is presented in Figure 7, which shows the mean value with the standard error. The figure indicates that the power of streetlamps has around a 42% influence, with a standard error of 7%. The second most important feature is the normalised building area, with a mean value of 30% and a standard error of 4.5%. Among the other features, residential building and the number of buildings have some influence of 7% and 5%, respectively.

Figure 7. Feature Importance (permutation-based) percentage, solid bar is the mean of 1000 iterations and error bar is the standard error.

3.5. Partial dependence plot

The partial dependence plot illustrates the marginal effect of a feature on the median night-time lights radiance captured by the VIIRS sensor. Figure 8 shows that an increase in streetlamp power increases the radiance, and an increase in normalised building area below 10% has no effect on radiance, but above 10% shows an increase in radiance with an increase in normalised building area. Furthermore, there is not much marginal change in radiance with changes to different categories of streetlamps and buildings, except for the residential building category, which has a decreasing marginal effect on radiance.

Figure 8. Partial dependence (Radiance) plots, the solid purple curves are the mean of the decision trees from the result of the Random Forest Regression Model.

3.6. Performance of the random forest regression model

To assess the performance of the RFR model, train and test samples were randomly selected 1000 times, and the root mean squared error was recorded for each iteration. The root mean squared error with the median percentage change in radiance being 6.29% and the standard error being 1.15%. Figure 9 illustrates the performance of the RFR model, with the y-axis representing the predicted radiance and the x-axis representing the observed radiance.

Figure 9. Performance of Random Forest Regression Model, the dots represent VIIRS pixel samples, x-axis represent the median radiance and y-axis is the predicted.

4. Discussion

An approach based on machine learning was described in this study to identify the most influential factors of ANTL and to predict ANTL using streetlamps and building attributes. The RFR model revealed that streetlamp power is the most important feature for predicting ANTL, as its contribution to the overall model is 42%. This is similar to the results obtained by Hiscocks and Gudmundsson (2010), Bara et al. (2019), Ściężor (2021) and Bará, Bao-Varela, and Lima (2023), but it differs from the findings of Kyba et al. (2021) who used VIIRS images and found that the contribution of streetlamps to ANTL was much lower at 13%. The difference is evident due to the lighting system in cities with high night-time activities, including busy road traffic and economic activities (Chen et al. 2015; Jia, Chen, and Li 2020; Levin and Zhang 2017). The City of Tucson possesses diverse economic activities such as industries, technology, healthcare, and tourism. In contrast, the City of Hobart relies mainly on tourism, and its night-time activities are not as varied. It is comparable to the cities of Reykjavik, Galicia, and Cracow in Iceland, Spain, and Poland, respectively. Therefore, with this evidence, we can generalise that streetlamps in small cities with minimal night-time activities have a higher contribution to ANTL.

The influence of the streetlamp’s luminous efficacy (luminous per watt) on ANTL was explored, and the results showed almost no contribution to the model. Additionally, the impact of different types of streetlamps on ANTL was explored, and it was surprising to find that there was not much influence (2.5%), which contradicts the results of previous studies by Barentine et al. (2018) and Hung et al. (2021). High-Pressure Sodium Lamps were expected to have a greater contribution due to their peak spectra being above 500 nm, which the VIIRS sensor can capture. While LED lights have two peaks, one below and one above 500 nm, the former peak is not captured.

The other features were building attributes, and we used the building footprint area and normalised it with the pixel area. The normalised building area has a 30.5% mean contribution to the RFR model, making it the second highest contributor after streetlamp power. Previous research (Bara et al. 2019; Cheon and Kim 2020; Liu et al. 2019; Liu, de Sherbinin, and Zhan 2019; Shi et al. 2019; Wang et al. 2019; Xu, Coco, and Gao 2020), has shown that the use of building attributes, rather than just the area of buildings, has a greater influence on ANTL. However, our results do not necessarily align with these findings, as the normalised building area below 10% has very little contribution to ANTL, while above 10%, the opposite is true – increasing the normalised building area increases ANTL. This may be because of two reasons: the higher normalised area corresponds to either number of building such as crowded residential buildings or a large building like the shopping malls and parking facilities. In both cases, there might be high leakages of indoor lights and the number of streetlamp might be higher in these areas.

The building categories were also examined, and it was found that residential buildings and commercial facilities have approximately 7% and 2% contribution to the model, respectively. However, an increase in commercial facilities increases ANTL, while an increase in the residential area decreases ANTL. The number of buildings in a pixel has only a 5% contribution to ANTL, as a single building with a large, normalised building area might have more ANTL than many buildings with smaller normalised building areas. A single building with a large, normalised building area is usually the parking facilities, shopping malls, hospitals, and corporate offices which do not necessarily use the blinds or curtains to stop the indoor light leakages, however, in residential areas, people value their privacy and prefer to prevent indoor light leakages using the blinds or curtain.

The vegetation and the ground surface where the streetlamp light first strikes are not accounted for in this study. The impact of vegetation was well-studied using the VIIRS dataset, and it was reported that it has almost no contribution (Jia, Chen, and Li 2020), as VNP46A2 has already undergone Seasonal Vegetation Correction (Wang et al. 2022). Therefore, it was not included in the analysis. Similarly, Bará, Bao-Varela, and Lima (2023) demonstrated that the ground surface where the ANTL is reflected does not accurately represent the actual reflectance of the illuminated surfaces. A pixel in standard ground reflectance products (e.g. MODIS) is a combination of the reflectance from streets, façades, and roofs in urban areas. Only a small portion of the reflected light from asphalt and concrete, which are commonly used materials for pavements and roads, is captured in these products. For this reason, the reflectance of the ground surface was also not included as a predictor feature.

VIIRS satellite images have a resolution of 500 m x 500 m per pixel, capturing a significant amount of information, such as ANTL emitted by streetlamps, buildings, vehicles, and billboards. However, we tried to proxy some information on streetlamps and buildings, and ANTL from vehicles and billboards is still missing. Additionally, it should be noted that not all streetlamps may be switched on, and some may be broken or not functioning. We did not have daily data on streetlamp status, so we assumed that all streetlamps were switched on every night. ANTL spilling from buildings is difficult to capture, but high buildings with windows and open spaces (e.g. parking buildings) may emit more. However, we did not have data on the height of the buildings, the number of windows, or the type and number of lamps within the boundaries of the buildings. A promising avenue for future research is the use of very high-resolution night-time imagery to identify individual light sources. This information would further advance our ability to explain the contribution of individual light sources to the radiance signal in ANTL satellite imagery.

5. Conclusion

In conclusion, this research has presented an approach based on machine learning for identifying the most influential factors of ANTL and predicting ANTL using streetlamps and building attributes. The results of the Random Forest Regression model show that streetlamp power is the most important feature for predicting ANTL, with a contribution of 42% to the overall model. The normalised building area is the second highest contributor at 30.5%. The number of buildings has a 5% contribution, respectively, while building categories, such as residential buildings and commercial facilities, have a contribution of 7% and 2%. The partial dependence plot demonstrates the marginal effect of these features on ANTL, with an increase in streetlamp power and normalised building area above 10% resulting in an increase in ANTL. The performance of the RFR model was also analysed, with a median percentage change in the radiance of 6.2%. However, this research has some limitations, including the resolution of satellite images and the lack of data on daily streetlamp operation and building attributes. Future research could overcome these limitations by using high-resolution night-time imagery to further explore the location and spatial distribution of individual light sources.

Acknowledgements

We would like to express our sincere gratitude to Robert Stevenson from Hobart City Council for generously providing the streetlamp’s data, which greatly contributed to the results presented in this paper. We also extend our thanks to the anonymous reviewer for their valuable comments and suggestions that helped improve the quality of the manuscript. Furthermore, we would like to acknowledge the invaluable support and guidance provided by our co-supervisors Heather Lovell and Jaganath Aryal, as well as the insightful feedback from Darren Turner during the initial review. Their contributions have been crucial in shaping the direction of this research.

Disclosure statement

No potential conflict of interest was reported by the authors.

Data availability statement

The data that support the findings of this study were derived from the following resources available in the public domain:

1. VIIRS Satellite Images: https://ladsweb.modaps.eosdis.nasa.gov

2. Streetlamps: https://data-1-hobartcc.opendata.arcgis.com/datasets/hobartcc::street-lighting-sample-data/about

3. Building Footprints: https://www.thelist.tas.gov.au/app/content/data/geo-meta-data-record?detailRecordUID = e5753e25-78d4-4b33-b55b-4fb41a14b1c6