1. Introduction

2. Develop a Broadly Applicable Metric

2.1. Index Determination and Data Collection

Xiang et al. [20] use calibrated night-time light images to study spatial-temporal changes in light pollution in China’s PAs from 1992 to 2012 and find that the impact of light pollution can be influenced by various factors, such as the local level of development, population, biodiversity, and geography. To better understand the complex relationship between these factors and the extent of light pollution, it is crucial to establish a comprehensive set of indicators. These factors are identified, analyzed, and distilled into 12 indicators, which have been used to develop a location-based light pollution risk assessment index (LBLPRAI). The index is designed to provide a standardized way of assessing the level of light pollution risk across different locations.

The LBLPRAI is a valuable tool for policymakers and stakeholders to evaluate the severity of light pollution in specific locations and to prioritize appropriate mitigation measures. The 12 indicators include disposable income per capita, floor area of the building, number of cars owned per capita, night light intensity, electricity consumption per capita, the proportion of the urban population, number of species, vegetation coverage, medial humidity, average temperature, and amount of precipitation. These indicators have been carefully selected to represent the different aspects of light pollution and capture each location’s unique cha-characteristics to demonstrate the effectiveness of LBLPRAI and specific data are collected for 12 indicators in five typical Chinese cities, as reported in the 2022 China Statistical Yearbook and the 2022 China Sleep Research Report. By examining the data for each indicator, a better understanding of the relationship between the extent of light pollution and the various factors that contribute to it in different locations can be gained.

Figure 1. Location-based light pollution risk assessment index.

Figure 1. Location-based light pollution risk assessment index.

3. LBLPRAI Applied to Four Diverse Types of Locations

4. Three Possible Intervention Strategies to Address Light Pollution

Figure 7. The relationship between potential impact and indicators.

Figure 7. The relationship between potential impact and indicators.

4.2. Potential Impacts

Firstly, potential impact indicators are selected to examine the effectiveness of the three proposed measures and explore their potential impacts. Since some communities that choose to implement low-light policies may experience an increase in crime rates, we can select the possible impact indicator of crime rate and denote it as $z_1$. Similarly, reducing the use of lighting may lead to an increase in traffic accident frequency, so we select the potential impact indicator of accident rate and denote it as $z_2$. Light pollution also has an impact on wildlife and plants, so we select the potential impact indicator of “Sleep Time Per Capita” and denote it as $z_3$.

Different strategies will not only lead to changes in the risk level of light pollution but also affect potential indicators. The focus of partial least squares regression (RLS) research [29,30] developed in recent years is that multiple dependent variables can model multiple dependent variables regression, which can model under the condition that multicollinearity exists between independent variables and has a solid ability to explain dependent variables. Partial least squares regression analysis is used to establish the relationship between different indicator variables and three potential impact indicators.

Let $x_1,x_2,\dots ,x_{10}$ represent the indicator variables, and $z_1,z_2,z_3$ represent the potential impact indicators. We have $n=5$ evaluation objects, $m=10$ indicator variables, and $p=3$ potential impact indicators. After data standardization, the data matrices $A={\left(a_{ij}\right)}_{n\times m}$ and $B={\left(a_{ij}\right)}_{n\times m}$ is constructed.

The first pair of components from two variable sets are extracted while maximizing their correlation.

$$\begin{array}{c}\max \theta =\rho A^{T}B\gamma ,\\ \left\{\begin{array}{c}{‖\rho ‖}^2=1,\\ {‖\gamma ‖}^2=1.\end{array}\right.\end{array}$$

(16)

Suppose the regression model is

$$\left\{\begin{array}{c}A=u{\sigma }^T+A_1,\\ B=u{\tau }^T+B_1,\end{array}\right.$$

(17)

where $A_1$ and $B_1$ say in the residual error matrix, $u=A$ , $\sigma ={\left[{\sigma }_1,{\sigma }_2,\dots ,{\sigma }_p\right]}^T,\tau ={\left[{\tau }_1,{\tau }_2,\dots ,{\tau }_p\right]}^T$ for the parameter vector in the regression model, using the least squares estimate parameter vector:

$$\left\{\begin{array}{c}\sigma =\frac{A^{T}u}{{‖u‖}^2},\\ \tau =\frac{B^{T}u}{{‖u‖}^2}.\end{array}\right.$$

(18)

Let the rank of $A={\left(a_{ij}\right)}_{n\times m}$ be $r<\mathrm{m}\mathrm{i}\mathrm{n}(n-1,m)$, has $r$ component $u_1,u_2,\dots ,u_r$, so that

$$\left\{\begin{array}{c}A=u_1{\sigma }^{\left(1\right)T}+\dots +u_r{\sigma }^{\left(r\right)T}+A_r,\\ B=u_1{\tau }^{\left(1\right)T}+\dots +u_r{\tau }^{\left(r\right)T}+B_r.\end{array}\right.$$

(19)

Using $u_i=A{\rho }^{\left(i\right)}$ to get the partial least squares regression equation of $p$ potential influence indexes:

$$z=Cx+b,$$

(20)

where $z={\left[z_1,z_2,\dots ,z_p\right]}^T$, $x={\left[x_1,x_2,\dots ,x_m\right]}^T$.

The collected data is used in the model to observe each independent variable in the interpretation of $z_i(i=\mathrm{1,2},\dots ,p)$, and the regression coefficients of each coefficient are plotted as follows:

Figure 8. Regression coefficient diagram.

Figure 8. Regression coefficient diagram.

It can be seen from Figure 9 that disposable income per capita has a significant impact on the three potential variables, and the increase in night light intensity can reduce the crime rate to a certain extent.

Examining three regression equation model accuracy to $({\widehat{z}}_i,z_i)(i=\mathrm{1,2},\dots ,p)$ is the coordinate value, and the prediction graph is drawn for all sample points:

In this prediction chart, data points are uniformly distributed near the diagonal line, indicating that the fitting effect of the equation is satisfactory.

4.3. Analysis and Evaluation

In order to reflect the impact of intervention strategies on the level of light pollution risk and the three potential impact indicators, the difference between the output value after adopting the intervention strategy and the true value without intervention will be calculated. The change in light pollution risk level is calculated as follows:

The change in light pollution risk levels is

$$∆P=P\left(W^i|E^i,F^i,T^i\right)-P\left(W^i|E^i,F^i,T^i;{\mu }_1,{\mu }_2,{\mu }_3\right).$$

(21)

The change in crime rate is

$$∆z_1=z_1-z_1\left({\mu }_1,{\mu }_2,{\mu }_3\right).$$

(22)

The change in accident rate change is

$$∆z_2=z_2-z_2\left({\mu }_1,{\mu }_2,{\mu }_3\right).$$

(23)

The change in sleep time is

$$∆z_3=z_3\left({\mu }_1,{\mu }_2,{\mu }_3\right)-z_3.$$

(24)

Taking urban community one as an example, if strategy (1) is taken to plan the lighting intensity road lighting system and parameter values are set as the initial value 0.5, end value 1, and step size 0.005, the light pollution risk level and the change amount of three potential influence indicators are obtained along with the curve of parameter ${\mu }_1$.

Figure 10. (a) Intervention strategy (1) Impact on light pollution level and crime rate; (b) Intervention strategy (1) impact on accident rate and sleep time.

Figure 10. (a) Intervention strategy (1) Impact on light pollution level and crime rate; (b) Intervention strategy (1) impact on accident rate and sleep time.

If intervention strategy (2) is taken to increase vegetation coverage, with the initial parameter value set to 0.5, the end value to 1, and the step size to 0.005, we can obtain the curves of the changes in light pollution risk level and the three potential impact indicators with respect to the parameter ${\mu }_2$.

Figure 11. (a) Intervention strategy (2) Impact on light pollution level and crime rate; (b) Intervention strategy (2) impact on accident rate and sleep time.

Figure 11. (a) Intervention strategy (2) Impact on light pollution level and crime rate; (b) Intervention strategy (2) impact on accident rate and sleep time.

Taking intervention strategy (2) can lead to a significant reduction in light pollution risk level, but its impact on the three potential impact indicators is minimal.

If intervention strategy (3) is taken, with the initial parameter value of 0.5, ending value of 1, and step size of 0.005, the change in light pollution risk level and the three potential impact indicator variables are plotted against the parameter ${\mu }_3$.

Figure 12. (a) Intervention strategy (3) Impact on light pollution level and crime rate; (b) Intervention strategy (3) impact on accident rate and sleep time.

Figure 12. (a) Intervention strategy (3) Impact on light pollution level and crime rate; (b) Intervention strategy (3) impact on accident rate and sleep time.

Adopting intervention strategy (3) can lead to less mitigation of light pollution risk levels while also significantly reducing the crime rate and decreasing the accident rate. The impact on sleep time is not significant. Therefore, it can be seen that the reduction of building density has an important impact on the light pollution risk level and Crime rate.

5. Effect of Intervention Strategies on LBLPRAI at Two Locations

5.2. Influence Model Solving

Rural community and urban community two are selected as the active sites of intervention strategies. Three intervention strategies are used separately for these two sites, and a simulated annealing algorithm [32,33] is used to solve Eq. (27). The initial temperature $T_0=100$ and temperature attenuation coefficient $\rho =0.95$ were set. The number of iterations is 3000 times, and a total of 6 times of solving.

Table 3. Solution result.

Table 3. Solution result.

Rural Community	$\mathit{\mu }$	$\mathit{H}$	Urban Community 2	$\mathit{\mu }$	$\mathit{H}$
Intervention Strategy (1)	0.53	0.02	Intervention Strategy (1)	0.82	0.25
Intervention Strategy (2)	0.66	0.03	Intervention Strategy (2)	0.54	0.04
Intervention Strategy (3)	0.89	0.01	Intervention Strategy (3)	0.74	0.11

It can be seen from the results that intervention strategy (2) is used in the rural community. Namely, increasing the vegetation coverage rate is the most effective measure. In urban community 2, intervention strategy (1) is used. That is, the planning of the illumination intensity road lighting system is the most effective measure.

Among them, the use of intervention strategy (2) in the rural community can reduce the light pollution risk level by 1.8%, crime rate by 9%, accident rate by 1.1%, and sleep time by 0.52%. In urban community 2, the intervention strategy (1) can reduce the light pollution risk by 17.2%, reduce the crime rate by 4%, increase the accident rate by 1.7%, and reduce the sleep time by 0.37%, which has little impact on sleep.

6. Conclusions and Future Work

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