Application Bootstrap to Estimate the Confidence Intervals of NO2 Levels in the Kriging Method

NO2 levels must be monitored continuously to minimize negative environmental impacts. In general, the estimation of NO2 levels using the Kriging method produces point estimates. In this study, we developed an interval estimate for NO2 levels by applying the quasi-random Bootstrap resampling method. We used data on NO2 levels in 14 areas in South Tangerang City in 2021. The data is stationary, so the appropriate estimation method is ordinary kriging. To develop the 95% confidence interval, we applied 1000 resamplings to the Bootstrap. The estimation results show that the lowest 95% confidence interval for NO2 levels is in the range of 25.23123 – 27.82351 μgr/m3 in Pamulang Timur Village, and the highest 95% confidence interval for NO2 levels is in the range of 45.59886 – 46.08371 μgr/m3 in the Ciater Village.Keywords: Bootstrap, Confidence Interval, Kriging, Quasi-Random.  AbstrakKadar NO2 perlu dipantau secara terus menerus untuk meminimalisir dampak negatif terhadap lingkungan. Pada umumnya, estimasi kadar NO2 menggunakan metode kriging menghasilkan estimasi titik. Pada penelitian ini akan dikembangkan estimasi selang untuk kadar NO2 dengan mengaplikasikan metode resampling quasi-random bootstrap. Data yang digunakan adalah kadar NO2 pada 14 wilayah di Kota Tangerang Selatan tahun 2021. Data tersebut stasioner sehingga metode estimasi yang digunakan adalah ordinary kriging. Untuk pembentukan selang kepercayaan 95% diaplikasikan 1000 resampling pada metode bootstrap. Hasil estimasi menunjukkan bahwa selang kepercayaan kadar NO2 terkecil berada pada rentang nilai 25,23123 – 27,82351  yang berlokasi di Kelurahan Pamulang Timur dan selang kepercayaan kadar NO2 terbesar berada pada rentang 45,59886 – 46,08371  yang berlokasi di Kelurahan Ciater.  


INTRODUCTION
The nitrogen dioxide (NO2) level is one of the crucial components affecting air quality.NO2 is a reddish-brown toxic gas with a sharp smell.When it exceeds the set threshold, NO2 levels can cause the air to appear brownish, leading to acid rain that can result in lung and respiratory infections.It also plays a role in forming fine particles and ground-level ozone.Apart from posing a threat to human health, air pollution also incurs significant economic losses (Zhu, et al., 2019), affecting transportation, water, and energy exchange at the land-air interface, thus influencing climate change (Zheng, et al., 2016).Elevated NO2 levels can even lead to fatalities (Öztürk & Öztürk, 2023).
Efforts to reduce NO2 pollution often involve implementing stricter emission standards for vehicles and industrial sources, promoting cleaner technologies, and encouraging sustainable transportation practices.Monitoring and controlling NO2 levels are crucial to protect human health and the environment.Therefore, some research recommends preventive measures against NO2 pollution, including consuming foods rich in vitamins C and E, using masks, enforcing smoke-free areas (Darmawan, 2018), and using activated carbon cabin air filters in vehicles to prevent exposure to NO2 pollutants for drivers and passengers (Matthaios, et al., 2022).
Reducing airborne NO2 levels can be achieved by regulating emissions through emission standards, promoting public transportation, and encouraging electric vehicles (Krecl, et al., 2021).Traffic management is also necessary to reduce congestion, especially in city centers, and the implementation of emission-free zones (Tang, et al., 2020).Other efforts are using clean and environmentally friendly industrial technologies (Ajmal, et al., 2022) and establishing air quality monitoring systems to monitor NO2 pollution levels and provide information to the public about the health impacts of NO2 pollution and how they can protect themselves from exceeding NO2 levels (Manusmare & Gajarlawar, 2023).
Several methods have been developed to estimate NO2 levels.(Wu, et al., 2021) developed a spatial-temporal kriging regression model to map NO2 concentrations in China.(Bertero, et al., 2020) Monitored NO2 concentrations in Marseille, France, focusing on using private bike fleets.(Lee & Lee, 2019) predicted annual and monthly average NO2 concentrations in the United States using land-use regression (LUR) analysis.This study also assessed environmental risks, exploring the relationship between NO2 concentrations and potentially exposed individuals in 377 metropolitan statistical areas (MSA).
Generally, the kriging estimation methods in the mentioned studies provide point estimates.Therefore, this study discusses interval estimates (in the form of confidence intervals) for NO2 levels by applying quasi-random Bootstrap resampling.The data used are NO2 levels in 14 regions of South Tangerang City in 2021.Preliminary research indicates that the data are stationary, so the appropriate estimation method is ordinary kriging.The estimated NO2 levels using this method are then resampled using quasi-random Bootstrap to develop confidence intervals.

METHOD
This study focuses on NO2 levels at South Tangerang City.We use data on the NO2 level at 14 regions in 2021 (Table 1).The distribution map of NO2 levels can be seen in Figure 1.According to this table, the minimum NO2 level is 24.10 (/ 3 ), the maximum is 51.00 (/ 3 ), the average is (/ 3 ), and the variance is 78.43 (/ 3 ).This study uses the simple kriging interpolation method to estimate the NO2 levels.These estimations will be resampled using Bootstrap to determine the confidence interval.The first step is checking the data stationarity to decide the appropriate type of kriging method.If the data is stationary (does not have a trend), then the appropriate method is simple or ordinary kriging.Conversely, the appropriate method is universal kriging.
Next, we form a matrix of distances between sample points using the equation: where () and y are the coordinates of the sample's location.Subsequently, these data pairs are divided into several classes, which are calculated using the Sturges equation (Scott, 2010): where  is the number of class intervals, and  is the sample size.Next, calculate the experimental semivariogram using the equation (Beers & Kleijinen, 2003): where (ℎ) is the semivariogram value between   and   + ℎ, (  ) is an observation on point   , (  + ℎ) is an observation on point   + ℎ, and (ℎ) is the number of point pairs at a distance ℎ.We will compare the experimental and the theoretical semivariogram values.Theoretical semivariogram values are calculated using three models, i.e., Spherical, Exponential, and Gaussian, as follows (Sari, et al., 2015): b. Exponential c. Gaussian where ℎ is the location distance between the sample, and  is the sill (variogram value for distance when the magnitude is constant).The sill value is the same as the data variance.The value of  represents the range (the distance when the semivariogram value reaches the sill).
After getting the experimental semivariogram, sill, and range values from the three theoretical semivariogram models, complete the structural analysis, matching the experimental semivariogram with the theoretical semivariogram.This analysis was carried out by calculating the Root Mean Square Error (RMSE) of the two semivariograms using the equation: where (ℎ) is the experimental value of the semivariogram, and  ̂(ℎ) is the theoretical semivariogram value.A model with the smallest RSME will be the best model.
The NO2 levels are estimated using the ordinary kriging method at unsampled areas using the equation: where  ̂( 0 ) estimates unsampled locations, and   is weighted for (  ) with ∑   = 1  =1 . This research contributes to developing the confidence intervals based on the point estimation resulting from equation ( 8).We resampled the point estimation using the Bootstrap method.The detailed steps used are as follows.
This stage is called quasi-random Bootstrap.

1000
. Use the following equation to calculate a (1 − ) confidence interval for NO2 levels in unsampled points: ̂ =  ̂( 0 ) +  /2 × , Where  ̂ dan  ̂ are the lower and upper bound of the confidence interval, and  /2 is a normal distribution table value with significance level .

RESULTS AND DISCUSSION
Figure 2 shows the scatter plot between the NO2 level on the X-axis (left) and the Y-axis (right).Based on this figure, it can be seen that the plot of NO2 levels spreads randomly (have no trend) both on the X and Y axes.So, the NO2 level data is stationary.Therefore, the appropriate estimation method is ordinary kriging.4) -( 6)) is zero when  = .The theoretical semivariogram values for the Spherical, Exponential, and Gaussian models are listed in Table 3.Based on the smallest RSME value in Table 3, it can be concluded that the best model to estimate NO2 levels is the Exponential.This estimate was calculated using equation ( 8) at 40 South Tangerang City area points, as shown in table 4. Meanwhile, the map of the estimation results is shown in Figure 2. Based on Table 4, the largest estimated value of NO2 levels is in the Ciater area at 45.84128 (/  ), and the smallest estimated value is in the East Pamulang area with an estimated value of 26.52737 (/  ).Table 5 shows the Bootstrap quasi-random samples that contain vector  ⃗ ⃗⃗ and several Bootstrap resampling from vector  ⃗ ⃗⃗ at 14 points.Vector  ⃗ ⃗⃗ is the result of transforming observational data to become uncorrelated based on equation (9).It then transformed  ⃗ ⃗⃗ into quasi Bootstrap samples  ⃗ * () using equation ( 10) for  = 1, . . ., 1000.Table 6 contains  ⃗ * () .These  ⃗ * (1) to  ⃗ * (1000) will be used as new samples to estimate NO2 levels at 40 unsampled regions using the ordinary kriging method using equation (8).Table 7 contains the standard error for  ̂( 0 ) * (1) to ̂( 0 ) * (1000) , which is calculated using equation ( 11), the lower and upper bound of the 95% confidence interval for NO2 levels at 40 unsampled regions.From this table, it can be seen that the smallest 95% confidence interval is in the value range 25.23123 -27.82351 at East Pamulang, and the largest 95% confidence interval is in the value range 45.59886 -46.08371 at Ciater.From the lower and upper bounds of the estimation of NO2 levels at 40 unsampled regions, they are still in the good category following the Decree of the Minister of the Environment Number: KEP 45/MENLH/1997 concerning air pollutant standard indices.According to Table 7, NO2 levels in South Tangerang City are in the good category.The results of this study can be used as a reference by local governments in establishing regional policies or regulations that focus on controlling air quality: maintaining appropriate policies and improving/adding policies needed to reduce pollution from NO2. Apart from motorized vehicles, previous research shows that higher NO2 levels can come from cooking fuels and biomass burning (Quackenboss, Spengler, Kanarek, Letz, & Duffy, 1986) (Ryan, Spengler, & Halfpenny, 1988) (Park & Ko, 2018).NO2 levels can be reduced by implementing a motor vehicle restriction policy.In DKI Jakarta, NO2 levels have decreased during the 2019-2020 COVID-19 pandemic by the Large-Scale Social Restrictions (PSBB) policy (Prasetyo, Bashit, Yusuf, & Rassarandi, 2023).(Widya, et al., 2020) suggests that local governments prioritize maintaining a greater percentage of greening when implementing urban planning and design.
The results of NO2 level estimates can provide insight into NO2 distribution patterns in various regions, helping governments and environmental organizations identify potential pollution sources and design more effective policies to reduce their negative impacts.Additionally, understanding NO2 levels can be used to monitor interim developments and measure the effectiveness of government mitigation measures.By understanding NO2 levels, we can work on better strategies to maintain global air quality and environmental and public health.

SUMMARY
This article successfully developed a 95% confidence interval to estimate NO2 levels in South Tangerang City.These confidence intervals developed from point estimation using the ordinary Kriging method.The point estimate and 95% confidence interval for the smallest NO2 levels are in East Pamulang, while the largest NO2 is in Ciater.In general, NO2 levels in South Tangerang City are a good category following the Decree of the Minister of Environment Number: KEP 45/MENLH/1997 concerning air pollutant standard indices.

Figure 3 .
Figure 3.The plot of distance between data pairs vs experimental semivariogram values

Table 1 .
NO2 Level in 14 Regions of South Tangerang City

Table 3 .
Experimental and Theoretical Semivariogam Values

Table 4 .
Point estimates of NO2 levels at 40 areas of South Tangerang City using the Exponential Model.

Table 7 .
Standard error and 95% Confidence Interval for NO2 level at 40 unsampled areas.