ESTIMATING THE CONCENTRATION OF NO 2 WITH THE COKRIGING METHOD IN THE CAPITAL CITY OF JAKARTA

ABSTRACT


INTRODUCTION
Air quality is deteriorating globally at an alarming rate due to increasing industrialization and urbanization.In particular, nitrogen dioxide (NO2) concentrations are increasing significantly due to anthropogenic activities [1], with most of the NO2 generated by road vehicles and industrial activities [2].The increase in transportation activities is the leading cause of air pollution risks that negatively affect public health, especially in big cities.Both indoor and outdoor air pollution can cause various diseases in humans and can even lead to death [3].Based on satellite data, air pollution is mainly concentrated in the Java region, especially in the Jakarta metropolitan area and some parts of Sumatra.In DKI Jakarta, it is estimated that the average resident could lose 5.5 years of life expectancy if air pollution levels like in 2019 continue throughout their lifetime.In some areas, the reduction in life expectancy is even more severe, reaching more than six years [4].Nitrogen dioxide gas (NO2) is one of the important contributing factors to air pollution.NO2 contributes to particle pollution and acid deposits and is a precursor to ozone, the leading cause of photochemical haze [5].Meanwhile, Sulfur Dioxide (SO2) is another substance that is a source of pollutants and can cause acid rain and aerosol sulfate particle pollution.Increased concentrations of substances such as SO2 and NO2 can endanger the population's health and are evidenced by the high mortality rate in some developing countries due to poor air conditions [6].
Jakarta has been known as a polluted city with a high air pollution index [7].The capital city of Jakarta is the center of the economy in Indonesia, with many residents and industries.However, industry presence also brings negative impacts because some produce emissions and pollution directly released into the air [8].The parameters used in calculating the ISPU following KEP-45/MENLH/10/1997 are particulates with a size of 10 µm (PM10), sulfur dioxide (SO2), carbon monoxide (CO), ozone (O3) in the form of oxidants, and nitrogen dioxide (NO2) [9].The Meteorology, Climatology, and Geophysics Agency (BMKG) established eleven air quality monitoring locations in Jakarta [10].However, it is not enough to measure air quality at these locations because it is essential for the community and government to know the air conditions in the area where they live.It is closely related to the branch of statistics, namely Geostatistics [11].Therefore, it is necessary to estimate the concentration of pollutants, especially NO2.One method that can be used in this estimation is Cokriging, which considers secondary variables to predict primary variables.The cokriging method can produce more accurate predictions compared to the regular kriging method and this method can be used to handle situations where the spatial structure of the observed variables changes over time or space.In this study, the variable SO2 becomes a secondary variable considered to predict the primary variable NO2 in five administrative areas in DKI Jakarta, namely Tanjung Priok, Johar Baru, Gelora Bung Karno, Pancoran, and Halim Perdanakusuma.From this research, it is hoped that it can be an illustration for the community regarding the description of the level of air pollution in the region so that it can be material for consideration and monitoring in the level of air pollution through NO 2 levels in the five regions in DKI Jakarta.

Data
The data used in this study are quantitative data consisting of content NO 2 in μppm and SO2 gas content in the DKI Jakarta area.This research data comes from publications on the Meteorology Climatology and Geophysics Agency website for air quality content in February 2023.Measurement of NO2 levels was carried out with the passive gas method using passive sampler equipment in eight locations, namely Ancol, Bandengan (Delta), Bivak, Grogol, Kemayoran, Kementen, TMII, and Monas.Sample analysis was conducted at the BMKG air quality laboratory using a spectrophotometer.Meanwhile, the measurement of SO2 gas in the exact location using an ion chromatography device.

Research Variables
The variables used in this study consisted of primary and secondary variables, with the primary variable being the content of NO 2 and the second being SO2 content as shown in Table 1.The estimation areas taken in this study include Tanjung Priok, Johar Baru, Gelora Bung Karno, Pancoran, and Halim Perdanakusuma.

Variogram and Semivariogram
Variogram is a statistical tool essential for spatial data estimation.This is because if two spatial values are located close to each other, they are relatively more similar compared to two spatial values that are far apart.The variogram is formulated as follows To perform estimation on spatial data, a tool is employed to depict, model, and calculate the spatial correlation between random variables () and ( + ).This tool is known as a semivariogram.The magnitude of the semivariogram is half of the variogram value [12] .

Experimental Covariance
The experimental auto-covariance can be expressed as follows [13]: While the experimental cross-covariance can be expressed as follows [13]: Where:  : Number of distinct pairs separated by distance h   : Observed value of the first regional variable at location   +ℎ : Observed value of the first regional variable at location  + ℎ  ̅ : Average of the first regional variable  +ℎ : Observed value of the second regional variable at location  + ℎ  ̅ : Average of the second regional variable

Theoretical covariance
The theoretical covariance model that can be used is the spherical covariance model [13]: where P (nugget effect) is the approximation of auto covariance and cross-covariance values at a distance around zero; Q (sill) is the maximum value reached by auto covariance and cross-covariance; r (range) is the distance when covariance reaches its maximum value; h is the distance between locations;  ≥ 0,  ≥ 0 and  > 0.

Cokriging
One type of Spatial method is Cokriging.Cokriging is a Spatial interpolation method that uses two variables, namely primary and secondary variables, in the process [14].Cokriging is an extension of autokriging because it considers the additional correlated information in the auxiliary variables.It appears more complex because the additional variables increase the complexity of the notation.[15].Cokriging uses the correlation between smooth and course model data to improve prediction accuracy, unlike other Kriging variants [16].Cokriging must fulfil the assumptions of dependency and heterogeneity.Secondary variables are correlated with primary variables and contain essential information about primary variables.If the correlation value between these variables is high, the Cokriging results are promising.The Cokriging interpolation method is a linear combination of primary and secondary variables [13].
where  ̂0 is the estimated value of z at location 0 (approximate location); Therefore, in matrix form, it becomes as follows.
where  is the covariance matrix of primary and secondary variables between observed locations, the following equation calculates the value of the spherical covariance model.
where  is the approximation of auto covariance with cross-covariance at a distance around 0,  (sill) is the maximum value reached by auto covariance, and cross coefficient where the sill value is equal to the variance of the data.At the same time,  (range) is the distance when the covariance reaches the maximum value.
is the variation vector between the observation and the estimated location  0 .The vector containing weights for primary and secondary variables and the Lagrange multiplier is denoted by .The estimator for  is

Research Analysis Steps
The stages of analysis in this study can be carried out as follows: 1. Providing variable value data NO 2   at the latitude and longitude coordinates of the observation location   = (  ,   ) for  = 1.2.… 8 and the value of the variable SO2   at the observation location   = (  ,   ) for  = 1,2, … 8 and the coordinates of the estimation location  0 = ( 0 ,  0 ) for five sub-districts.
2. Forming a distance matrix between observation locations by calculating the Euclidean distance.The distance between the i-th location located at the coordinates of latitude and longitude (  ,   ) to the j-th location located at the coordinates of latitude and longitude (  ,   ) obtained using the following equation 3. Calculating the distance between the estimation location located at the latitude and longitude coordinates ( 0 ,  0 ) with each observation location at the coordinates of latitude and longitude (  ,   ) obtained by the following equation 4. Calculating experimental auto covariance and cross-covariance with Equation (3) and Equation (4).Meanwhile, other locations each produced SO2 levels of 7 μppm for Ancol, Bandengan (Delta), and Kemayoran at 6 μppm, Bivak and Grogol at 5 μppm.The observation of NO 2 in February 2023 has an average of 5.875 μppm.The elevated levels of NO2 at Ancol may be attributed to the area's heavy traffic, particularly during peak hours.NO2 is a byproduct of vehicular emissions, and congested traffic conditions can lead to increased NO2 emissions.Additionally, the use of high levels of fossil fuels in a specific area can contribute to higher NO2 and SO2 emissions.Therefore, it's crucial to consider both traffic patterns and fuel usage as factors affecting air quality in these areas.

Correlation Between Research Variables
The primary variable in this study is NO2 content.while SO2 content is a secondary variable.Correlation testing between the two variables was conducted.The results of the correlation testing between the two research variables can be seen in Table 2 below: Table 2 shows that the two variables are moderately correlated.Thus, this result supports using the Cokriging method in estimating the NO2 variable by using information from the SO2 variable as a secondary variable.

Estimation of NO2 Content with Cokriging Method
The first step taken to estimate the NO2 content was to calculate the distance from one location to other observation locations using Equation (2).Furthermore, the distance between each observation location and the location to be estimated was calculated using Equation (3).The next step was to calculate the value of experimental auto covariance and experimental cross-covariance following Equation (4).After obtaining the experimental auto covariance value, the next step was determining the spherical auto covariance.Estimating the values of P. Q. and r is required to get it.The values of P, Q, and r for spherical auto covariance are determined from the distance plot against experimental auto covariance.Figure 3 below presents a plot of distance against the experimental auto covariance value of the first variable (NO 2 ): Figure 3 illustrates the relationship between the distance between observation locations and the experimental autocovariance value for the first variable, NO 2 .This plot is a critical component in the process of estimating NO2 content.The obtained values, P = 1.124375,Q = 1.615625, and r = 0.049216 play a key role in calculating the spherical autocovariance for NO2.P indicates the range over which spatial dependence is significant, suggesting that NO2 concentrations exhibit significant spatial dependence up to approximately 1.124375 units.Q, on the other hand, signifies that spatial dependence becomes negligible at a distance about of 1.615625 units.The value of r (0.049216) indicates a relatively weak spatial dependence of NO2 concentrations between observation locations.In summary, Figure 2 and the derived P, Q, and r values provide valuable insights into the spatial autocorrelation structure of NO2 concentrations, aiding in the estimation and modelling of NO2 content across various locations.These findings are essential for environmental and geospatial analysis, contributing to a better understanding of spatial patterns and variabilities in air quality data.Meanwhile, the distance plot against the experimental auto covariance between the second variable is as follows:  Based on Figure 5 the value of P = 0.246875, Q = 9.178125, and r = 0.042419 for the calculation of spherical cross-covariance between the first variable and the second variable.Thus, the spherical auto covariance value of the first variable ( 2 ) is formulated as follows: The spherical auto covariance value of the second variable variance (SO2) is formulated as follows: The spherical cross-covariance value between the two variables can be formulated as follows: (ℎ) = { (0.246875 + 9.178125) (1 − 1.5ℎ 0.042419 + ℎ 3 2(0.04219) 3 ) .0 ≤ ℎ ≤ 0.042419 0 .ℎ > 0.042419 After obtaining the value of spherical auto covariance and spherical cross-covariance between variables at each point, a C matrix can be formed and calculate the auto covariance between variables at the  After obtaining the weight vector w, the estimated NO2 content is calculated based on the Equation (5).The estimation results can be seen in Table 3.Based on the estimation results in Table 3 above, the following results are obtained: 1. Tanjung Priok The estimation results from the Cokriging method show that the NO2 content in Tanjung Priok is 24.362481 μppm, which is still below the quality standard value set by BMKG of 80 μppm.It shows that the environmental conditions in the area around Tanjung Priok are very dense.Tanjung Priok is located in the North Jakarta Administrative City, Indonesia, known as Indonesia's principal port and one of the busiest ports in Asia.In addition, Tanjung Priok is also the center of industry and trade in North Jakarta, with ports, docks, warehouses, logistics facilities, and processing industries in the vicinity.With such a dense environment, the air quality in Tanjung Priok is likely to be poor.

Johar Baru
The estimation results from the Cokriging method show that the NO2 content in Johar Baru is 15.005356 μppm, which is still below the quality standard value set by BMKG of 80 μppm.Johar Baru is located in Central Jakarta and is one of the most densely populated urban villages.Although this location is in a strategic area of downtown Jakarta, there are critical, slum, and crowded dwellings.Therefore, it is crucial to analyze NO2 levels to evaluate air quality in such a densely populated area.With the estimated results that are still below the quality standard, it can be seen that the air quality in Johar Baru is still within the limits allowed by the standards set by BMKG.

Gelora Bung Karno (GBK)
Estimation results from the Cokriging method show that the NO2 content in Gelora Bung Karno (GBK) is 7.496268 μppm.Gelora Bung Karno is the largest sports complex in Indonesia and one of the largest in Southeast Asia.The complex is often used for various activities and events that attract many people.However, piles of garbage in the GBK area have become a topic of conversation because after the event, there is a build-up of garbage.It can affect environmental conditions and air quality around GBK.Meanwhile, the estimation results show that the NO2 content at GBK is within the allowed limits.
Although it still needs attention to waste and environmental issues, the air quality in the GBK area seems to be well maintained based on the estimation results.

Pancoran
The estimation results from the Cokriging method show that the NO2 content in Pancoran is 12.376980 μppm.Pancoran is one of the areas in South Jakarta, Indonesia, located in the Southern part of Jakarta city center.The area is known for its high population density, with various settlements ranging from densely populated settlements to residential complexes.Traffic congestion is also one of the challenges in this area.Under such conditions, the estimated results of the Cokriging method indicate the presence of relatively high NO2 content in Pancoran.It suggests the possibility of poor air quality in the area, which could impact the health and environment around Pancoran.
The estimation results from the Cokriging method show that the NO2 content in Halim Perdanakusuma is 12.376980 (μppm).Halim Perdanakusuma is an area located in East Jakarta.The area is known to be very congested with vehicular traffic due to its proximity to Halim Perdanakusuma Airport.The traffic density causes high pollution from vehicle fumes in the vicinity.It indicates that the air quality in the area may be affected by high vehicle pollution levels.

CONCLUSIONS
The following are conclusions from the results of the analysis and discussion of the research that has been done: 1.After measuring SO 2 and NO 2 levels in several areas around Jakarta, it was found that there are differences in the amount of SO2 and NO2 levels in each area.The area with the highest SO2 levels is Monas with 10 μppm, while the areas with the lowest SO2 levels are Kementen and TMII with 4 μppm.Meanwhile, Ancol had the highest NO2 levels at 19.6 μppm and Grogol had the lowest NO2 levels at 16 μppm.The average SO2 level in all measured areas was 5.875 μppm, while the average NO2 level was 17.375 μppm.It can be concluded that there is a need for efforts to maintain air quality in these areas to stay within the quality standard limits set by the government.
2. Based on the estimation results using the Cokriging method.the estimated content in Tanjung Priok was 24.362481.Johar Baru was 15.005356, Gelora Bung Karno (GBK) was 7.496268, Pancoran was 12.376980, and Halim Perdanakusuma was 12.376980.From these results, it can be concluded that the content in Tanjung Priok, which is a coastal area, has a difference from the estimation results in other Jakarta areas, and is the highest compared to other areas measured.At the same time, the lowest content is in GBK.

Figure 1 .
Figure 1.Illustration and Relation of Nugget Effect, Sill, and Range (a) Variogram (b) Covariance

5 . 7 . 5 ) 8 . 1 2 .Figure 2 .
Plotting the distance between locations (ℎ) against the experimental covariance 6. Determining the values of P, Q, and r from the plot in step 5 Calculating the value of the spherical covariance model (ℎ) that fits in Equation (Forming matrices C and D 9. Calculating the inverse of matrix C 10. Finding the weight value by forming a matrix  =  −  11.Calculating the expected value of variables at the location  0 .which is  ̂0 in Equation (Descriptive Statistics of NO2 and SO2 Concentration Data The data used in this study comes from the monitoring results of eight observation locations in the DKI Jakarta area, namely, Ancol, Bandengan (Delta), Bivak, Grogol, Kemayoran.Kementen, TMII, and Monas.presented in Figure Histogram of Concentration Data (a) NO2 (b) SO2 Based on Figure 2 (a), it can be seen that amount of NO2 levels in the DKI Jakarta area has the highest levels at the Ancol observation location of 19.6 μppm and the lowest NO2 levels at the Grogol observation location of 16 μppm, Bandengan (Delta) by 18 μppm.Bivak by 16.2 μppm, Kemayoran and TMII by 17.4 μppm, Kementen by 17.6 μppm, and Monas by 16.8 μppm.The average observation result of NO2 in February 2023 was 17.375 μppm.Based on Figure 1(b), the highest levels of SO2 are in the Monas observation location at 10 μppm and the lowest levels of SO 2 in the Kementen and TMII areas at 4 μppm.

Figure 3 .
Figure 3.The plot of Distance Between Observations against Autocovariance of NO2

Figure 4 .
Figure 4.The plot of Distance Between Observations against SO2 Autocovariance Based on Figure 4. the values of P = 3.359375, Q = 4.640625, and r = 0.042419 are obtained to calculate spherical auto covariance between SO2 variables.The distance plot against the experimental crosscovariance between the first and second variables is as follows:

Figure 5 .
Figure 5. Plot of Distance Between Observations against Plot of Distance Against Experimental Cross Covariance eight measurement locations.NO 2 is based on the formula   (ℎ), and SO2 is based on the formula   (ℎ), forming the D matrix.the weight vector w is calculated by performing matrix multiplication between matrix C and matrix D. The following is the result of the calculation of the vector w  =  −  = [ 0.

Table 1 . Definition of Research Variables No Variables Definition
1. … .  is the primary variable data at the nearest location;  1 .… .  is the data of secondary variables at the nearest location; and  1 .… .  and  1 .… .  are the weights of Cokriging that must be determined.
is a random variable that represents u at the n closest locations sampled, and  1 .… .  is a random variable that represents v at the m closest locations sampled.The Cokriging system can be obtained by summing up each equation.i.e., n + m +2 = 0. and then rearranging each part.∑  {    } +  =1 ∑   {    } +  1 = { 0 .  };  = 1.… .