Temporal and Spatial Distribution Characteristics of NOx Emissions of City Buses on Real Road Based on Spatial Autocorrelation

To characterize the spatial and temporal distribution of NOx exhausted by urban buses, we measured real-world on-road NOx emissions from these vehicles in the city of Kunming, China, using an onboard monitoring platform. To fill the data gaps and produce a complete data set, we combined Bayesian network modeling and probabilistic inference. The complete data set was then used to generate an NOx emission heat map, and spatial autocorrelation was applied to evaluate the distribution characteristics. The results show that our method for filling in the missing data provides highly accurate values, with spatial autocorrelation indices of 0.648, 0.836, 0.935, and 0.798 for the morning, midday, afternoon, and evening, respectively. The NOx emissions showed spatial correlation during all four periods, whereas the pollutive emissions showed spatial aggregation. According to the heat map, the NOx concentrations peaked during the midday and the afternoon. Furthermore, regardless of the period, the largest emissions accumulated in Road Sections 1–3 and 6–9, and the highest as well as the fastest-growing emission intensity occurred in Road Sections 5–9.


INTRODUCTION
Air pollution is an important global risk factor for disease and death (Lim et al., 2012;. Measurement of air pollution is critical for epidemiology and air quality management, especially for ground-based urban air pollution detection (Brauer et al., 2015;Carvalho, 2016). In recent years, with the rapid development of the urban economy, the number of vehicles has sharply increased, and traffic emissions have become an important source of urban air pollution (Zhang and Batterman, 2013;Su et al., 2015). Due to the rapid development of urbanization in China, urban air pollution has shifted from local single-point pollution to complex regional pollution sources (Chai et al., 2006). One of the important sources of composite air pollution in China is vehicle exhaust emissions, which are especially important for pollutants such as fine particulate matter (PM2.5), carbon monoxide (CO), nitrogen oxides (NOx), and volatile organic compounds (VOCs) in urban air . Urban diesel buses are the main contributors to urban NOx emissions. Through photochemical reactions NOx can produce photochemical smog, which is extremely harmful to the human body (Wang et al., 2011;Li et al., 2012;Liu et al., 2013). Strengthening the control of NOx from urban public transport is important to reduce urban air pollution and optimize quality of life. Therefore, it is important to study the spatial and temporal distribution characteristics of urban public transport NOx emissions and to analyze its correlations to improve urban air quality and strengthen air quality management Zhang et al., 2019).
Due to the particularities of the urban bus operating environment, which consist of frequent starting, braking, idling, and low-speed driving conditions, the engine is mostly running at lowspeed, high-torque, and idle-speed conditions. To control motor vehicle exhaust emissions more effectively, researchers analyzed the spatial and temporal distribution characteristics and laws of vehicle exhaust emissions based on different models and methods. A statistics-based Monte Carlo simulation method was used to analyze the uncertainty of emissions estimates by simulating a large number of vehicle emissions data points (Lv et al., 2019). The Corinair method was used to estimate the emission reductions brought about by urban bus modernization and to estimate the contributions of particulate matter and gaseous pollutants emitted by city buses in the Krakow region (Bogacki and Bździuch, 2019). Hao et al. (2017) and Carslaw et al. (2019) summarized the results of remote-sensing measurements of vehicle emissions in the United Kingdom, providing detailed information on NO2 and total NOx (NO2 + NO) emissions and analyses of NOx emissions trends in recent years.  used a Global Positioning System (GPS) receiver to collect per-second activity data, used 2-second speed and acceleration to determine the bus operating mode, and applied the vehicle-specific power (VSP) to estimate the corresponding emissions. Chen et al. (2018) used a chassis dynamometer to explore the impact of various factors on the emissions of heavy-duty diesel vehicles and to test and analyze Euro VI standard heavy-duty diesel vehicles under different loads, fuels, driving environments, and resistance conditions. He et al. (2016) used a large number of methods to obtain real-time dynamic traffic flow information and used the Computer Programme to Calculate Emissions from Road Transport (COPERT) model to analyze the spatiotemporal characteristics of Beijing vehicle emissions. Wang et al. (2012) simulated the exhaust emissions of diesel vehicles under different working conditions and analyzed their emission characteristics. Chen et al. (2015) investigated and analyzed the various conditions of Chengdu light-duty gasoline passenger vehicles and used the International Vehicle Emission (IVE) model to analyze their exhaust emission characteristics and to establish a local emissions inventory. Kan et al. (2018) carried out an autocorrelation analysis of vehicle exhaust emissions in Nanjing through the portable emissions measurement system (PEMS). Different methods and ideas can be used to obtain the desired results and create a database and inventory of local vehicle pollutant emissions characteristics (Wang and Li, 2016).  built a high-resolution temporal-spatial vehicle emission inventory of the city of Foshan based on detailed hourly traffic data and a COPERT emissions model. Kan et al. (2018) proposed a method that estimated fuel consumption and emissions at a fine-grained level based on vehicle GPS trajectories and microscopic model Comprehensive Modal Emission Model (CMEMs). Alam et al. (2017) estimated transit bus emissions by using Motor Vehicle Emission Simulator (MOVES) embedded drive cycles with local data.
In these studies, real traffic conditions were included to characterize temporal and spatial distribution; however, the emission data were calculated by emission models rather than from actual road emissions. PEMS have been widely used to record various types of vehicle emissions data under real driving conditions, but cannot reflect the long-term emission characteristics of transit buses (Apte et al., 2017). This paper is based on a study of the spatial and temporal distribution characteristics of NOx from urban buses on real roads, using a data-filling method combining a Bayesian network and probabilistic reasoning to fill in the missing entries in the data stored in the tensor model. Then the data set was generated again for storage, and a tensor model was used to facilitate data storage and extraction. Spatial autocorrelation analysis combined with the ArcGIS online platform was used to determine the spatial and temporal distribution characteristics of pollutant emissions, which was helpful for understanding the spatial and temporal distribution characteristics of urban bus NOx emissions.

Data Sources
The No. 80 bus in Kunming was selected as the research object. The data used in this study came from an online vehicle exhaust monitoring platform that was established to obtain dynamic real-time vehicle exhaust data for specific routes throughout the day. A terminal device was installed on the bus, which includes an NOx sensor, a GPS receiver, an onboard diagnosis system (OBD) data reader and a wireless data transmission unit. The NOx sensor is an electrochemical sensor, which can directly measure the bus NOx emission concentration second by second. The GPS system can provide navigation and positioning information, such as real-time longitude, latitude, and altitude, and positioning function to obtain the coordinates of each point. The collected data are transmitted to the corresponding platform by General Packet Radio Service (GPRS). The time for data collection and experimentation in this study was 20 weeks, extending from 2017 January 2 to 2017 May 22. The data collection hours were approximately 06:00-22:30, covering both working and non-working days and including the actual operation of the whole route throughout the day.

Research Methods
The real-time NOx emissions obtained from the online monitoring platform were extracted, integrated, and stored in the tensor model. The missing data points were then filled in using a Bayesian network and probabilistic reasoning to produce a complete data set. Finally, spatial autocorrelation coefficients generated by the ArcGIS software platform were used to study the spatial and temporal distribution characteristics of NOx.

Instantaneous Emission Calculation
We extracted real-time NOx emissions quality data from the online monitoring platform and calculated the instantaneous emission rates, which were used to calculate the corresponding emission factor. Therefore, the complete working condition data and the corresponding NOx transient emission rates (NOx instantaneous wet-based concentrations) were obtained. The NOx transient emission rate is obtained according to Eq. (1): In the formula, NOx is the instantaneous emission mass of gaseous pollutant (g s -1 ), NOxconc is the instantaneous wet-based concentration of each gaseous pollutant in the original exhaust gas (ppm), and Gexh is the instantaneous exhaust flow rate (kg h -1 ).
The instantaneous pollutant emissions of the corresponding road sections were accumulated to obtain the total pollutant emissions of each section.

Introduction to Tensor Models
Tensors, also known as N-mode matrices, are higher-order generalizations of scalars, vectors, and matrices (Mislevy, 1991;Ali and Foroosh, 2016;Günther et al., 2017). In the sense of isomorphism, a zero-order tensor (r = 0) is a scalar, a first-order tensor (r = 1) is a vector, and a second-order tensor (r = 2) is a matrix. A ∈ R I1, I2, ..., In can be thought of as a tensor of order N.
The NOx data used in this experiment included 17 platforms and 16 regional sections of the whole route, starting from Kunming station and ending at the western passenger station. The total length of the study route was about 10.8 km, and the total time was 20 weeks of real-time diesel bus emissions data. According to the real-time emission characteristics, a five-dimensional tensor form of spatial/time (59,400) × day (7) × emission (2) × position (16) × week (20) was constructed. There were 59,400 dimensions per day, representing the NOx emission data read second by second on that day; there were 7 dimensions in a day, representing the data of the week, and there were 20 dimensions in a week, representing the tensor model of a 20-week pattern. There were 16 location dimensions, which meant that there were 17 bus stations and 16 regional sections, and there were 2 emission dimensions, namely emission concentration and instantaneous emission rate. In this study, the tensor structure was selected to store data because the data conversion process was convenient. For a large number of data sets, the tensor model can more easily extract, process, store, and transform data, which is conducive to saving time and improving efficiency. For example, Tensor (960, 4, 1, 3, 12) represents the concentration of NOx emissions in the database on the fourth day of Week 12 at 06:16 in Position 3, as shown in Fig. 1. From the above description, the NOx emission concentration and instantaneous emission rate at each corresponding point in time and space can be accurately obtained. This study used the tensor model to store NOx emission information. The required data set can be constructed quickly, and the corresponding relationships of NOx emission characteristics in space and time can be revealed.

Missing Data Processing
Due to various reasons such as damage to experimental equipment, irregular data entry, or limited data acquisition equipment capacity, the missing data phenomenon often occurred in real databases (Sidiropoulos et al., 2017). Based on the analysis of urban bus exhaust emissions by big data, this paper abandoned the traditional missing data-filling algorithm (Acar et al., 2010) to use another based on the Bayesian network and probabilistic reasoning, which is suitable for a large number of data sets. Unlike the commonly used Bayesian network construction algorithm, this study started from the mining of attribute correlations to build the network for the specific application premise of missing-value filling and filled in the data on the basis of Map-Reduce.
A Bayesian network is a graphical probabilistic network based on probabilistic reasoning, and the Bayesian formula is the basis of the probabilistic network. A Bayesian network is represented by a direct acyclic graph, where each node represents a variable and each directed edge between two points represents the casual relationship between two variables. Using the various relations between the Bayesian network variables, the joint probability distribution of these variables is decomposed into several independent conditional probability distributions. The formula is shown as Eq. (2): where π(xi) is the parent node set of the variable, and when π(xi) = Ø, p[xi/π(xi)] = p(xi). The independence of this condition in the Bayesian network reduces the complexity of the model and brings convenience to uncertainty reasoning with high-dimensional data.
In the data used in this study, the attributes were highly correlated. When the Bayesian network was constructed, the choice was made to explore from the perspective of attribute correlation rather than from the casual relationship between variables, which provided a large amount of available effective inference information and greatly improved the credibility of the reasoning probability. For the application type in this study, it was only necessary to infer the missing data according to the known relevant information, and only the related variables that have an impact on the missing variables need to be noted. The experimental data came from the actual traffic data sets Date1 and Date2 of the test center. To test the performance of the algorithm in a big-data environment, Date1 and Date2 were synthesized according to the correlation coefficient, and Bayesian networks with 19 edges and 12 nodes and with 25 edges and 17 nodes were generated respectively to generate test data. Table 1 gives a partial raw data set in which data with the * symbol represent data to be extracted by generating a missing data element, and Table 2 represents the corresponding attribute of the actual missing data.
Probabilistic reasoning is the process of deducing unknown information from information with probabilistic properties. Probabilistic reasoning in Bayesian networks deals with two types of problems: the posterior probability and the maximum-posterior hypothesis problem. The former is used to calculate the posterior probability distribution of the unknown variables, whereas the latter is used to solve the combination of the values of the unknown variables to maximize the posterior probability. It is formally defined as a given evidence variable E = e, and the value of the query variable q* satisfying Eq. (3) can be found as follows: Q is successively equal to each missing variable, and its possible value can be inferred from known information.
When using large amounts of real-time data, serial processing is very slow, and therefore parallel computation is often used to calculate the inference probabilities of the data (Jin, 2013;Jin et al., 2013). The whole probabilistic inference process was divided into three parts: Para Collect, Para Estimate, and Impute, which served to collect parameters, to estimate parameters, and to fill in missing values, respectively, and which were executed sequentially.
After this, the corresponding probabilistic inference was made in the real missing data set. The three attributes of concentration, exhaust, and quality were selected, the Batch Normalization (BN) algorithm was executed on a parallel computer, and the obtained experimental results were compared (Farhangfar et al., 2007;Jin, 2013). Table 3 shows the test results. The data set used in this study was very large and would have been inconvenient to display and operate; therefore, small pieces of real data were used for comparison, but the algorithm was executed according to the original data set. The large real-time data of pollutants leads to a large number of nodes, but it cannot offset the advantage of running time obtained by the parent node and the child node in the Bayesian network, so as to improve the computing efficiency.
Next, the NOx correlation coefficients were analyzed by the data-filling methods, which were also used to fill in data for concentration, exhaust flow, and quality in the calculation process. In Table 3, pt/pf represents the average probability of "true" and "false" values of the three variables. Table 3 shows that the algorithm can effectively distinguish the "true" value from other low-probability values and obtain a probability closer to the actual truth value; Top represents  the proportion of the maximum probability of the truth value among all the alternative values among all the inferred filling values obtained by calculation. This discussion makes it clear that the reliability of this algorithm is represented by the probability value obtained by probabilistic reasoning. The higher the probability value, the closer the truth value is to the actual value, and the greater is the accuracy of the data filling.

Spatial Autocorrelation
Spatial autocorrelation refers to the potential interdependence between observed data points of some variables within the same distribution region (Martin, 1996). The spatial autocorrelation coefficient is used to measure the spatial distribution characteristics of physical or ecological variables and their influence on the field. It can also be used to characterize the spatial distribution characteristics of attributes. Urban bus exhaust emissions have obvious spatial distribution characteristics, and therefore the spatial autocorrelation analysis method is very suitable for analyzing the spatial distribution characteristics of these emissions. This study used the ArcGIS software to perform spatial autocorrelation analysis of pollutant properties.
Global spatial autocorrelation provides a description of the spatial characteristics of the observed values of variables over the whole study area. This analysis was performed to test whether the dependence degree of independent variables over the whole region has an aggregation effect. Global spatial autocorrelation statistical methods include Moran's I, Geary's C, and the Getis-Ord G. Moran's I index is the most commonly used and is calculated as in Eq. (4): where I is the global spatial autocorrelation index; y represents the observed value of a particular spatial unit; y̅ is the average value of this attribute value; n is the number of regional units; and ωij is the spatial weighting coefficient matrix, which represents the neighborhood relationship of each spatial unit. Local spatial autocorrelation refers to whether there is a correlation between the observed values in each spatial unit in the study area and its surrounding units. If there is no such property, the local spatial autocorrelation position that may be hidden will be discussed. If such a property exists, the spatial heterogeneity will be analyzed. The global Moran's I coefficient can reveal the aggregation degree of similar spatial attributes, thus indicating the degree of spatial correlation; however, it cannot identify the exact spatial location of an aggregation area. Local spatial autocorrelation can compensate for this deficiency (Zhao et al., 2009). The calculation of local spatial autocorrelation includes G statistics and LISA; in this study, local Moran's I (LISA) was used and can be calculated as follows: where Ii is the local autocorrelation coefficient of region i and ωij is the spatial weighting matrix.
The variation range of the global Moran's I index is between (-1,1). When Moran's I > 0, the study area presents positive spatial autocorrelation, and the attribute values present a clustered spatial distribution. As the Moran's I index becomes closer to 1, the positive correlation becomes stronger. When Moran's I < 0, the study area presents negative spatial autocorrelation, and the attribute values present a dispersed distribution pattern. As the Moran's I index becomes closer to -1, the negative correlation becomes stronger. A high value of local Moran's I indicates that regional units with similar variable values are clustered in space, whereas a low value indicates that dissimilar regional units are adjacent in space. When Moran's index is close to 0, there is no spatial autocorrelation between attribute values, and they are randomly distributed in space (Wang et al., 2014).

Temporal Distribution Characteristics
Figs. 2 and 3 show the NOx emissions of the No. 80 diesel bus in Kunming during the course of one week. Fig. 2 shows the all-day emissions characteristics of NOx on weekdays and Fig. 3 the characteristics on non-weekdays. Figs. 2 and 3 illustrate that there is no obvious regular emission characteristic discriminating between weekdays and non-weekdays. The pollutants show similar changes over time, that is, there are obvious distribution of high and low peaks in a given period. The peak hours were mainly around 7, 11, 17, and 21 and corresponded to the peak hours of morning, afternoon, and evening traffic flow. The overall emission levels on weekdays were higher than on non-weekdays, and this significant difference was consistent with overall traffic flow in cities on different days and the daily travel of pedestrians.
The time emission characteristics of NOx have obvious high and low peaks, which are similar to the conclusions of Tang et al. (2018) on the time distribution characteristics of pollutants emitted by motor vehicles in Hangzhou based on real emission data from the motor vehicle emissions management database. Because this article described the daily time variation characteristics from Monday to Sunday, compared with Tang et al.'s emission inventory based on annual and monthly changes, it can describe the emission characteristics of pollutants at different times of the day in more detail. In the course of the day, the changes in high and low peaks were more obvious in each time period, and the pollutant emission amounts in each time period were significantly different from those in other time periods. Therefore, this paper better reflects the temporal emission characteristics of pollutants.

Trends in Emissions during Working Days and Non-working Days
As shown in Fig. 4, NOx emissions on weekdays were higher than on non-weekdays as a whole, with the average bus speed on weekdays being approximately 26 km h -1 and that on nonweekdays being approximately 30 km h -1 . In the four peak areas, the rate of change of NOx on weekdays was higher than on non-weekdays; the reason for this lies in the fact that passenger flow is generally higher in the peak period on weekdays, and to increase passenger volume, ease traffic, and facilitate pedestrians, the departure frequency increase markedly in these time slots, leading to a significant increase in pollutant discharge in this period. Because there was no significant increase in human and vehicle flow on non-working days compared with that on working days, the dispatching frequency was relatively uniform. During the time periods of 16:00 and 20:00, the non-working-day emissions exceeded the working-day emissions; the former is due to the increase of NOx emission due to the increase of bus departure frequency, and the latter is to meet the increase of non-working-day pedestrian travel volume, in line with the pedestrian travel law.
There is an obvious "weekend effect" in the concentration of NOx in Kunming. The concentration of NOx on weekends is lower than that on weekdays. The research results are similar to the observation results of Huang (2011) in Shanghai and similar to the study results of Wu (2013) on the temporal-spatial distribution of NOx in Xi'an. NOx emissions in Xi'an were similar to those reported in this paper, and the peak alternation was obvious in different time periods according to the daily variation. The weekend effect of NOx in Kunming was closely related to the difference in human work and rest arrangements between weekends and weekdays (Tang et al., 2010). Volume 21 | Issue 6 | 200059

Spatial Emission Characteristics in Different Time Periods
The NOx autocorrelation coefficient for real-time operation of the Kunming No. 80 bus was calculated by the ArcGIS software, and its spatial aggregation and heterogeneity were also analyzed. The results were obtained from multiple random trials with the ArcGIS software, and the mean value was obtained, as shown in Table 4. The spatial autocorrelation coefficients of the four time periods were all positive and high, indicating that they had obvious aggregation characteristics in space; in other words, adjacent exhaust emissions concentrations were the same, showing an obvious spatial high-low aggregation pattern.
GIS spatial autocorrelation analysis showed spatial clustering or heterogeneity of points with higher or lower exhaust emissions, showing positive/negative global spatial autocorrelation, that is, the results of a comparison between the emission values of a spatial area and its surrounding areas. By combining these two analysis methods, the heterogeneity of NOx spatial distribution in four time periods (the morning hours are from 6 to 8, the noon hour is from 11 to 13, the afternoon time is from 16 to 18, and the evening session is from 20 to 22) located along the whole operation route was determined. Then the emission changes for different sections in the same time period were compared, and a brief analysis was performed on the influencing factors of emission changes for different sections in different time periods along the whole route. Fig. 5 shows a thermal diagram of the whole route at different time periods.
The platform, intersection, and traffic-light positions along the whole route are marked in Fig. 5(a). The spatiotemporal emission characteristics of the whole route were comprehensively analyzed by taking into account the main factors affecting pollutant emissions. Figs. 5(a), 5(b), 5(c), and 5(d) present heat maps of NOx emission concentrations and show that there were significant differences in NOx emissions at different time periods along the whole bus route during one day, according to the color intensity of the movement routes in the four time periods. The overall emission-level variation in the different time periods was obvious, which conformed to normal urban traffic flow and the actual traffic situation. In addition, different sections of the whole route during the same time period indicated an obvious emission color, and the whole driving route was affected by platforms, traffic lights, and intersections as shown in Fig. 5(a), resulting in obvious changes in emission levels along different sections of the whole route at the same time period.
According to the combined results of the four time periods in Fig. 5 and the spatial autocorrelation analysis in Table 4, the exhaust emissions at different time periods were significantly different, and the exhaust emissions at different sections during the same time period were obviously different, indicating an obvious time/space variation in bus exhaust emissions. According to the analysis results in Table 4, Moran's I coefficients were all positive, which indicated that the urban bus exhaust emissions presented clear spatial distribution characteristics in their particular road sections. Moran's I coefficient for NOx was lower in the morning and at night, indicating that unit spaces of dissimilar regions were adjacent. In other words, the distribution of sample points was dispersed and had some spatial heterogeneity, and the emissions concentration was low. Moran's I coefficient for NOx was higher at noon and in the afternoon, indicating that its sample point distribution was relatively clustered and its spatial clustering is relatively obvious, especially in the afternoon. The local spatial autocorrelation coefficient was as high as 0.935, indicating that regional units with similar variables were spatially clustered. The main reason for this situation was that the No. 80 bus runs at idle speed and low speed for a long time during the evening rush hour. The starting point is located at the railway station and the passenger station is near the terminal. At rush hour in these areas, the flow of people and cars peaks for the day, and the emissions reach their daily maximum.
The results of pollutant autocorrelation analysis are consistent with the spatial distribution of pollutants obtained by Li and Zhang (2011), which had obvious spatial clustering characteristics. The results of the thermal map analysis are similar to the results for the thermal map of the Beijing motor vehicle emissions network made by Guo et al. (2017). High emission intensity and high emissions occur at road sections (platforms, traffic lights, and intersections) where abnormal values of traffic flow appear, and the emissions change significantly in each section. Fig. 6 shows the distribution characteristics of NOx on the corresponding sections of the entire bus route at different times. Fig. 6 shows that NOx emissions are significantly different in different sections at different times. The emissions from Sections 1-3 and 5-8 at different periods were significantly higher than those of other sections at the same time because the emissions of Sections 1-3, including the starting-point railway station, a section with all-day traffic congestion, and sections with multiple intersections and traffic lights, were significantly higher than those from other sections. The four Sections 5-8 pass through a dense residential area, although there were no heavily congested intersections or intersections with traffic lights. Due to this environment, driving conditions became more complicated, the bus was always moving at low speed and idle speed, and frequent deceleration to yield to pedestrians and frequent acceleration to start and  leave from a stopped condition increased significantly. Because of these conditions, the emissions from this section of road were high throughout the day, which was consistent with the actual traffic conditions, and therefore it was a high-emission section.

Emission Intensity of Each Section
Exhaust emission intensity reveals the impact of pollutants on surrounding pedestrians and residents. The greater the exhaust emission intensity, the greater is the harm that it will do to surrounding residents and pedestrians. Fig. 7 shows the time-space variation characteristics of NOx emission intensity at different sections during different time periods. NOx emissions on roads containing major intersections and adjoining dense residential areas were 1.8-3.2 times higher than average, and the NOx emission intensity of the road section containing the main intersections was 0.5-1.2 times the average value, whereas the NOx emission intensity of the road section containing dense residential areas was 2-3.8 times the average. During the peak period, NOx emissions were 1.5-2.8 times the average, and the NOx emissions intensity was 1.1-1.8 times the average. Combining the effects of NOx emission intensity, emissions, and time, it was found that NOx emissions in dense residential areas and those containing major intersections increase the hazard to pedestrians by 3-8% (dense residential areas) and by 15-33% (road intersections).  Fig. 7 shows that the highest intensity of NOx emissions during the day occurred in the afternoon, followed by noon, then evening, and finally morning, which was consistent with the spatiotemporal emission characteristics of the whole road section as described above. In Fig. 7, the rates of change of emission intensity in Sections 6-8 at each period were 2.56, 5.31, and 3.04 kg km -2 , respectively, representing high emission intensity. Because these five roads are located in complex and dense residential areas, platforms have been built relatively close together to facilitate travel by surrounding residents, and as a result, the length of each road section is relatively short, being 390, 301, and 296 m respectively. Therefore, the emission intensities of Road Sections 6-8 are 1.1, 2.7, and 1.9 times higher than average, respectively, mainly because short road sections have been set up for the convenience of surrounding residents. NOx emissions in each time period were similar to those reported by Li et al. (2017) in their study on vehicle emissions inventory in Foshan. In the morning, at noon, and in the afternoon, the pollutant discharge rate was high, and the pollutants reached their daily peak around 17:00. However, the difference in this study was the identification of an evening pollutant discharge peak instead of a slow decline from 17:00 onwards.

CONCLUSIONS
This study investigated the spatial and temporal distribution of NOx emissions exhausted by diesel buses by applying spatial autocorrelation to emission data-specifically, heat maps based on the temporal variation, intensity, and quantity of the emissions-for the Kunming No. 80 bus. The following conclusions can be drawn: (1) In this paper, Bayesian network and probabilistic reasoning are used to fill the data of concentration, exhaust and quality. The results show that the true probability of Date1 is 0.94, 0.89, and 0.92, respectively, and the true probability of Date2 is 0.86, 0.76, and 0.79, respectively. By selecting true values with high probabilities-96%, 90%, and 93% for the first set and 92%, 85%, and 84% for the second-we reduced errors in filling the data, thereby drastically enhancing the accuracy of our calculations. (2) The concentrations of the NOx emissions exhibited obvious peaks and troughs throughout the day, and the quantity of discharged pollutants clearly varied between high-and low-emission periods.
(3) The heat maps for the afternoon and evening revealed higher pollutive emissions, and during these periods, all of the nodes and roads displayed a high-emission trend. However, during the morning and evening, the pollutants displayed a lighter color and sparser distribution, and the emissions were lower and less varied over the entire route. The spatial autocorrelation indices for the morning, midday, afternoon, and evening-0.648, 0.836, 0.935, and 0.798, respectivelyindicated spatial correlation between the four periods as well as a degree of heterogeneity during the morning and evening for the NOx, although the aggregation of this species was difficult to observe owing to the time constraints. (4) Sections 1-3 and 6-9 produced large emissions during every period and contributed to the majority of the pollutants measured along the entire route. The highest and fastest-growing emission intensity was found on the road segment comprising Sections 5-9, though.

ACKNOWLEDGMENTS
The authors gratefully acknowledge financial support from National Natural Science Foundation of China (51968065)

DISCLAIMER
Reference to any companies or specific commercial products does not constitute an endorsement, recommendation or favoring by the company.