Exploring Urban Air Quality with MAPS: Mobile Air Pollution Sensing

# Exploring Urban Air Quality with MAPS: Mobile Air Pollution Sensing

Jun Song Ke Han

Department of Civil and Environmental Engineering,
Imperial College London, London SW7 2BU, UK

Corresponding author: k.han@imperial.ac.uk
###### Abstract

Mobile and ubiquitous sensing of urban air quality (AQ) has received increased attention as an economically and operationally viable means to survey atmospheric environment with high spatial-temporal resolution. A necessary and value-added step towards data-driven sustainable urban management is fine-granular AQ inference, which estimates grid-level pollutant concentrations at every instance of time using AQ data collected from fixed-location and mobile sensors. We present the Mobile Air Pollution Sensing (MAPS) framework, which consists of data preprocessing, urban feature extraction, and AQ inference. This is applied to a case study in Beijing (3,025 km, 19 June - 16 July 2018), where PM2.5 concentrations measured by 28 fixed monitoring stations and 15 vehicles are fused to infer hourly PM2.5 concentrations in 3,025 1km1km grids. Two machine learning structures, namely Deep Feature Spatial-Temporal Tree (DFeaST-Tree) and Deep Feature Spatial-Temporal Network (DFeaST-Net), are proposed to infer PM2.5 concentrations supported by 62 types of urban data that encompass geography, land use, traffic, public, and meteorology. This allows us to infer fine-granular PM2.5 concentrations based on sparse AQ measurements (less than 5% coverage) with good accuracy (SMAPE, R), while accounting for the regional transport of air pollutants outside the study area. In-depth discussions are provided on the heterogeneity of fixed and mobile data sources, spatial coverage of mobile sensing, and importance of urban features for inferring PM2.5 concentrations.

Keywords: air quality; ubiquitous sensing; big data; machine learning

## 1 Introduction

Severe deterioration of urban air quality (AQ) around the globe, especially in developing countries due to aggressive urbanization and motorization, has posed barriers to economic development and major threats to public health. Health Effects Institute (2018) estimates that 95% of the world’s population is exposed to air quality considered unsafe by the World Health Organization (WHO). WHO further estimates that 3.7 million deaths in 2012 were caused by outdoor air pollution, nearly 90% of which were in developing countries. In China, up to 1.3 million deaths per year are due to air pollution, and the monetary value based on death and illness is $1.4 trillion in 2010 and rising. In the United Kingdom, an estimated 40,000 people per annum die prematurely due to air pollution. Detailed information about air pollution, including its sources and dynamics on a city scale, is of critical importance to public health and sustainable urban management (Lü et al., 2015). For decades, fixed-location AQ monitoring stations have provided AQ information for various purposes including information dissemination, AQ inference/prediction, and policy appraisal. In the case of Beijing, as shown in Figure 1(a), 21 fixed AQ monitoring stations administered by the National Meteorological Information Center (NMIC) are located in a 3,025-km area, offering hourly measurements of gaseous pollutants (NO, CO, SO, O) and particulate matters (PM2.5, PM10). Local AQ in urban areas varies in relatively small temporal and spatial scales, driven by a combination of factors including meteorological conditions, land use types, geographical features, transport and population activities. Figure 1(a)-(b) show two adjacent fixed monitoring stations in Beijing and their PM2.5 measurements. Exhibiting similar trends, however, the two time series show considerable differences for certain times. This is caused by local variation of AQ that cannot be adequately observed by sparsely distributed monitoring stations. Mobile sensing has the potential to provide denser coverage and more detailed information on AQ with finer spatial and temporal granularities. Mobile and ubiquitous air quality sensing has received increased attention recently as an economically and operationally viable means to survey urban atmospheric environment based on portable, low-cost sensors (Chong and Kumar, 2003; White et al., 2012). Compared to fixed monitoring stations, the network of mobile sensors has the potential to offer high-resolution and dense coverage of urban atmospheric environment at a comparatively low capital cost (Kumar et al., 2015). The mobile AQ measurements of gaseous air pollutants and particulate matters can be communicated wirelessly to a central server for processing, analysis, and applications (US DoE, 2010). A number of initiatives have taken place world wide to collect AQ information based on mobile sensing and communication technologies, as reported by Wallace et al. (2009), Wang et al. (2009), Mead et al. (2013), Maag et al. (2018) and Alvear (2018). We refer the reader to Kumar et al. (2015) for a comprehensive review and discussion of mobile AQ sensing. The global market for ubiquitous AQ sensing is rapidly expanding with a 14.3% compounded average growth rate, reaching$530m by 2024 (Industry Research, 2019). In China, which has one of the largest AQ sensing markets, government investment and private funding are unmatched by the technological development (e.g. in data science and machine learning), which is the key driver towards the next generation of intelligent AQ management systems. Among the first to bridge this gap, this paper combines mobile/fixed AQ sensing with urban big data and machine learning to infer fine-granular (1km1km, hourly) PM2.5 concentrations in a large urban space (Beijing, 3,025 km). The fixed AQ data were collected by 21 NMIC monitoring stations as well as seven micro stations; see Figure 1(a). The mobile AQ data were collected by 15 probe vehicles traveling throughout the city of Beijing in 28 days; see Figure 1(c)-(e). This combined coverage of fixed and mobile AQ sensing is the largest of its kind in terms of spatial extent and granularity, which offers detailed AQ information in large urban space not previously seen in similar studies (Zheng et al., 2013; Marjovi et al., 2017; Qi et al., 2018). Furthermore, since local AQ is influenced by a number of factors, AQ inference requires comprehensive datasets that characterize relevant urban features (see Table 1 and Figure 5).

Figure 2 illustrates the grid-based (1km1km) PM2.5 concentrations in Beijing on 25 June 2018 from 7:00-21:00. The top of the figure shows the hourly average PM2.5 concentration in the city (published by the NMIC), which shows similar increasing trend as the images produced by the proposed method. However, the latter suggest significant spatial variations, which warrants ubiquitous sensing and fine-granular spatial inference to inform the public and support policy making. This paper offers a methodological framework and empirical findings that constitute the first scientific guideline for the deployment of mobile AQ sensing and grid-based AQ inference.

The rest of the paper is organized as follows. Section 2 reviews some relevant literature and highlights the key challenges in data-driven AQ inference, followed by contributions made in this paper. Section 3 sets out the main objectives and illustrates the overall framework of this paper. We provide a detailed description of data used in this study in Section 4. Section 5 details the machine learning framework. The Beijing case study is presented in Section 6, followed by some concluding remarks in Section 7.

## 2 Related work, technological barriers, and solutions

### 2.1 Bottom-up air pollution models

The environmental science community has been studying the emission, chemical interaction and physical transport of air pollutants using a bottom-up approach, based on knowledge of the emission source and a number of theoretical or empirical assumptions. For example, the Gaussian Plume Dispersion Model (Gibson et al., 2013) has been applied to roadside dispersion modeling based on vehicle emission rates and the assumption that the pollutants disperses in both vertical and horizontal directions (Zhang et al., 2013). The Operational Street Pollution Model (Hertel et al., 1991) is an atmospherical simulation model for street canyons, which combines the Gaussian Plume Model with a box model that account for the recirculation of pollutants in the streets (Ottosen et al., 2015). The Gaussian-type models rely on the stationarity assumption, which limits its applicability to instantaneous or time series-based emissions and AQ data. Computational Fluid Dynamic Models (Chu et al., 2005; Parra et al., 2010) uses differential equations and numerical schemes to simulate fluid or gas flows with boundary conditions defined by data. This has been widely implemented in software (Glatzel et al., 2008), but typically involves significant computational time and memory consumption. Chemical Transport Models (Simpson et al., 2012) predicts air quality by simulating chemical processes involving multiple species in the atmosphere. It can be also used with an inversion approach to estimate gas emissions on a global scale (Chen and Prinn, 2006). The CMAQ model and software (EPA, 2019) target multiple pollutants at multiple scales, and offer decision support tools to assess the impact of AQ related management measures. These bottom-up models offer high model fidelity pertaining to the physical and chemical processes of air pollution, but they tend to be computationally expensive and rely on assumptions that limit their integration with high frequency and ubiquitous AQ sensing data.

### 2.2 AQ inference and prediction based on machine learning

In contrast to the bottom-up approach, another line of research aims to infer and predict AQ by learning its spatial and temporal correlation with explanatory factors such as urban layouts, traffic activities, and meteorological conditions, using machine learning techniques. Zheng et al. (2013) propose a spatial-temporal classifier and a co-training framework to infer the air quality index in Beijing using fixed-location sensing data. Qi et al. (2018) also consider fixed monitoring station data in Beijing to infer and predict PM2.5 concentrations based on semi-supervised learning. Mobile air quality sensing has been recently introduced to AQ inference. Marjovi et al. (2015) use mobile data collected in Lausanne, Switzerland, and built a Probabilistic Graphical Model for street-level estimation of Lung-Deposited Surface Area. However, such estimation is limited to street segments within the coverage of mobile sensors, and the probabilistic approach does not perform well with temporally and spatially sparse mobile data, which hinders deployment in large metropolitan areas. Hu et al. (2017) apply several regression methods to estimate CO concentration surface in Sydney based on fixed and mobile sensing data, but without using any additional explanatory data or urban features to reasonably generalize their results beyond statistical fitting. Marjovi et al. (2017) propose a deep learning framework for inferring AQ based on multiple data sources. However, such estimation results are restricted to the street level, with limited temporal resolution (daily, weekly, monthly). These studies have advanced data-driven tools for estimating air quality based on ubiquitous sensing, but there is still a lack of AQ inference framework that is capable of producing fine-granular pollution maps (1km1km, hourly) based on fixed and mobile sensing data with limited spatial-temporal coverage, while ensuring the robustness and accuracy of the results by leveraging multi-source urban datasets.

### 2.3 Machine learning based on spatial-temporal data

The proliferation of urban big data in the past decade, enabled by information and communication technologies and pervasive sensing, has resulted in rapid development of spatial-temporal data analytics (Birant and Kut, 2007) and computational architectures (Tang et al., 2015). Studies have proposed different ways to capture spatial and temporal correlations, either separately or jointly. Deep neural networks such as Long-Short-Term Memory (LSTM) allow long-term temporal dependencies as well as short-term variations to be simultaneously captured in time-series prediction (Zhao et al., 2017). Zhang et al. (2017) forecast the flow of crowds in an urban area using convolutional neural networks (CNN) by viewing traffic intensity in a region as a pixel on an image. The model can make short-term predictions through learning historical images representing the same traffic quantity over time. Shi et al. (2015) combine CNN with LSTM (ConvLSTM) to perform precipitation nowcasting, where both the input and prediction target are spatial-temporal sequences. Yao et al. (2018) predict spatial and temporal taxi demands using historical data based on a Multi-View Spatial-Temporal Network to simultaneously capture spatial correlations and temporal dependencies as well as semantic relations. However, we note that in all these studies, either the training labels are available for the entire spatial domain at a particular time (e.g. precipitation, taxi demand), or they are available at several discrete locations with non-interrupted time series (e.g. fixed-location AQ sensing, traffic flow). None of these studies have considered problems like mobile sensing based AQ inference, which on its own presents a challenge in that the training labels are irregularly distributed in the space-time domain.

### 2.4 Key challenges in air quality analyses based on mobile sensing

AQ inference based on fixed and mobile sensing has met the following challenges.

1. Unlike AQ inference and prediction based on fixed monitoring stations, where the labels are continuously observable over a period of time at a given location, mobile sensing renders sparse and irregularly distributed labels in space and time, depending on the trajectories of the probe vehicles.

2. Mobile sensors need to be calibrated based on reference instruments to correct bias for ambient temperature and relative humidity effects (Mead et al., 2013), which has been done in our mobile datasets. However, due to different surveying environments of the sensors, noticeable difference exist between mobile (street-level) and fixed (typically on high grounds or secluded areas) measurements. Therefore, fusing fixed and mobile data needs to account for the heterogeneity of their sources.

3. Model overfitting is a risk due to either limited testing datasets (as in the case of fixed sensing), or unbalanced representation of relevant factors that influence urban AQ. It is crucial to consider datasets with a comprehensive coverage of urban characteristics relevant to pollutant concentrations.

4. Existing machine learning methods for AQ inference only consider influencing factors within the study area, overlooking pollutants transported from nearby regions (in Beijing, up to 60% of air pollution is caused by regional transport in March 2019). Relying solely on endogenous factors to infer AQ results in low accuracy and high risk of overfitting, and compromises the interpretability of the results.

### 2.5 Significance of this paper

This paper tackles the aforementioned challenges by proposing a Deep Feature Spatial-Temporal (DFeaST) learning framework based on a wide variety of urban datasets including geographical, land use, transportation, population, and meteorological features. In addition to these endogenous features, data from 12 monitoring stations outside the study area are used to formulate macro features, which allow the machine learning model to account for pollution attributed to regional transport. The machine learning framework is flexible in accommodating sparse and irregular distribution of labels in the space-time domain, and is capable of learning fixed and mobile AQ labels while taking into account the potential heterogeneity of their sources (such as different elevation of the sensors). The main contributions of this paper are as follows.

1. We propose two learning structures for AQ inference based respectively on boosted decision trees (DFeaST-Tree) and Fully Convolutional Networks (DFeaST-Net). Both frameworks employ the technique of convolution to efficiently and automatically capture the main spatial-temporal features extracted from urban datasets. Moreover, the proposed methods can accommodate irregularly and sparsely distributed PM2.5 labels.

2. To address the inherent inconsistencies between fixed and mobile sensing data, we propose a method to correct 111In this paper we use the word ‘correction’ to avoid confusion with the calibration process widely adopted in mobile air quality sensing. Note that the mobile measurements have already been calibrated before used for this research. grid-level mobile data based on location, time of day, temperature and relative humidity. The correction is meant to reduce noises introduced by the discrepancies between fixed and mobile data. AQ inference with and without (in which case a categorical feature is introduced to distinguish the two sources) such correction are compared and discussed in depth.

3. Among existing literature of AQ inference and prediction based on machine learning, this paper is the first to consider data sourced beyond the study area to account for the regional transport of air pollutants. Such information, which is coined macro feature in this paper, not only improves the inference accuracy by reducing overfitting over internal features defined within the study area, but also offers quantifiable evidence for pollution attribution.

4. In a case study in Beijing, we use 62 types of urban data, covering geography, land use, transport, public, and meteorology, to infer hourly PM2.5 concentrations for 1km1km grids in a 3,025 km area. The proposed methods are compared with several benchmarks and show superior accuracy (SMAPE , R). To our knowledge, this paper offers the first high-resolution, grid-based PM2.5 maps for a large metropolitan area based on fixed and mobile sensing data.

5. Based on the case study, we provide in-depth discussions on the reconciliation of fixed and mobile data, impact of mobile sensing coverage, and importance of urban and macro features. Intuitive interpretation of the inference results are included to demonstrate the suitability of the machine learning framework for the intended purpose.

This paper offers insightful findings on the deployment of mobile AQ sensing infrastructure and treatment of mobile AQ data. It is found that mobile PM2.5 data tend to be higher than those measured by nearby NMIC stations. While correcting the mobile data using fixed-location data (in other words, reconciling the two), which is a widely seen practice, leads to improved inference accuracy, the results should not be treated as ground-level concentrations. This paper presents a method to perform ground-level AQ inference without reconciling fixed and mobile data, which yields similarly accurate results with greater interpretability. A sensitivity analysis on the coverage of mobile sensing suggests that less than 5% of fixed/mobile sensing coverage (see Figure 3) is sufficient to reach SMAPE and R based on the proposed methods. To our knowledge, these findings constitute the first quantifiable guidance for the deployment of mobile AQ sensing.

## 3 Preliminaries

### 3.1 Scope of work

The main purpose of this study is to infer fine-granular urban air quality conditions. In particular, we focus on the concentration of PM2.5 as it has highly adverse health effects and increases mortality risks to the public under long-term exposure. Findings made in this paper will not only provide scientific and detailed assessment of public exposure, but also provide authorities with evidence-based strategies for sustainable urban planning and management.

The study area is a 55km55km square in Beijing, covering the Sixth Ring Road as shown in Figure 1(a). This is divided into 3,025 1km1km spatial grids. The temporal scope is 7:00-24:00 (18 hours per day) for 28 days (2018/06/19 to 2018/07/16), with an hourly resolution. All the PM2.5 concentration and urban features will be represented in terms of the spatial-temporal units defined below.

###### Definition 3.1.

(Unit) Let be the set of 1km1km spatial grids in the study area, and be the set of 1-hr time periods. We have that , (hrs/day) (days) (hrs). A unit refers to an element .

###### Definition 3.2.

(PM2.5 Inference) Given the subset containing labeled units, where we use to denote the average PM2.5 concentration (obtained via fixed or mobile sensing) of unit , the problem of PM2.5 inference is to estimate the PM2.5 concentrations for all .

###### Definition 3.3.

(Feature) Given the spatial grids, a static feature is a matrix characterizing certain aspect of the individual grids (e.g. POI, transportation infrastructure). A dynamic feature is a tensor describing the location-specific dynamics of certain quantity (e.g. traffic congestion, relative humidity).

To get a sense of the scale of the PM2.5 inference problem, in Figure 3(a) we show the number of labeled units at every hour throughout the study period. The hourly sensing coverage is mostly between 50 and 150 spatial grids, which is less than 5% of the total study area, hence spatial sparsity. Furthermore, Figures 3(b-d) illustrate the temporal sparsity of mobile sensing. The challenge posed by sensing data sparsity is addressed in this paper by exploring their spatial-temporal correlations at different units in conjunction with the various urban features, as outlined in the next section.

### 3.2 Overall framework

Figure 4 shows the key components and process flow of the MAPS system, which consists of three main components.

• Collection and pre-processing of AQ sensing data, which include fixed/mobile PM2.5 measurements and relevant information (time, coordinates, temperature, relative humidity). Data pre-processing involves noise reduction and removal of invalid measurements, as well as correction of the mobile data using fixed-location data. This part is detailed in Section 4.1 and Appendix A.

• Urban feature extraction, which expresses internal or external factors that affect or indicate PM2.5 concentrations. A total of 52 static and 10 dynamic features under four main categories are used to represent emission sources, urban characteristics and external factors that are related to local air quality. The explicit spatial or temporal characteristics of these urban features allow machine learning algorithms to capture the spatial-temporal correlations of pollutant concentration, which is crucial for AQ inference. This part is detailed in Section 5.1.

• Data fusion and AQ inference based on the DFeaST framework, which combines structured AQ data with urban features to learn their interdependencies in space and time. This allows us to not only infer PM2.5 concentrations in the entire study area, but also understand their relationships with urban features on a quantitative level, which serves as the scientific basis for pollution attribution. This part is detailed in Section 5.

## 4 Data description

### 4.1 Air quality measurements

The 21 NMIC stations and 7 micro-stations within the study area provide hourly concentrations of particulate matters (PM2.5, PM10) and inorganic gaseous pollutants (CO, CO, SO, NO), along with meteorological parameters (temperature, wind speed and direction, relative humidity, pressure, and water vapor pressure). The mobile AQ data include PM2.5 and PM10 concentrations as well as temperature and relative humidity, which are collected by mobile sensors. The trajectories of the 15 vehicles that carry the mobile sensors have been map-matched onto streets; see Figure 1(c). The collection period of the mobile data is 7:00-24:00 (18 hours) from 2018/06/19 to 2018/07/16 (28 days).

The mobile PM2.5 measurements were pre-processed, geo-meshed and aggregated into units, before corrected using fixed-location data as references; more details are presented in Appendix A. The unit-based spatial and temporal coverage of the fixed/mobile sensing is illustrated in Figure 3. Although mobile sensing offers far greater spatial coverage than fixed sensing, the former provides temporally sparse measurements for a given spatial grid; see Figure 3(b)-(c). While such sparsity can be remedied by deploying more mobile sensors, which is costly, it remains a challenge to fuse fixed and mobile data for AQ inference, given their heterogeneous spatial-temporal characteristics.

### 4.2 Multi-source urban datasets

An overview of various urban datasets considered in this paper for AQ inference is provided in Table 1.

Geography & Land Use - includes land use type (e.g. building, factory, commercial area) and points of interest (POI). 21 categories of POIs are considered, which include restaurants, shopping, schools, hotels, firms, scenic spots etc. Within a 1km1km spatial grid, the numbers of different types of POIs, as well as the percentages of landmass they occupy (Area of Interest, AOI) are calculated. In addition, the percentages of green and water covers, as well as digital elevation are included to further characterize the geographic features of the grid.

Transport - contains static road network structure and dynamic traffic conditions. Within a 1km1km spatial grid, the road network information contains number of signalized intersections and the lengths of primary, secondary, tertiary and quaternary roads. These static features are related to traffic volume and fleet composition, as well as the frequency of stop-and-go driving cycles, which are known to contribute to vehicle emissions. The dynamic traffic information is represented by the percentages of roads with light, medium and heavy traffic conditions. Such a categorical feature is a direct indicator of congestion levels, and is related to vehicle speed and emissions.

Public Vitality - refers to the intensity of social media activities enabled by Location Based Services (LBS). These include Wechat and Sina Weibo log-ins, posts and comments, which are indicators of public vitality in the area. The public vitality data are deemed relevant to instantaneous population density and indirect indicators of land use type (such as business districts and rural areas). The Wechat data is hourly based and the Sina data is aggregated into annual average based on the period Jun 2015 - Jun 2018.

Meteorology - contains hourly information of local temperature, pressure, relative humidity, wind direction and speed, which are measured at 13 meteorological stations (9 within the study area). The hourly meteorological data were used to spatially interpolate grid-based quantities using the inverse distance weighting method.

The aforementioned urban datasets are pre-processed and aggregated into units (or grids if they are static). Some examples of these processed urban features are shown in Figure 5.

## 5 Deep Feature Spatial-Temporal framework for AQ inference

The PM2.5 concentration of a given unit is temporally dependent on, and spatially correlated to, its adjacent units in the space-time domain. Unlike AQ inference based on fixed monitoring stations (Zheng et al., 2013; Qi et al., 2018), the labels provided by mobile sensing are sparsely and irregularly distributed in the space-time domain; see Figure 3(d) for example. To tackle this challenge, we propose two learning structures, respectively named Deep Feature Spatial-Temporal Tree (DFeaST-Tree) and Deep Feature Spatial-Temporal Network (DFeaST-Net). The former is based on boosted decision trees (GBDT/XGBoost), and the latter is based on a Fully Convolutional Network (FCN). Both structures rely on carefully devised feature space to account for the spatial-temporal correlations of the physical characteristics of urban units.

### 5.1 DFeaST-Tree

The problem of urban air quality inference based on fixed/mobile sensing involves multi-source and heterogenous datasets that significantly differ in space-time resolution, numerical scale, and veracity. Therefore, it is crucial to define and extract relevant features with appropriate spatial and temporal structures to capture not only internal factors contributing to local AQ (such as transportation, buildings, meteorology), but also indicators of external influence (such as regional pollutants transport). We propose a feature extraction framework illustrated in Figure 6. In particular, three types of features are considered: local, neighboring and macro features.

#### 5.1.1 Local features

Local features include geographic & land use characteristics, transport, public vitality, and meteorological conditions (see Section 4.2) that are defined for each unit. The local features alone do not take into account spatial and temporal correlations among the urban features and PM2.5 concentrations.

#### 5.1.2 Neighboring features

Neighboring features are defined for each given unit, by including features of neighboring units in space and time. This allows us to capture the spatial-temporal correlations among the urban features. The extraction of neighboring features follows the technique of convolution (Nielsen, 2015), and we distinguish between static and dynamic features as follows.

The static features ( in our case study) are treated as input images of size , forming an input volume . Two sets of filters, and are applied to with stride 1 and padding 0 ( in our case study). Specifically, the -th channel (or ) of (or ) is a mean filter multiplied by a random weight:

 Aik=wik×19×1(3,3),Bik=ωik×125×1(5,5)1≤i≤L,1≤k≤Ns

where and are i.i.d following standard Normal distribution. denotes the matrix of one’s. Convolution with these two sets of filters, followed by the rectifier as activation, results in two feature maps

 VA=⊕(V1A,…,VLA),VB=⊕(V1B,…,VLB) (5.1)

where

 ViA=f(V∗Ai),ViB=f(V∗Bi)1≤i≤L (5.2)

Here, is the convolution operator; is the concatenation operator. The mean filters perform arithmetic average within their receptive fields, while the random weights are used to sample different combinations of the input features. Finally, the output is ; see Figure 6(top).

The dynamic features ( in our case study) are convolved in a similar way. For every time , the input volume consists of the dynamic features of the present and previous time steps to account for the temporal dependencies. We then apply three sets of filters , , , ( in our case study) as follows: For ,

 Cik=vik×1(1,1),  Dik=νik×19×1(3,3),  Eik=μik×125×1(5,5)
 VtC=⊕(Vt,1C,…,Vt,MC),  VtD=⊕(Vt,1D,…,Vt,MD),  VtE=⊕(Vt,1E,…,Vt,ME) (5.3)
 Vt,iC=f(Vt∗Ci),Vt,iD=f(Vt∗Di),Vt,iE=f(Vt∗Ei) (5.4)

The output for time is ; see Figure 6(middle).

#### 5.1.3 Macro features

In many cities in China and around the globe, poor air quality may be caused by power production and industrial and agricultural activities surrounding populated areas. To account for the regional transport of pollutants without significantly expanding our study area, we utilize PM2.5 data from fixed monitoring stations outside the study area as additional features (coined macro features). Our premise is that such data are likely to be temporally cross-correlated (that is, with possible time lags) with the background pollutant concentration in Beijing. By introducing the macro features, we also reduce the risk of model overfitting as the AQ inference results are less dependent on locally defined features.

We collect PM2.5 concentration data from 12 NMIC stations outside the study area as shown in Figure 6(bottom). By analyzing these time series with time shifts depending on the distance of the stations and average wind speed, we may indirectly account for the transport dynamics of PM2.5. Specifically, , let be the hourly time series provided by the -th NMIC station. For a given time , we define the macro features for units as , where is the set of backward time shifts ( (hrs) in our case study). Alternatively, the macro features can be viewed as a set of images:

#### 5.1.4 Hybrid boosted decision trees

DFeaST-Tree uses the aforementioned inputs, including local, neighboring and macro features, to perform AQ inference based on boosted decision trees such as Gradient Boosting Decision Trees (GBDT) and XGBoost. GBDT is a nonlinear regression and classification method based on an ensemble of weak learners (decision trees) (Friedman, 2000). XGBoost builds on GBDT by further supporting distributed processing frameworks and offering a number of improvements including additive training and column subsampling (Chen and Guestrin, 2016). Both frameworks are capable of learning complex differentiating features or their combinations.

We further consider a hybrid model that combines boosted trees with linear regression to effectively explore high-dimensional feature space with learning efficiency that surpasses either component on their own (He et al., 2014). In this hybrid model, the GBDT/XGBoost-based transformation is used as supervised feature encoding, and the combination of features associated with each leaf (path) is used directly as the input feature of linear regression. The overall learning structure of DFeaST-Tree is summarized in Algorithm 1.

### 5.2 Deep Feature Spatial-Temporal Network (DFeaST-Net)

DFeaST-Tree relies on pre-processed features (local, neighboring and macro) to capture the spatial-temporal correlation of urban characteristics related to AQ inference. In this section we propose a streamlined approach based on Fully Convolutional Network (FCN), which iteratively and automatically updates the weights of the filters through a loss function and back-propagation. This process is illustrated in Figure 7.

There are a total of dynamic, static, and macro features ( in our case study). Given any , the FCN first convolves around an input volume consisting of dynamic, static and macro features associated with the time . Two sets of filters, and ( in our case study) are applied with learnable parameters (the same parameters are used for all the time steps), followed by the rectifier to yield two feature maps . The two feature maps correspond to different receptive fields of the filters. We further incorporate feature maps from the previous time step to account for the temporal dependencies:

 Yt=⊕(VtF,VtG,Vt−1F,Vt−1G)∈R55×55×4P,

We then apply another convolution layer with a filter with learnable parameters , followed by the rectifier to yield the final output map for time .

Unlike many other spatial-temporal machine learning problems, the training labels in our case are distributed irregularly in space and time, depending on the trajectories of the probe vehicles. To address this, we apply a Label Mask, which filters invalid output elements in based on the training labels.

The loss function is defined via the symmetric mean average percentage error (SMAPE), as

 Loss(σ,λ)=∑i∈UL(Ti−Ii)2(Ti+Ii)2 (5.5)

where denotes the set of units with training labels; and are respectively the true and inferred values. The training procedure of DFeaST-Net is summarized in Algorithm 2.

## 6 Case study

### 6.1 Experimental setup

In the Beijing case study where and , a total of 46,032 units were labeled (with either fixed or mobile sensing), of which 20% (9,200 units) were held as an independent test set (as part of the cross validation). The test data are evenly sampled at each time step .

The following metrics of accuracy are considered:

 MAE=1NN∑i=1|Ti−Ii|,RMSE= ⎷1NN∑i=1(Ti−Ii)2,SMAPE=2NN∑i=1|Ti−Ii||Ti+Ii|×100%

where MAE, RMSE and SMAPE stand for mean absolute error, root mean square error and symmetric mean average percentage error, respectively. is the number of test points, and and are ground-truth and inferred PM2.5 concentrations of a given test unit. Furthermore, we use R between inferred results and ground truth to indicate the level of spatial-temporal variations in the PM2.5 concentrations that are accounted for by the inference methods.

The following benchmarks are tested alongside the proposed methods for comparison:

• Spatial interpolation (SI) are applied to infer PM2.5 concentrations for every based on two well-known methods: Inverse Distance Weighting (IDW) and Kriging. The spatial interpolation makes no reference to the urban features.

• K-Nearest Neighbors (KNN) is a regression method that uses the nearest training points in the feature space to perform inference.

• Support Vector Regression (SVR) performs nonlinear regression with kernels given by the Radial Basis Function, based on similar principles of the Support Vector Machine classifier.

• DFeaST-Tree is applied to AQ inference using GBDT and XGBoost+LR with different combinations of local, neighboring and macro features.

• DFeaST-Net is applied with local and macro features.

Finally, we note that the fixed and mobile sensing data are treated in two different ways:

• The PM2.5 data source is distinguished using an additional categorical feature (i.e. fixed or mobile), which is converted using one-hot coding. In this case the mobile data are not corrected.

• The mobile PM2.5 data are corrected based on fixed-location data as detailed in Appendix A. In this case we no longer distinguish between fixed and mobile data for the machine learning.

### 6.2 Performance of different methods and feature inputs

Table 2 compares the different methods using different combinations of the local (L), neighboring (N) and macro (M) features. In this table, all the grid-based PM2.5 data are distinguished by their sources (fixed or mobile).

The results in Table 2, all based on 5-fold cross validation, clearly show superior performance of DFeaST-Tree and DFeaST-Net over the benchmark methods in terms of all four performance metrics. In addition, comparing ‘L’ with ‘L+M’, or ‘N’ with ‘N+M’, clear shows that the macro features significantly improves the accuracy regardless of the methods used. Furthermore, within the DFeaST-Tree framework the neighboring features ‘N’ (or ‘N+M’) outperforms the local features ‘L’ (or ‘L+M’), suggesting that it is important to capture the spatial and temporal relationships among urban features as we have done using convolution. The significance of the proposed neighboring and macro features is also highlighted when the methods KNN and SVR are used: Despite their overall lower accuracy compared to the proposed methods, the performances of KNN and SVR are much improved when using ‘N+M’ instead of ‘L’.

Overall, GBDT and XGBoost+LR demonstrate similar accuracies, and slightly outperform DFeaST-Net. Figure 8 shows the scatter plots of the testing points (five folds combined, over 46,000 points) produced by these three methods. The Pearson linear correlation test () and R () suggest that all three methods provide good inference results.

Finally, we provide a visualization of the inference results for 5 July 2018 in Figure 9. The hourly PM2.5 concentration maps show relatively high and steady concentrations during most of the day before a sudden drop between 16:00-19:00, which was likely caused by a thundershower in late afternoon (http://www.tianqihoubao.com/lishi/beijing.html). This trend is confirmed by the hourly average values published by official sources (NMIC), as shown on the top of Figure 9. We also see that the proposed AQ inference methods are capable of producing fine-granular PM2.5 maps that show significant spatial variations and realistic temporal dynamics.

### 6.3 Fixed and mobile sensing

Grid-based PM2.5 concentrations obtained from fixed-location and mobile sensing sometimes show discernible discrepancies due to the different collection environments. This issue can be addressed either by correcting the mobile data following Appendix A or distinguishing fixed and mobile data using a categorical feature. Table 3 compares these two approaches based on the proposed machine learning methods.

The results show that ‘Not distinguish’ (i.e. correcting the mobile data) leads to similar SMAPE as ‘Distinguish’, but lower MAE and RMSE (by over 20% for DFeaST-Tree and 5%-6% for DFeaST-Net). This suggests that distinguishing the two data sources tends to miss larger values of PM2.5 concentration. To further confirm and visualize this, we show the fixed and mobile labels at 9:00 and 10:00 on 20 June 2018 in Figure 10. As most NMIC stations, which serve as reference instruments for mobile data correction, are located in high grounds or secluded areas, the correction process tend to scale down the mobile values in many cases, as confirmed in Figure 10. Furthermore, while the uncorrected mobile data may contain very high values (which may be owing to their collection environment, i.e. heavily polluted urban streets), the proposed AQ inference tends to ignore these extreme values. This is attributed to the robust mechanisms within DFeaST-Tree to avoid overfitting, at the cost of higher MAE and RMSE when distinguishing fixed and uncorrected mobile data (see Table 3).

Understandably, the reconciliation of fixed and mobile data by correcting the latter tends to reduce their discrepancies and thereby improving the inference accuracy. However, we note that the corrected mobile data are no longer representative of ground-level pollutant concentrations, but are artifacts generated to shorten the gap with fixed-location data.

To further understand the effects of fixed and (uncorrected) mobile data on each other, in Table 4 we summarize the performances of different combinations of training and testing data. In particular, Cases (i)-(ii) test the internal consistencies of fixed and mobile data, while (iii)-(iv) examine the level of integration of fixed and mobile data. As Table 4 shows, when the test set consists entirely of fixed-location data (i, iii) instead of mobile data (ii, iv), the MAEs and RMSEs are lower by more than 40%. This means that mobile data may contain substantial noises given their complex surveying environments. Nevertheless, the fact that (i, iii) has higher SMAPE than (ii, iv) reveals that those potential noises are associated with high PM2.5 concentrations, as confirmed by Figure 10. In addition, using combined fixed+mobile sensing (iii, iv) always produces better outputs than using them on their own (i, ii). From the comparison of (i) and (v), we see that although fixed-location data are sufficient to infer data of the same kind, they can misinterpret ground-level mobile data by a significant margin, which offers evidence that fixed-location sensing, owing to their spatial-temporal sparsity or surveying environment (high grounds, secluded areas), is incapable of capturing detailed urban atmospheric environment picked up by mobile sensing. Finally, Case (vi), which is taken from Table 2, lands between (iii) and (iv) in terms of performance metrics. This makes sense as the overall performance on fixed and mobile test datasets is the weighted average of (iii) and (iv).

### 6.4 Impact of mobile sensing coverage

One of the key practical aspects of mobile sensing is the amount of mobile coverage required to reach certain level of inference accuracy. This translates into the relationship between the number of training data provided by mobile sensing and the accuracy of the proposed inference methods. Taking DFeaST-Tree (XGBoost+LR with neighboring and macro features) as an example, we test its accuracy on an independent test set of size 9,200 consisting of both fixed and mobile labels. The training set initially contains only fixed labels, before being gradually augmented with mobile ones. The corresponding accuracy metrics are shown in Figure 11.

Figure 11 shows the accuracies with both uncorrected and corrected mobile data. The same trends are observed in both scenarios: The errors are high when the training set contains only fixed data, and the ‘elbow’ point occurs where mobile data first appear in the training set, even in low quantity. The accuracy of the method continues to improve as more mobile data are included in the training set. Nevertheless, with every increment of mobile data the margin of improvement decreases. This means that the proposed methodological framework does not require a significant amount of mobile data to reach satisfactory inference results; indeed, in our case less than 5% of the spatial coverage suffices to achieve the results reported in Table 2.

### 6.5 Feature analysis and interpretation of the inference results

One of the advantages of boosted decision trees such as GBDT is its capability to calculate weights/importance of different input features. The importance of a feature is defined as the average importance among all the decision trees within the model, where the importance in a single tree is the sum of reductions in the loss function at all the split points for which the feature is responsible. In other words, the importance of a feature measures its contribution to loss reduction by offering a better fit between model outputs and observations. These quantities are loosely related to the attribution of air pollution, which is a delicate matter and will be discussed in a more rigorous manner in a future work.

Figure 12(a) shows the relative importance of main feature categories, among which the top five are meteorology, POI&AOI, macro feature (i.e. regional transport of pollution), traffic conditions and population vitality. These are consistent with public consensus and expert opinions regarding the likely cause of air pollution in Beijing (Parsons, 2013). Figure 12(b) shows the importance of meteorological features, of which the three most important are wind speed, pressure and water vapor pressure (which is related to relative humidity). These findings are consistent with the descriptive analysis presented in Zheng et al. (2013).

Figures 12(c)-(d) are concerned with macro features. The relative weights of individual NMIC stations outside the study area indicate likely paths of regional transport. In particular, Dingling and Changping, which are located to the Northwest, have the highest weights, followed by Yufa and Liuli River, which are located to the Southwest. This highlights two main directions of PM2.5 transport (Northwest and Southwest) during 19 June - 16 July 2018. The wind rose diagram in Figure 12 provides supportive information regarding the physical transport of PM2.5.

## 7 Conclusion

In this paper, we propose the MAPS (Mobile Air Pollution Sensing) framework for air quality (AQ) inference enabled by a network of fixed and mobile AQ sensors. While ubiquitous AQ sensing with low-cost and mobile sensors has become widely accessible, we are the first to use fixed and mobile AQ data as well as relevant urban datasets to produce fine-granular, grid-based PM2.5 maps for large urban space. This involves identifying relevant factors affecting the emission, dispersion, transport and dissipation of air pollutants via a wide source of urban datasets, including macro features that captures the regional transport of pollutants beyond the study area. A Deep Feature Spatial-Temporal (DFeaST) machine learning framework is proposed to efficiently encapsulate 62 types of urban features while capturing their spatial-temporal correlations. A case study in Beijing suggests that the MAPS framework can effectively infer hourly PM2.5 concentrations at a granularity of 1km1km with superior accuracy (SMAPE, R) over several benchmarks.

There are several issues pertaining to mobile AQ sensing that are addressed in this paper. In particular, the inherent inconsistencies between fixed and mobile AQ measurements are reconciled by either treating them as two different sources (via a categorical feature) or correcting the mobile data using fixed-location data. Another issue is that the mobile labels are sparsely and irregularly distributed in the spatial-temporal domain. This can be handled by the boosted decision trees (DFeaST-Tree) or the Fully Convolutional Network (DFeaST-Net) using a label mask.

The following specific findings are made from the case study.

• Including macro features improves not only the accuracy but also the interpretability of the inference results.

• Using neighboring features (as opposed to local features) is an effective way to account for the spatial and temporal correlations of urban features and PM2.5 data.

• Although fixed-location data are sufficient to infer data of the same kind, they can misinterpret ground-level mobile data by a significant margin, hence the need for mobile sensing when it comes to AQ inference.

• Correcting the mobile data using fixed sensing data as reference improves the inference accuracy, especially in terms of MAE and RMSE. But the corrected mobile data no longer represent ground-level pollutant concentrations.

• Compared to fixed-location data, uncorrected mobile data contain greater noises that render higher inference errors, and those noises are typically associated with high PM2.5 concentration values.

• Using combined fixed and mobile data for training produces more accurate inference results than using them on their own.

• Adding more mobile sensing labels to the training set improves the inference accuracy, but the margin of improvement decreases.

• In the Beijing case study, less than 5% of fixed/mobile sensing coverage (see Figure 3) is sufficient to reach SMAPE and R using the proposed methodological framework.

• For the Beijing case study between 19 June and 16 July 2018, the top three most relevant features of PM2.5 concentration are meteorology, POI&AOI, and macro features (i.e. regional transport). The primary paths of regional transport are from Dingling & Changping (Northwest) and Yufa & Liuli River (Southwest).

## Appendix A Preprocessing of mobile data

The mobile data collected by sensors mounted onto vehicles were smoothed to filter random noises, before being corrected to reconcile with fixed-location data. The reference instruments are the NMIC and micro AQ stations, which provide hourly PM2.5/PM10 measurements at 28 distinct locations.

The mobile data include time stamp, location (coordinates), PM2.5 concentration, temperature and relative humidity. The time series of these measurements in the raw dataset are fragmented, meaning that there are time periods without valid data; see Figure 1(e). To resolve this issue, we divide the time series into disjoint sub-series containing continuous measurements. Then we apply smoothing techniques (moving average and robust local regression) to each sub-series to reduce the temporal variation and extreme values.

The preprocessed PM2.5 concentration, temperature and relative humidity measurements are mapped onto appropriate units based on their time stamps and coordinates, and the measurements within the same unit are averaged to derive unit-based PM2.5 concentration, temperature and relative humidity. A simple filter is applied to discard units with too few or unrepresentative mobile data points. The resulting unit-based mobile data coverage is illustrated in Figure 3(c).

The correction of unit-based mobile PM2.5 data is performed using multivariate regression involving the location, temperature and relative humidity. Specifically, the correction factors to be applied to the mobile data are assumed to depend on the location , time , temperature temp and relative humidity RH. The multivariate regressions that are linear or quadratic in temp and RH can be expressed as:

 {yf=β0+β1⋅ym+β2⋅s+β3⋅t+β4⋅temp+β5⋅RHoryf=β0+β1⋅ym+β2⋅s+β3⋅t+β4⋅temp+β5⋅RH+β6⋅temp2+β7⋅RH2 (A.6)

where and are respectively fixed and mobile PM2.5 measurements. We let be the subset of units containing both fixed and mobile data, and use the following training set for regression , , , , , , . Figure 13 shows the correction results based on the linear and quadratic regression (A.6), which suggests similar performances. The latter leads to slightly higher R-square value (0.74) and Pearson correlation coefficient (0.86), and is selected in this paper to obtain corrected mobile data.

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