A unified empirical modeling approach for particulate matter and NO₂ in a coastal city in China

Abstract

Modeling air pollutants on a fine spatiotemporal scale is necessary for health studies that focus on critical short-term exposure windows. A unified empirical modeling approach is useful for health studies; however, it is unclear whether this approach can be used in a coastal city for air pollutants driven by local emissions and regional meteorological factors. An advanced empirical modeling approach was used to develop exposure models from October 2012 to December 2019, for particulate matter with aerodynamic diameters less than or equal to 2.5 and 10 μm (PM_2.5 and PM₁₀) and nitrogen dioxide (NO₂) in the coastal city of Shanghai, China. Air pollutant concentrations were obtained from daily measurements at 55 administrative monitoring sites that were integrated into three-day average concentrations. Data on a large array of geographic variables were collected, and their dimensions were reduced using the partial least squares regression method. A geostatistical model using the land-use regression approach in a universal kriging framework was developed to estimate short-term exposure concentrations. The prediction ability of the models were determined by leave-one (site)-out cross-validation (LOOCV) and external validation (EV). Compared to the LOOCV results, the EV results for PM_2.5 and PM₁₀ were consistently reliable, but the EV for NO₂ had a larger root mean squared error. The temporal random effects involved in the model structure were interpreted using sensitivity analyses. This affected the short-term PM_2.5 and PM₁₀ model predictions. This unified empirical modeling approach was successfully used for particulate matter in Shanghai, where air pollution is affected by complex regional and meteorological conditions. These exposure models are going to be applied for making exposure predictions at residential locations for short-term exposure predictions in the “Growth trajectories and air pollution” (GAAP) study in Shanghai that focuses on maternal and early life exposure to air pollutants.

1. Introduction

Accurate spatiotemporal exposure modeling is needed to provide ambient exposure to air pollutants for health studies, especially for maternal health studies focusing on exposure during critical gestational exposure windows linked to adverse birth outcomes (Klepac et al., 2018; Lamichhane et al., 2015; Woodruff et al., 2009). Recently, new approaches have been applied to develop spatiotemporal exposure models. The most popular of these new approaches include using spatially and temporally varying data as predictors, such as satellite data (Xie et al., 2015), and using advanced algorithms to obtain a comprehensive explanation of the interactions between predictors, such as machine learning (Di et al., 2016). These approaches are commonly used in regional and national models (Chen et al., 2018; Di et al., 2019). These models extend their modeling domain to a broad spatiotemporal range, which are able to obtain exposure estimates in areas with sparse or no monitoring stations (Di et al., 2017), and are able to obtain historical estimates during a period when observations are not available (He et al., 2020). However, for an area- or a city-specific cohort study, the national model may not be capable of providing exposure estimates on a fine spatial scale, such as point locations at participant residences. This may be because the spatial resolution of the predictors is usually less than 1 km, and a general temporal trend in a large region cannot represent the localized temporal air pollutant variations. For example, the PM_2.5 growing process in Beijing (located in North China) and Shanghai (located East China) was different because of the chemical composition and driven factor heterogeneity, such as emission- or meteorology-driven factors (Liu et al., 2020; Sun et al., 2019).

In terms of accurate spatial estimates, the land-use regression (LUR) has been widely used for long-term exposure modeling in health studies (Beelen et al., 2013; Brauer et al., 2008; Eeftens et al., 2012a). The LUR models apply many geographic variables, such as road network, population and land use, and can provide fine spatial exposure estimates to characterize within-city contrasts, especially for combustion-related primary pollutants, such as NO₂ (Eeftens et al., 2012b; Hoek, 2017). Hybrid spatiotemporal models combining LUR and other techniques, such as satellite observations (Beckerman et al., 2013), have been developed to allow fine temporal resolution (Hoek, 2017). Unless one or more temporally variated variables were used for spatiotemporal model development, an advanced spatiotemporal modeling approach incorporates one or several smoothed temporal trends and the LUR approach in a universal kriging structure (Keller et al., 2015). This approach was designed for the Multi-Ethnic Study of Atherosclerosis and Air Pollution (MESA Air) study to deal with the temporally unbalanced measurement dataset (Keller et al., 2015; Wang et al., 2015). This modeling approach has been successfully applied to the six criteria pollutants in exposure modeling studies in China (Xu et al., 2019b; Zhang et al., 2020). In this study, a unified spatiotemporal model for air pollutants was developed using this modeling approach in Shanghai, where the air pollution is driven by both emission and meteorological conditions (Liu et al., 2020). Comparing the performance of such a model across air pollutants in such coastal cities is valuable.

Moreover, we developed the spatiotemporal exposure models to provide short-term ambient exposure estimates specifically for the “Growth trajectories and air pollution” (GAAP) health study and as one part of the “Impact of preconception and onward exposure to air pollution on growth trajectories of infants and children” study in Shanghai, China. The GAAP study investigates early-life exposure to air pollutants over a long period, beginning during the preconception period and continuing into the first two years of life, and assesses the potential critical time windows, as adverse birth outcomes and potentially adverse health outcomes may be linked to air pollution exposure during the preconception and in utero periods (Backes et al., 2013; Clark et al., 2010; Klepac et al., 2018). The participants in the GAAP study includes approximately 20,000 children and their parents. The exposure models aim to provide the ambient exposure metrics of PM_2.5, PM₁₀ and NO₂ at participant residences on a three-day time scale throughout the research period.

2. Materials and methods

2.1. Fixed monitoring sites in Shanghai

Air pollution data of PM_2.5, PM₁₀ and NO₂ from October 2012 to December 2019 were retrieved from the Shanghai Air Quality Monitoring Network (Shanghai Environmental Monitoring Center). This monitoring network included 55 fixed sites, 21 of which were located in the central urban area of Shanghai (Figure S1).

2.2. Measurements

The Shanghai spatiotemporal exposure model (SH-ST) was used for the GAAP study, which focused on air pollutant exposure during early life developmental periods. It included maternal periods, which are genearlly counted in weeks. Thus, the SH-ST model used three-day (approximatelly half of a week) temporal segments for model development and exposure estimates to avoid computational burdens. Daily measurements at the 55 monitoring sites were integrated into three-day averages using two or three daily measurements (more than 50% available data). The three-day average concentrations for each pollutant were log-transformed before modeling to address the original dataset skewness.

2.3. Geographic Variables Collection

We collected a large array of geographic variables including the following two types: a) direct variables that can be directly inputted for modeling, including population, topology, land use type, emission source-related features and points of interest (POI); and b) compiled variables that need to be compiled at first, such as being categorised based on volume or size, including road network, normalized difference vegetation index (NDVI), and satellite data.

The direct variables were all spatial variables. We collected the population density data from the Resource and Environment Science and Data Center (https://www.resdc.cn/). Point sources of emission and topographic information were extracted from OpenStreetMap (https://www.openstreetmap.org/). The land use data for the Shanghai area were derived from the Finer Resolution Observation and Monitoring of Global Land Cover (FROM-GLC) dataset with a 30 m resolution (Gong et al., 2013). Additionally, for POI variables, we collected the locations of seven types of POIs (restaurants, bus stops, ports, parking lots, bus terminals, gas stations, and temples) in Shanghai. The POI data were accessed and extracted from the Chinese map provider AMAP (https://www.amap.com/). The search for POIs used an application programming interface based on categories and keywords, and the purpose of using POI data for geostatistical model development was to capture important sources that were missed by land use data (Xu et al., 2019a).

The original data of the compiled variables have both spatial and spatiotemporal dimensions. The spatial variations of the road network were collected from OpenStreetMap and classified into four types (type A–D) based on traffic features and national road categories. Type A roads denote limited-access roads that represent both intra- and inter-city expressways without stop signs. Type B roads denote a combination of national and provincial level roads and arterial roads with more than five lanes. Type C and D roads denote county- (a county has a lower administrative level than a city in China) and town-level roads, respectively. The NDVI and satellite variables were spatiotemporal data and were integrated into spatial variables by year and season (cold and warm seasons). For satellite variables, we used aerosol optical depth (AOD) as a potential variable for model development for PM_2.5 and PM₁₀. The AOD dataset was retrieved by the Multi-Angle Implementation of Atmospheric Correction (MAIAC) algorithm from measurements of the Terra ((crossover at 1:30 pm local time)) and Aqua (crossover at 10:30 am local time) Moderate Resolution Imaging Spectroradiometer (MODIS) instruments (Xiao et al., 2017). The AOD measurements were on the MCD19A2 green band at 0.55 μm. Daily AOD data at a resolution of 1-km resolution were collected. We extracted the data of each pixel to the central point and assigned the value to the monitoring sites using the nearest neighbor. As the daily AOD matrix had a lot of missing data, it was compiled into several spatial variables, such as seasonal distributions, based on the daily AOD when sufficient data were present. Details of the geographic variables are outlined in Section 2.2 in the supplementary information.

Geographic variables for fixed monitoring sites were screened using several criteria to exclude minimal variations or potentially highly influential points (Keller et al., 2015). Specifically, we excluded the following variables: a) more than 80% of the monitoring sites with the same value; b) more than 2% of the observations were outliers (more than five times the standard deviations [SD] away from the mean); c) the maximum value of a land-use variable was less than 10% across all the monitoring sites (for land-use variables, the value is a percentage of a land-use surface over the entire buffer surface); or d) the SD of the distribution of the variable for GAAP cohort participants was more than five times the SD of the distribution of the variable for the 55 monitoring sites. The first four screening criteria were based on our previous studies (Xu et al., 2019b) and the fifth one was specifically applied to the GAAP study in Shanghai. From the original 298 geographic variables, 206 variables were selected and used for PM_2.5, PM₁₀, and NO₂ model development. The details of the original geographic variables are shown in Table S1.

2.4. Model development

Model framework

The SH-ST model has a hierarchical model structure that was built on a universal kriging framework. It was previously developed for the Multi-ethnic Study of Atherosclerosis and Air Pollution (MESA Air) study (Keller et al., 2015). This hierarchical model is as follows:

$$C\left(s,t\right)={\beta }_0\left(s\right)+\sum _{i=1}^{ntrend}{\beta }_i\left(s\right)f_i\left(t\right)+\nu \left(s,t\right)$$ (Equation 1)

where $C\left(s\mathit{,}t\right)$ is the predicted air pollutant concentration at location s and time t; ${\beta }_{\mathit{0}}\left(s\right)$ is a spatially varying long-term mean (LTM), i.e. the mean of short-term concentrations) at location s; $ntrend$ is the number of temporal trends ($f_i\left(t\right)$) that are computed by long-term measurements and smoothed by an empirical orthogonal function (Fuentes et al., 2006; Sampson et al., 2011); ${\beta }_i\left(s\right)$ are spatially varying coefficients; and $\nu \left(s\mathit{,}t\right)$ are the spatiotemporally varying residuals that mainly include a temporally independent random effect and a spatially correlated kriging part.

The spatially independent ${\beta }_{\mathit{0}}$ and ${\beta }_i$ are calculated on reduced-dimension summaries obtained from the geographic variables using partial least squares (PLS) regression. Spatially varying PLS scores were used as predictors for the model development. The details of the model structure and the PLS process have been previously published (Xu et al., 2019b).

Model structure

The main model structure in previous studies used 1–2 temporal trends and 2–3 PLS components (Keller et al., 2015; Wang et al., 2015; Xu et al., 2019b). In this study, we used cross-validation (CV) to determine the number of temporal trends and the PLS components for each pollutant. The annual mean in 2017 across the 55 monitoring sites was used as an outcome variable in the PLS process because most available measurements at the 55 monitoring sites were observed in 2017. The details of CV for determining the number of temporal trends and PLS components are described in Section 2.3 in the supplementary information. Based on our previous study (Xu et al., 2019b), spatial smoothing was conducted for the LTM (β₀) and residuals (ν), but not for the temporal trends (β_i). The temporal random effect was added to the main model structure as part of ν(s,t) to elucidate temporally uncorrelated large-scale deviations that were not captured by the smoothed temporal trend (Lindstrom et al.).

Software

We used the “SpatioTemporal” package (version 1.1.9) in R (version 3.4.0, R Core Team, http://www.R-project.org/) for model development, and used the PLS package (version 2.6–0) in R to obtain PLS scores. Geographic calculations were performed using the open-source database PostgreSQL (https://www.postgresql.org/) with the GIS extensions of PostGIS (https://postgis.net/). Mapping was performed using QGIS (version 3.16, http://www.qgis.org/).

2.5. Model validation

Leave-one (site)-out cross-validation

Leave-one (site)-out cross-validation (LOOCV) was performed to evaluate the SH-ST model performance. The testing group consisted of observational data from one of the 55 monitoring sites and the training group consisted of the observational data from the remaining 54 monitoring sites that were used for model fitting. The fitted model was then used to predict the testing group and this process was repeated until predictions for all 55 monitoring sites were generated. The observations (y_i) and predictions ($\widehat{y_l}$) were computed on their original scales (back-transformed from the log). The root mean squared error (RMSE), calculated by $\sqrt{\frac{1}{n}{\sum }_{i=1}^n\left(y_i-{\widehat{y}}_i\right)}$ (n denotes the number of monitoring sites), and mean squared error (MSE)-based R² (R²_mse), calculated by max$\left(0,1-\frac{{RMSE}^2}{\raisebox{1ex}{${\sum }_{i=1}^n{(y_i-\stackrel{-}{y})}^2$}\!\left/ \!\raisebox{-1ex}{$n$}\right.}\right)$, were used to assess the accuracy of the SH-ST models. Here, n denotes the number of observations, $\stackrel{\mathit{-}}{y}$ is the mean of the observations, and R²_mse is a measure of fit to the 1:1 line and is typically smaller than the linear regression-based R² (R²_reg), which is a measure of fit to the regression line (Xu et al., 2019b). In this study, LOOCV was conducted for both short-term (three-day average concentrations) and long-term (mean of the three-day average concentrations, i.e., LTM) predictions. The LOOCV for the LTM was used to evaluate the spatial performance of the model.

External validation

We also applied external validation to observational concentrations from the four monitoring sites. As shown in Figure S1, three (site “sh279”, “sh253” and “sh227”) of the selected four sites were in the central urban area in Shanghai and the remaining site ( “sh86”) was in the suburban area. These four sites had more missing data than other sites; thus, they were selected for external validation. The SH-ST models were developed by fitting the remaining 51 monitoring sites (approximately 90% of the total monitoring sites) and made predictions for the four sites for external validation.

2.6. Sensitivity analysis

Sensitivity analyses were conducted on model structure and geographic variables. To interpret the temporal random effect, we performed sensitivity analyses by removing it from the model structure. We developed spatiotemporal models without the temporal random effect and named them non-random effect-spatiotemporal (NRE-ST) models. The LOOCV results of the SH-ST and NRE-ST models for each pollutant were compared. Additionally, we calculated the normalized mean bias (NMB) to compare the model performance between pollutants. The NMB was obtained using the equation ${\sum }_{i=1}^n\left({\widehat{y}}_i-y_i\right)/{\sum }_{i=1}^n\left(y_i\right)$, where ${\widehat{y}}_i$ and $y_i$ denote the prediction and observation, respectively.

For geographic variable sensitivity analysis of the model performance, we evaluated the relationship between the geographic variables and PLS scores that were used as predictors for modeling. First, we calculated the correlation coefficients between each PLS component of the LTM and the geographic variables. The first PLS score of LTM (LTM-PLS1) was the most crucial predictor affecting the spatial variations of the predictions. The correlation coefficients between the LTM-PLS1 and each geographic variable can spatially represent the sensitivity of each geographic variable in model development. Second, weighted variable importance in projection (VIP) was evaluated and geographic variables with high VIP values for LTM-PLS1 were selected and compared across pollutants. Details of the VIP are provided in Section 5.1 in the supplementary information.

3. Results

3.1. Measurements

The three-day average concentrations of PM_2.5 were used as dependent variables for model development. Figure S2 shows the three-day average PM_2.5 measurements at the 55 fixed monitoring sites from October 2012 to December 2019. From 2014 to 2017, apart from the 10 national monitoring sites, an additional 45 monitoring sites were gradually established in Shanghai. During this period, missing data were existed because of the maintenance monitoring. This cause the observational dataset to be unbalanced on a temporal scale. Figure S2 shows the three-day average concentrations of PM_2.5 across the 55 monitoring sites. High temporal correlation was found for the observations of PM_2.5 across the 55 monitoring sites with a median correlation coefficient of 0.95 (range of 0.65–1.00). Similar temporal trends were found for PM₁₀ with a same median correlation coefficient of 0.95 (range of 0.75–1.00). The correlation coefficients across the 55 monitoring sites for NO₂ (Figure S2) had a larger median of 0.89 and a larger range of −0.13–1.00 compared with those for PM_2.5 and PM₁₀. Seasonal variations in PM_2.5 were shown in Figure S2. Notably, PM_2.5 concentrations were higher in winter (January, February, and December) than those in summer (June, July, and August) in each year. A decline in PM_2.5 concentrations was observed from 2016 to 2019.

3.2. Model structure

Temporal trend

The number of temporal trends was determined from the CV results for different numbers of smoothed temporal trends (Figure S4). The number of temporal trends was one for the PM_2.5, PM₁₀, and NO₂ models. The temporal trends, as a part of the SH-ST model, explained some variability in the short-term observations (log-transferred three-day average concentrations) at the temporal scale. Table S2 shows the linear regression R² of the smoothed temporal trend of the observations across the 55 monitoring sites. For the SH-ST model of PM_2.5, the temporal trend explained an average of 41% (range: 32%–47%) of the variability of the observations. The SH-ST model for PM₁₀ had a slightly wider R² range (30%–50%) than the SH-ST model for PM_2.5. Contrarily, for the SH-ST model of NO₂, a larger mean value of 51% and a wider range of 15%–69% were found compared with the PM_2.5 and PM₁₀ models.

PLS component

Figure S5 shows the LOOCV results for different numbers of temporal trends during the PLS process; the number of PLS components was three for PM_2.5 and PM₁₀ and four for NO₂. The first PLS component explained most of the variation in the geographic variables (92.1%–92.4% for the three pollutants). Figure 1 shows the correlation coefficients between the LTM-PLS1 for the PM_2.5, PM₁₀, and NO₂ models and the geographic variables. Overall, for the three pollutants, most of the correlation coefficients were comparable and had the same direction of effects, except for the land use percentage of water (LU: water) and the distance to the vessel routes in the Yangtze River (Dist to Yangtze route). The geographic variables of NDVI (NDVI: winter, summer, q75, q50, and q25), land use percentage of impervious surface and cropland (LU: impersfc and cropland), distance to type A and B roads (Dist to roads A and B), and the number of bus stops (No. of bus stops) were highly correlated with the LTM-PLS1, which had an absolute value of correlation coefficients greater than 0.5. The correlations between geographic variables and LTM-PLS1 for the PM₁₀ model were similar to the correlations for the NO₂ model; however, some of the correlation relationships for the PM_2.5 model were weaker than those for the PM₁₀ and NO₂ models. Specifically, the population density, land use percentage of grassland, and variables representing non-road emissions, such as length of rivers and distance to ports, had smaller effects on the LTM-PLS1 in the PM_2.5 model than those in the PM₁₀ and NO₂ models. AOD variables had a larger correlation coefficient for the PM_2.5 model than that for the PM₁₀ model. The AOD variable was not used for NO₂ model development because AOD was retrieved at visible wavelengths that are insensitive to gaseous pollutants (Kahn et al., 1998). The correlations between the temporal trends and the other 2 or 3 PLS components for the three pollutants are shown in Figure S8.

Figure 1.

Correlation between the LTM-PLS1 for the PM_2.5, PM₁₀, and NO₂ models and the geographic variables. For the variables with buffers, the bars represent the mean value of correlation coefficients across buffers for each kind of variable, and the upper and lower error bars represent one standard deviation from the mean.

3.3. Model performance

Table 1 shows the LOOCV results of the SH-ST models for PM_2.5, PM₁₀, and NO₂ for short-term and LTM predictions and the EV results for short-term predictions. In LOOCV, all SH-ST models exhibited moderate to good performance (R²_mse > 0.6) for short-term and long-term predictions. The PM_2.5 and PM₁₀ models performed excellently for three-day average predictions, while the NO₂ model performed better for LTM predictions than the PM_2.5 and PM₁₀ models. The LOOCV results for the three-day average predictions split by year are listed in Table S5. The PM_2.5 model performed excellently for short-term predictions over the years, with R²_mse in the range 0.92–0.96; however, different yearly performance was found for the PM₁₀ and NO₂ models. The PM_2.5 and PM₁₀ models consistently showed excellent EV results, with a slightly smaller RMSE and larger R²_mse than those of the NO₂ model. In contrast, the EV for NO₂ had a worse performance for short-term predictions, with the EV RMSE almost 40% larger than the LOOCV RMSE.

Table 1.

LOOCV and EV results of the PM_2.5, PM₁₀, and NO₂ models for the three-day average and LTM predictions.

	LOOCV
	Three-day average				LTM b
	No.a	RMSE (μg m−3)	R2mse	R2reg	No.b	RMSE (μg m−3)	R2mse	R2reg
PM2.5	39029	5.82	0.94	0.94	55	2.01	0.72	0.73
PM10	38921	8.91	0.91	0.91	55	3.48	0.67	0.67
NO2	39522	7.50	0.83	0.83	55	3.07	0.87	0.87
	EV
	three-day average				LTM c
	No.a	RMSE (μg m−3)	R2mse	R2reg	No.	RMSE (μg m−3)	R2mse	R2reg
PM2.5	1988	4.80	0.96	0.96	—	—	—	—
PM10	1995	8.51	0.90	0.90	—	—	—	—
NO2	2021	10.31	0.67	0.73	—	—	—	—

^a:A total number of available three-day average concentrations;

^b:The LTM were calculated by the available three-day average concentrations;

^c:EVs for LTM were not performed because the number of observational data was only 4.

Figure 2 depicts the short-term observations and predictions of the SH-ST models and NRE-ST models for PM_2.5. Many of the predictions were underestimated by the NRE-ST model. For PM_2.5, the NMB was −7.8% for the NRE-ST model and −4.7% for the NO₂ model (Figure S12). In contrast, for the SH-ST model, the NMB was −0.05% for PM_2.5 and −2.1% for NO₂. The PM_2.5 predictions were more underestimated by the NRE-ST model than they were by the SH-ST model. Table S6 shows the LOOCV results for the NRE-ST models of three pollutants. For the LTM predictions, the LOOCV results of the NRE-ST models were similar to those of the SH-ST models. In contrast, the NRE-ST models performed worse for short-term predictions than the SH-ST models, especially for PM_2.5. The difference in LOOCV R²_mse between the SH-ST and NRE-ST models for PM_2.5 was 0.55. The difference in LOOCV R²_mse was 0.26 for NO₂ and 0.50 for PM₁₀. The observations and predictions of the SH-ST and NRE-ST models for PM₁₀ are shown in Figure S12, and the LOOCV results for the NRE-ST model are shown in Table S6.

Figure 2.

The LOOCV predictions of SH-ST and NRE-ST models for PM_2.5.

3.4. Mapping of LTM predictions

Figure 3 presents the LTM predictions of the SH-ST models for PM_2.5 and NO₂ over the modeling period (October 2012–December 2019) at a 1 km spatial resolution, which represents a spatial contrast of air pollutants in the study area. The prediction map covered an area that was smaller than the administrative domain due to the availability of geographic variables. For NO₂, the hotspot with high concentrations were found around the central urban area where the roads and population were concentrated. In contrast, the map of PM_2.5 depicts an overall spatial pattern that has high concentrations in the west and low concentrations in the coastal area. Additionally, a clear line representing the high predicted LTM concentrations coincided with the Huangpu River. The LTM predictions of the PM₁₀ models are depicted in Figure S14.

Figure 3.

Maps of long-term mean predictions for PM_2.5 and NO₂ in Shanghai at a 1 km spatial scale.

4. Discussion

We developed spatiotemporal models in Shanghai, China, from October 2012 to December 2019, by leveraging daily measurements from 55 monitoring sites to build a series of SH-ST models for PM_2.5, PM₁₀, and NO₂, which have a unified model structure and use the same dataset of geographic variables. Our models predicted ambient exposure at a point location with a high three-day temporal resolution. This study is among the few that focus on developing spatiotemporal models for a specific cohort study in a Chinese megacity. To meet the purpose of this study, our models will provide support for exposure assessment during critical early life developmental periods for the GAAP study in Shanghai, China.

4.1. Model Performance and Predictability

In this study, the SH-ST models for PM_2.5, PM₁₀, and NO₂ showed good performance in LOOCV at both short-term (three-day average) and long-term scales. The LOOCV R²_mse ranged from 0.82 to 0.94, as shown in Table 1. The model fitting R²_mse and R²_reg achieved almost 1 as an advanced model development approach. We used the LOOCV results of the SH-ST models for short-term estimates to represent the model performance on a spatiotemporal scale, and used those for LTM estimates to represent their performance at a spatial scale. The model performance of previous studies is summarized in Table S7. The model fitting R² ranged from 0.61 to 0.95 for all models in these previous studies (Liu et al., 2016; Meng et al., 2015; Meng et al., 2016; Song et al., 2021; Zhang et al., 2018). Some of these studies have performed CV, and their CV R² for short-term estimates were 0.89 and 0.87 for PM_2.5 and PM₁₀, respectively (Meng et al., 2016; Zhang et al., 2018). For NO₂, the CV R² for long-term exposure was 0.75 (Meng et al., 2015). The model fitting and CV RMSE of these studies were larger than the LOOCV RMSE in this study.

Among the previous studies in Shanghai and corresponding studies in the surrounding area of the Yangtze River Delta (Ma et al., 2016; Xiao et al., 2017; Yang et al., 2018), most of the spatiotemporal models were developed based on satellite data and could not provide exposure estimates at a finer spatial scale of less than 1 km. A comparison of model predictability at unmeasured locations was conducted by mapping of the spatial variation of long-term predictions at a 1 km spatial scale (Figure 3). The PM_2.5 mapping in this study and the previous studies (Liu et al., 2016; Song et al., 2021) showed reginal dilution with a decline from the west to the east (coastal area) of Shanghai. Additionally, the ambient PM_2.5 variation at a fine spatial scale was captured by our model, which may be attributed to ship emissions near the Huangpu River and coastal areas (Li et al., 2018).

4.2. Model Structure and Interpretation

Although the predictive performance of a model is indispensable, it is informative to interpret its structure (Chen et al., 2019). The SH-ST models have a clear unified model structure that mainly consists of a spatially variated LTM, a spatially variated parameter multiplied by a temporal trend, and a temporally variated random effect within the residual, as shown in Equation 1. Here, we discuss the meaning of each segment within the structure of the SH-ST models for PM_2.5, PM₁₀, and NO₂.

For the three pollutants, the temporal trends explained 0.32–0.47 of the three-day average observations across the 55 sites, as shown in Table S3. The linear regression R² of the log-transformed observations on the smoothed temporal trend of the PM_2.5 model was similar to that of the PM₁₀ model. Contrarily, the R² of the NO₂ model across the monitoring sites had a larger mean and maximum value than those of the PM_2.5 and PM₁₀ models. This is consistent with our previous study in Beijing (Xu et al., 2019b),which showed that the temporal variability in PM observations could not be well explained by the smoothed temporal trend. However, compared to the cosine smooth basis function, we found that the SVD smooth temporal basis function could capture more temporal variability in the observations (Figure S7).

For the other segments of the model structure, we focused on the temporal random effect in the SH-ST model for PM_2.5. Although the three-day average observations were log transformed before modeling, we attempted to interpret the temporal random effect in its original scale (μg m⁻³), which is equals to the difference in the LOOCV predictions between the SH-ST and NRE-ST models across the 55 monitoring sites. The temporal random effect showed a small variance across the 55 monitoring sites at each three-day time point over the study period (Figure S9). Thus, the median of the random effects across the monitoring sites was used to represent the values of the temporal random effect, as shown in Figure S10. Meteorological factors, such as dew temperature and wind speed shown in Table S3, explained 20% of the variability in the temporal random effect, but temporal random effect values may also be affected by regional transportation or dilution. Thus, we summarized how the temporal random effect and wind direction varied during the modeling period. As shown in Figure S10, the values of the temporal random effect were below 0 when the wind direction was dominated by east and southeast. In contrast, the temporal random effect was high (> 40 μg m⁻³) when the air flow came from the northwest, west, and south, especially in winter. In agreement with our study, previous studies on the chemical composition and sources of ambient PM_2.5 in Shanghai and the surrounding Yangtze River Delta concluded that ambient PM_2.5 was dominated by secondary aerosols and sea salt was one of the main sources (Qiao et al., 2016; Zhao et al., 2015). A complicated situation was found in areas where a decline in the primary pollutants and an increase in secondary pollutants occurred simultaneously, as well as long-range and regional transportation (Liu et al., 2020; Sun et al., 2019; Zhong et al., 2021).

4.3. Sensitivity Analysis

Two types of datasets were used as inputs for model development. The first was air pollutant observations, which were used to generate temporal trends. The temporal trends were directly extracted by smoothing observations rather than predicting temporal variables, such as meteorological variables, satellite data, emission inventories, or a combination of them, as in other studies did (Di et al., 2019; Xue et al., 2019). The LOOCV basis functions of PM_2.5 at the two monitoring sites are shown in Figure S6. This indicates that the temporal trends calculated by an SVD smooth basis function were consistent if sufficient monitoring sites were involved. The second type of datasets was geographic variables, whose dimensions were reduced, and they were involved in model development using an LUR approach. The sensitivity of these variables to the PLS scores, which were used as predictors for PM_2.5, differed from those for the PM₁₀ and NO₂ (shown in Figure 1). This accounted for different spatial patterns of the LTM predictions among the three pollutants (shown in Figure 3 for PM_2.5 and NO₂ and Figure S14 for PM₁₀). This is consistent with the VIP analyses on geographic variables, where the distance to the coast and the distance to the Yangtze River route variables had a larger influence on PM_2.5, which can explain its spatial decline pattern from the inland to the coastal area. It should be noted that the variable of distance to the Yangtze River route had a counterintuitive direction of effect for the PM_2.5 model (Figure 2), which might be attributed to the effect of the spatial distribution of PM_2.5, rather than emission sources. In Figure 3, the PM_2.5 prediction map depicts a clear high pollution level of PM_2.5 around an area coinciding with the Huangpu River. However, neither a correlation nor a VIP approach can reflect the influence of the Huangpu River-related variables. It is necessary to evaluate the model performance by mapping predictions in an area at unmeasured locations, especially for a complicated model with multiple input variables. In the future, instead of variance-based sensitivity analysis, distribution-based or moment-independent strategies may be useful for advanced models (Pianosi and Wagener, 2018).

In addition to the model inputs, we also performed sensitivity analyses on a model setting of the temporal random effect. Temporal random effect can be elucidated by short-term variation, which explains more than 50% of the spatiotemporal variance in the three-day average PM_2.5 observations. These temporally uncorrelated estimations are usually due to large-scale meteorological events across the entire region; however, in Shanghai, the temporal random effect might be attributed to both secondary formation and regional transportation of PM_2.5 (Miao et al., 2021).

The AOD-related variables are computed for a specific spectrum (usually at 470 and 660 nm) by matching the average reflectance (Kumar et al., 2007). Despite it being obtained after screening for clouds, water, and snow/ice pixels, it may interfere with high reflectance surfaces, such as water. The PM_2.5 predictions in an area surrounded by water may be interfered by AOD data. We then rebuilt the PM_2.5 SH-ST model using a non-AOD model that excluded all corresponding AOD variables. Figure S13 presents the map of LTM PM_2.5 predicted by the non-AOD model and shows a clear and highly polluted line as. Therefore, we conclude that the highly polluted line showed in Figure 3 might be related to ship emissions.

4.4. Strengths and limitations

The SH-ST models were specifically developed for the GAAP study conducted in Shanghai. It provides a three-day average exposure metric for each participant in the GAAP study during the entire research period. Point prediction at the participant residences can prevent the misclassification of exposure level around a hotspot area next to an emission source owing to predictions at a relatively large spatial scale, such as satellite-based exposure estimates at a 1 km scale (Xiao et al., 2018). Moreover, the GAAP study can estimate exposure for each participant at a relatively short temporal scale which is helpful for assessing exposure windows (Klepac et al., 2018).

This study has several advantages over previous studies in such areas for the model development and prediction of PM_2.5, PM₁₀, and NO₂. First, the SH-ST models are developed on a unified and flexible model structure, allowing for the modeling of multiple pollutants at fine spatiotemporal scales. For short-term predictions, the models for the three pollutants outperformed most previous studies in Shanghai (Tables 1 and S7). In terms of long-term predictions reflecting the spatial prediction ability, the SH-ST models performed well for PM_2.5 and NO₂. The use of monitoring data for temporal trend smoothing avoids the challenges faced by models developed using temporal variables, such as difficulties in processing and properly interpreting satellite data for specific air pollutants (Duncan et al., 2014) and poor correlations between measurements and meteorological variables (Hu et al., 2014). Second, using PLS to reduce the dimensionality of the geographic variables allows us to use all of the geographic variable information for model development, as opposed to a variable selection approach conducted in Shanghai, which was developed on a few land use variables (Liu et al., 2016). This allowed our models to capture spatial variability by relying on more geographic variables and performing prediction at a fine spatial scale. Third, compared with our previous study conducted in Beijing, more geographic variables were used for the model development in Shanghai. For example, in this study, the use of AOD and many types of POI data played an important role in PM_2.5 and PM₁₀ predictions (Figure 1). Fourth, a clear model structure ensures that each model segment and its coefficients are interpreted. It helps understand the meaning of the model structure and avoids using “a black box” for prediction, such as machine learning approaches. Regardless of these advantages, this study has several limitations. First, the observational data from a few monitoring sites were used for external validations. Although it is useful to validate the model performance over the modeling period, only four monitoring sites were used for external validation, which may have misestimate spatial model performance. However, an external validation is needed for empirical models, especially for models that rely on few monitoring sites (Basagana et al., 2012; Kerckhoffs et al., 2019). In this study, the observational data were obtained from 55 monitoring sites, which were more than the number of monitoring sites in previous studies (listed in Table S7). Second, the temporal resolution of the SH-ST models was a three-day period, which is more than that of the models developed based on the daily satellite data. The SH-ST models were specific to a cohort study that focused on critical exposure windows during an early life period. The three-day average estimates provide the weekly estimates, as a longer temporal resolution could compromise the saving of the computing power.

4.5. Future work

Whether this unified empirical modeling approach can be used for air pollutants in Shanghai, a coastal city where air pollution is affected by complicated regional and meteorological conditions, should be explored further. In this study, the exposure models for PM_2.5 and PM₁₀ outperformed the NO₂ model. This modeling approach may achieve better performance for particulate matter compared with NO₂ because of the temporal random effect in its model structure and the application of the dimension reduction method for geographic variables. In the future, other empirical modeling approaches and methods to deal with geographic variables should be performed to compare primary and secondary air pollutants.

5. Conclusion

The Shanghai spatiotemporal (SH-ST) model successfully characterized ambient exposure concentrations of PM_2.5, PM₁₀, and NO₂ at the residence locations of the participants in a cohort health study in Shanghai. The model was developed based on a temporal basis function obtained from the observational data and used the entire information of the collected geographic variables. A relatively clear model structure was used for SH-ST model development and allowed the model to be interpretable. The spatiotemporal modeling approach can be used in areas where air pollution is affected by complex regional and meteorological conditions.