The estimation of hourly PM_2.5 concentrations across China based on a Spatial and Temporal Weighted Continuous Deep Neural Network (STWC-DNN)

Abstract

The continuous distributions of PM_2.5 concentrations and predictor variables in the surrounding regions influence the PM_2.5 concentrations in the prediction positions notably, yet few machine learning models quantified the spatially continuous interactions between PM_2.5 concentrations and predictor variations, which limits the prediction accuracy. To fill this gap, a Spatial and Temporal Weighted Continuous Deep Neural Network (STWC-DNN) was proposed. For STWC-DNN, three sub-networks, Single Pixel Network (SPN), Multiple Station Network (MSN), and Continuous Region Network (CRN) were designed to analyze the influence of predictor variables at the prediction position, the influence of PM_2.5 concentrations from surrounding stations, and the influence of continuous raster predictor variables from surrounding pixels respectively. STWC-DNN was experimented using hourly Himawari AOD data and the outputs were compared with a series of advanced models. STWC-DNN achieved higher accuracy than existing models and the sample-based, time-based, and station-based 10-fold cross-validation (CV) R² were 0.92, 0.90, and 0.79, respectively. The principle of establishing STWC-DNN sheds useful lights on the effective use of raster predictor variables and automatic spatiotemporal weight function to better estimate PM_2.5 and other airborne pollutants based on multiple data sources. The codes of STWC-DNN are now available at https://github.com/wangzh2022/STWC-DNN.

Introduction

With the rapid urbanization and industrialization, PM_2.5 (particulate matter with an aerodynamic diameter ≤ 2.5 μm) has become a severe environmental issue in China, some urban agglomerations in particular. PM_2.5 concentrations have a significant negative effect on public health, especially the increase of cardiovascular and respiratory-related morbidity and mortality (Lim et al., 2011, Crouse et al., 2012, Kloog et al., 2013). Therefore, growing efforts have been made on a comprehensive understanding of spatiotemporal variations of PM_2.5 concentrations (Ye et al. 2018) and their anthropogenic (Hagler et al. 2007) and meteorological drivers (Chen et al., 2017, Chen et al., 2018, Chen et al., 2019a, Chen et al., 2019b). These studies usually required long time-series and large-scale PM_2.5 concentration data. Since 2013, with increasing haze episodes, ground PM_2.5 observation stations have been widely made at 1497 stations across the country. However, high-resolution and high precision PM_2.5 concentration products, which are widely required in a diversity of applications, cannot be reliably obtained based on the interpolation using sparsely and unevenly distributed ground observation stations (Zhang et al. 2018).

Thanks to the rapid progress of satellite remote sensing technology, it has become a promising approach for estimating PM_2.5 concentrations using satellite-derived aerosol optical depth (AOD) products. Recently, a series of AOD products, mainly including the Moderate Resolution Imaging Spectroradiometer (MODIS) (Fang et al., 2016, He and Huang, 2018, Hu et al., 2014), GF-1 (Zhang et al. 2018), the Visible Infrared Imaging Radiometer Suite (VIIRS) (Wu et al., 2016, Hu et al., 2017, Yao et al., 2019), and the Multiangle Imaging SpectroRadiometer (MISR) (Liu et al., 2007, Ma et al., 2014, You et al., 2015), have been employed in previous studies to estimate PM_2.5 concentrations. However, one major limitation for most AOD products is the relatively coarse temporal resolution. The temporal resolution for these AODs products is generally produced at a daily basis or even more. Retrieved daily PM_2.5 products cannot effectively meet the requirement for exploring the effects of anthropogenic activities and meteorological conditions on PM_2.5 concentrations, which generally present notable variations on an hourly basis (Chen et al. 2020).

As a geostationary satellite, Himawari-8 can provide AODs with a spatial resolution of 5 km and a temporal resolution of 10 min (Level 2) or 1 h (Level 3) (Bessho et al., 2016, Yumimoto et al., 2016). Based on the Himawari-8 Level 3 AODs products, growing scholars attempted to estimate PM_2.5 concentrations using different algorithms. Wang et al. (2017) employed an improved linear mixed-effect model (LME) for the Beijing-Tianjin-Hebei (BTH) region and achieved a coefficient of determination (R²) of 0.86. Zhang et al. (2019) employed an improved seasonal LME model for Central China (CCH), BTH, Yangtze River Delta (YRD) and Pearl River Delta (PRD) and achieved R² of 0.82, 0.84, 0.80 and 0.74 respectively. Chen et al (2019) employed a stacking model for Central and Eastern China and achieved a R² of 0.85. Wei et al. (2021) proposed a Space-Time Light Gradient Boosting Machine (STLG) model for China and achieved a R² of 0.85. Although these studies proved the feasibility of estimating hourly PM_2.5 products at regional scales, major limitations remained. LME models cannot effectively estimate PM_2.5 concentrations in areas with limited stations (Wang et al. 2017), and thus not suitable for large-scale and continuous estimation. Since the stacking model ignored spatiotemporal variations, PM_2.5 products generated using this model suffered from abnormal values, similar to the salt-and-pepper noise, and caused large prediction biases (Wu et al. 2016). STLG model used the geographical distances of prediction position to stations to generate the spatial feature which would suffer from the uneven station distribution. Therefore, a robust and comprehensive model is required for better estimating PM_2.5 concentrations at a national scale.

A key step for AOD-based PM_2.5 estimation is the exploration of AOD-PM_2.5 relationship. In early years, linear models (Engel-Cox et al., 2004, Gupta and Christopher, 2009) have been a major approach for estimating PM_2.5 concentrations using AODs. However, AOD-PM_2.5 relationship is complicated and non-linear under different emission and meteorological conditions (Yang et al. 2019). Therefore, advanced models were proposed to better explain AOD-PM_2.5 relationship. Statistical models such as Geographically Weighted Regression (GWR) model (Hu et al., 2014, Song et al., 2015), LME model (Li et al., 2015), two-stage model (Hu et al., 2014, Ma et al., 2016), and Geographically and Temporally Weighted Regression (GTWR) model (Huang et al., 2010, He and Huang, 2018), have been employed to explain the nonlinear AOD-PM_2.5 relationship by adding random effects or local effects to regression models. Nevertheless, it remains challenging for using statistical models to precisely express the complicated, uncertain nonlinear AOD-PM_2.5 relationship. Compared with the statistical models, machine learning models can fit complicated relationships (Hu et al. 2017). Researchers employed such models as random forest (RF) models (Hu et al. 2017), and neural network (NN) models (Wu et al., 2012, Li et al., 2017a, Wang et al., 2019) to predict PM_2.5 concentrations at a prediction pixel by considering various predictor variables, including AODs data, and other auxiliary variables, such as meteorological and land use data, and achieved improved prediction accuracies.

Previous studies demonstrated the potential of applying machine learning to PM_2.5 concentration prediction. Nevertheless, spatiotemporal variations were limitedly considered in these machine learning models. On one hand, PM_2.5 concentrations in surrounding stations were considered in Spatial and Temporal Random Forest (STRF) model (Wei et al. 2019), Deep Belief Network (Geoi-DBN) model (Li et al. 2017b), Geographically and Temporally Weighted Neural Network (GTWNN) model (Li et al. 2020a), and SLGT model (Wei et al. 2021). For STRF and Geoi-DBN models, the spatiotemporal variation items, calculated through the spatiotemporal weight function, are used as extra input predictor variables. For GTWNN, the spatiotemporal variations are represented in a similar approach to the GTWR, yet the linear model in GTWR model is replaced with the Neural Network (NN) model. However, for these models, the spatiotemporal weight function is fixed and not adaptive according to actual data sources. A fixed weight function may cause large uncertainties when summarizing remarkable spatiotemporal variations in large areas. The accuracy of PM_2.5 concentration prediction would be affected significantly in regions where spatiotemporal variations do not fit the weight function. The missing data and the uneven station distribution would also result in low prediction accuracy. On the other hand, the diffusion of PM_2.5 concentrations is controlled by the surrounding spatial distribution of meteorological conditions (Chen et al. 2020). Even if the predictor variables of positions are the same, different diffusion conditions in the surrounding regions would lead to different PM_2.5 concentrations of the positions. The situation cannot be modeled in the most existing machine learning models which simply consider predictor variables at the prediction position, resulting in limited prediction accuracy.

To fill these gaps, we attempt to develop a Spatial and Temporal Weighted Continuous Deep Neural Network (STWC-DNN) for better estimating hourly PM_2.5 concentrations across China using Himawari-8 AOD products. For STWC-DNN, specific networks are proposed to automatically establish spatiotemporal weight functions to better consider the discrete meteorological influences on PM_2.5 concentrations. Moreover, in addition to discrete predictor variables, we further consider spatial continuous meteorological influences on PM_2.5 concentrations at the prediction pixel by employing raster data sources. The accuracy of estimated PM_2.5 concentrations is evaluated through sample-based, time-based, and station-based 10-fold cross-validation (CV) (Li et al. 2020b). To further evaluate the performance of STWC-DNN, the three 10-fold CV results of STWC-DNN are compared with some recent models, including the Multiple Line Regression (MLR) model, GTWR model, RF model, STRF model, Geoi-DBN model, GTWNN model, and SLTG model. Since previous models rarely considered spatially continuous variable data, the principle of establishing STWC-DNN sheds useful lights on the effective inclusion of multiple raster data for better estimating the concentration of PM_2.5, ground ozone and other pollutants. The codes of STWC-DNN are now available at https://github.com/wangzh2022/STWC-DNN.