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Enhancing Global Estimation of Fine Particulate Matter Concentrations by Including Geophysical a Priori Information in Deep Learning
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  • Siyuan Shen*
    Siyuan Shen
    Department of Energy, Environmental, and Chemical Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, United States
    *Email: [email protected]
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    Orcidhttps://orcid.org/0009-0006-9295-3205
  • Chi Li
    Chi Li
    Department of Energy, Environmental, and Chemical Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, United States
    More by Chi Li
    Orcidhttps://orcid.org/0000-0002-8992-7026
  • Aaron van Donkelaar
    Aaron van Donkelaar
    Department of Energy, Environmental, and Chemical Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, United States
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    Orcidhttps://orcid.org/0000-0002-2998-8521
  • Nathan Jacobs
    Nathan Jacobs
    Department of Computer Science and Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, United States
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  • Chenguang Wang
    Chenguang Wang
    Department of Computer Science and Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, United States
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  • Randall V. Martin
    Randall V. Martin
    Department of Energy, Environmental, and Chemical Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, United States
    Department of Computer Science and Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, United States
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ACS ES&T Air

Cite this: ACS EST Air 2024, 1, 5, 332–345
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https://doi.org/10.1021/acsestair.3c00054
Published March 27, 2024

Copyright © 2024 The Authors. Published by American Chemical Society. This publication is licensed under

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Abstract

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Global fine particulate matter (PM2.5) assessment is impeded by a paucity of monitors. We improve estimation of the global distribution of PM2.5 concentrations by developing, optimizing, and applying a convolutional neural network with information from satellite-, simulation-, and monitor-based sources to predict the local bias in monthly geophysical a priori PM2.5 concentrations over 1998–2019. We develop a loss function that incorporates geophysical a priori estimates and apply it in model training to address the unrealistic results produced by mean-square-error loss functions in regions with few monitors. We introduce novel spatial cross-validation for air quality to examine the importance of considering spatial properties. We address the sharp decline in deep learning model performance in regions distant from monitors by incorporating the geophysical a priori PM2.5. The resultant monthly PM2.5 estimates are highly consistent with spatial cross-validation PM2.5 concentrations from monitors globally and regionally. We withheld 10% to 99% of monitors for testing to evaluate the sensitivity and robustness of model performance to the density of ground-based monitors. The model incorporating the geophysical a priori PM2.5 concentrations remains highly consistent with observations globally even under extreme conditions (e.g., 1% for training, R2 = 0.73), while the model without exhibits weaker performance (1% for training, R2 = 0.51).

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Copyright © 2024 The Authors. Published by American Chemical Society

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Synopsis

This study examines the value of incorporating geophysical a priori information into a deep learning model on fine particulate matter air pollution.

1. Introduction

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Fine particulate matter (PM2.5) in the ambient environment is the leading environmental risk factor for global health due to its role in morbidity and mortality, with millions of attributable deaths each year. (1,2) Despite the importance of PM2.5, the distribution of ground-based PM2.5 monitors are extremely uneven, with only 10% of countries having more than three ground-based monitors per million inhabitants, while many countries have no operational PM2.5 monitoring at all. (3) A geophysical-hybrid combination of satellite aerosol optical depth (AOD) and chemical transport modeling, followed by statistical calibration with ground-based monitors, can provide high-quality long-term global (4−6) and regional estimates (7) of PM2.5 concentrations. Since machine learning and its subset of deep learning have the capability to enhance PM2.5 estimation accuracy by effectively incorporating multiple interconnected predictors, (8−12) we seek to advance the statistical calibration using a deep learning convolutional neural network (CNN).
While PM2.5 estimation from the geophysical-hybrid method is a valuable source of information for epidemiological and health-impact assessments of PM2.5 exposure, (1,13−16) the performance of machine learning methods and geophysical-hybrid methods has not yet been compared using similar input variables and similar datasets. Understanding and resolving differences between PM2.5 estimation from traditional statistical methods with machine learning methods is increasingly important. However, machine learning methods are susceptible to error for conditions with the limited PM2.5 monitor data for training that exist in most of the world. (17) Indeed, multiple machine-learning-based PM2.5 estimations (9,18−21) exhibit inconsistencies with observations (22−24) over certain areas with sparse monitoring, e.g., the Tibet Plateau. The location of monitors can bias exposure assessment even in developed countries with many monitors. (25,26) There is a need to develop constraints and evaluation methods for machine learning models, and to also quantify their sensitivity to monitor distribution.
Spatial autocorrelation refers to the consistent spatial variation of variables, which commonly arises in practical scenarios with the tendency for nearby sites to exhibit similar values. (27) Machine learning models are increasingly used in the field of air quality but remain susceptible to spatial autocorrelation of ground-level-based measurement in validation methods. (11,18−20,28) Understanding and assessing the effect of spatial autocorrelation on model performance is important to ensure the fidelity of models when estimating concentrations in remote regions with sparse ground-based monitors. We present a novel cross-validation method for air quality that effectively accounts for spatial autocorrelation. Directly estimating the effects of spatial autocorrelation enables a more accurate characterization of study limitations, thus contributing to a more comprehensive understanding of the quality of model estimates.
Here, we develop and optimize a deep learning residual convolutional neural network to improve the representation of global PM2.5 estimates from 1998 to 2019 at a monthly time scale at 1 km2 spatial resolution. We examine the value of incorporating geophysical a priori PM2.5 into the CNN model to estimate PM2.5 especially over sparsely-monitored areas. We introduce novel cross-validation (CV) methods for air quality to address the limitations of common spatial CV approaches that are susceptible to the influence of spatial autocorrelation. This work represents an advancement in both understanding the role of incorporating geophysical a priori variables in machine learning, as well as providing a framework for rigorous evaluation.

2. Data Sources and Methods

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Below we describe the structure of the CNN model and predictor variables followed by the measurement used for training and testing. We then describe a method to improve the performance of the CNN model by developing the loss function to include constraints in regions with few monitors and regularization to penalize error at low concentrations. We evaluate the robustness of the model as a function of the number of monitors and subsequently explore the impact on CNN model performance of excluding geophysical a priori PM2.5 information from a chemical transport model (GEOS-Chem). Additionally, we introduce a buffer leave-one-out (B-LOO) CV approach to the field of machine learning in PM2.5 estimation to evaluate this model, addressing the limitations of traditional spatial CV that largely ignores spatial autocorrelation.

2.1. Structure of the Convolutional Neural Network

We use a convolutional neural network (CNN), a deep learning framework developed by LeCun et al. (29) which is specifically designed to deal with the variability of data in multiple dimensions. (30) The architecture of a typical CNN usually consists of convolution layers that serve as key feature extractors in deep learning models, pooling layers that aid in downsampling and extracting essential information from feature maps, and flatten layers that can transform the input data into a one-dimensional (1D) vector or array to aid final predictions based on the extracted features. An attribute of the CNN model is that it can identify and learn from images making it highly effective for spatial tasks such as the spatial relationship of PM2.5 with predictors in its surrounding environment.
Figure 1 shows the structure of our CNN model. One input array consists of 29 channels (described in Section 2.3) in a block of 11 × 11 pixels surrounding a center pixel, with each pixel representing a 0.01° × 0.01° cell. The model uses a residual convolutional neural network that enables the direct flow of information across layers by using skip connections which can improve the performance of deep learning models. (31) Generally, having too few layers in a neural network may lead to underfitting where the model fails to capture the complexity of the data and performs poorly on both training and testing datasets, while having too many layers can cause overfitting, where the model becomes too specific to the training data and performs poorly on testing data. (32,33) We have optimized hyperparameters including epoch numbers, batch size, the initial learning rate, weight decay, numbers of layers, size of filters, initial input image size, and sensitivity to input channels both manually and with a grid search method. Based on our empirical tests covering hundreds of conventional possible combinations of parameters, we find that ten convolutional layers, max and average pooling layers, and one flatten layer are appropriate for our task. Further increases to the CNN structure complexity led to overfitting that manifested as increase to training R2 but decrease to cross-validation R2. We use a stochastic gradient-based optimization technique (Adam optimizer) (34) that is an iterative method for optimizing an objective loss function to update weight parameters in these layers during the training process. Instead of predicting the PM2.5 directly, we define the objective of predicting the bias (PM2.5,bias) between geophysical a priori PM2.5 and “true” PM2.5 to enable direct inclusion of this a priori information into the estimation processes. This approach is related to boosting geophysical PM2.5 concentrations using deep learning. We treat measured PM2.5 as truth during the training process as described in the next section.

Figure 1

Figure 1. Input array and structure of the residual convolutional neural network. The left panel shows the input array. The gridded square indicates the 11 × 11 pixel image of predictor variables cropped around a pixel of interest (blue pixel). The right panel shows the structure of the residual convolutional neural network. Rectangles represent the structure of the residual CNN, with blue for convolutional layers, pink for pooling layers, and orange for the flatten layer. Blue lines represent skip connections. Numbers in each convolutional layer indicate the number of input channels, the number of output channels, the width of the kernel, and the height of the kernel. Numbers in the pooling layer indicate the size of kernels. PM2.5,bias is defined as geophysical a priori PM2.5 minus “true” PM2.5.

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2.2. Incorporation of Ground-Based PM2.5 Measurement Data

Ground-based PM2.5 measurements are treated as label data for the neural network training using the difference between geophysical a priori PM2.5 and the measurement. Over North America, we obtained PM2.5 observations from the United States Environmental Protection Agency’s Air Quality System (AQS) and Environment Canada’s National Air Pollution Surveillance (NAPS) program. The PM2.5 measurements over Europe are from the European Environment Agency Air Quality e-Reporting system (https://www.eea.europa.eu/data-and-maps/data/aqereporting). Over mainland China, PM2.5 measurements were obtained from https://quotsoft.net/air/ which contains data captured by individuals from instantaneous data records on the website of the Ministry of Ecology and Environment of China. PM2.5 measurements for Taiwan were obtained from the Taiwanese Environmental Protection Administration (https://www.moenv.gov.tw/en/). Australian PM2.5 observations were separately downloaded for the Northern Territory State (http://ntepa.webhop.net/NTEPA/), Queensland State (https://www.data.qld.gov.au/dataset/), and New South Wales State (https://www.dpie.nsw.gov.au/air-quality/air-quality-data-services/data-download-facility). Additionally, PM2.5 measurement data were used from literature sources, the World Health Organization Global Ambient Air Quality Database, (35) and OpenAQ (http://openaq.org) which provides coverage from worldwide locations, including some of the Surface Particulate Matter Network (SPARTAN). (36,37) We include temporally continuous global ground-based information from van Donkelaar et al. (39) that represents missing ground-based observations within the time series using relationships with observations at available monitor locations, geophysical PM2.5 estimates, and simulated PM2.5, based upon the consistency of each data source with the coincidently observed data record. At least 18 daily observations were required to be considered representative of each month, and values beyond the 10th and 90th percentile within each month at each location were removed prior to averaging to limit the impact of outliers. Spatially collocated monitor data points within a 1 km2 cell were combined and considered as a single monitor location. Low-cost monitors were not included. (38) The locations of all sites are shown in Figure 2.

Figure 2

Figure 2. Location of ground monitors and corresponding annual average PM2.5 concentration in 2018. Black boxes represent regions used in Table 3 and Figure 6 and correspond to nested regions of the GEOS-Chem simulation.

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2.3. Processing of Predictor Variables

Table 1 describes the predictor variables included as input channels in the first convolutional layer. We used 29 predictors for each grid cell to estimate the bias of geophysical a priori PM2.5. In predictor selection, in addition to considering whether the predictor is relevant to AOD and PM2.5, we also decide whether to use the predictor by excluding or adding it to assess the impact on model performance.
Table 1. Predictor Variables (Channels)a
VariablesSourceInitial Spatial ResolutionbNumber of variables 
Geophysical a priori PM2.5van Donkelaar et al. (39)0.01° × 0.01°1*
Satellite retrieved AODMultiple satellite sources (39)0.01° × 0.01°1 
ηGEOS-Chem0.05° × 0.625° or 2.0° × 2.5°1*
Uncertainties of η: (1) From differences in simulated and retrieved AOD at simulation scales; (2) From large vertical gradients; (3) From topographic features at subgrid scale; (4) From aerosol features at subgrid scale within η; (5) From coastal effects at subgrid scalevan Donkelaar et al. (26)0.01° × 0.01°5*
GEOS-Chem outputs: Concentrations of PM2.5, nitrate, sulfate, ammonium, black carbon (BC), organic carbon (OC), secondary organic aerosols (SOA), dust, and sea saltGEOS-Chem V11–01; using simulation-specific updates described by Hammer et al. (6)0.5° × 0.625° or 2.0° × 2.5°9*
Latitude and longitude 0.01° × 0.01°2 
ElevationGMTED20100.01° × 0.01°1 
Surface BC and OC emissionsCommunity Emissions Data System (CEDS) (40)0.5° × 0.625°2 
Mineral dust and sea salt emissionsGEOS-Chem input0.5° × 0.625°2 
Meteorology fields─planetary boundary layer height (PBLH), relative humidity (RH), wind speeds (u, v), and temperatureModern-Era Retrospective Analysis for Research and Applications, Version 2 (MERRA2)0.5° × 0.625°5 
a

Variables with * are excluded in the CNN model without a priori PM2.5 estimations input in the robustness test.

b

The spatial resolution for GEOS-Chem output is 0.5° × 0.625° over the boxed regions of Figure 2 and 2° × 2.5° elsewhere.

A major source of information is the community open-source GEOS-Chem chemical transport model (http://geos-chem.org). (39) GEOS-Chem uses information on emissions, meteorological data, and equations that represent the physics and chemistry of atmospheric composition to simulate the time-varying 3-D concentrations of aerosol components that comprise PM2.5. The geophysical a priori PM2.5 estimates (39) are based on satellite AOD and GEOS-Chem simulations using the geophysical relationship:
PM2.5,geo=η(x,y,t)×AOD
(1)
where η is the spatially and temporally varying ratio between the monthly mean AOD at satellite sampling time and 24 h monthly mean PM2.5 simulated by the GEOS-Chem model. Uncertainties in η, as described by van Donkelaar et al., (39) represent parameters and processes that affect the relationship between AOD and PM2.5. Predictor variables include monthly AOD that merged seven satellite datasets (39) and outputs from GEOS-Chem global and nested simulation (V11–01; with updates described by Hammer et al. (6)), including PM2.5 and its components.
Additional variables are meteorological data, air pollution emission data, elevation, longitude, and latitude of each pixel. For the meteorological data, the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2; https://gmao.gsfc.nasa.gov/reanalysis/MERRA-2/), is used for fields of temperature, wind speed, relative humidity (RH), and planetary boundary layer height (PBLH). Three-hourly meteorology variables are averaged to monthly mean fields. Anthropogenic black carbon (BC) and organic carbon (OC) emissions are from the Community Emission Data System (CEDS) (40) inventory. Natural dust emissions (41) and sea salt emissions (42) are from standard inputs to the GEOS-Chem model. Elevation is from Global Multi-resolution Terrain Elevation Data 2010 (GMTED2010). (43) We also considered additional variables of population density, the Terra and Aqua combined Moderate Resolution Imaging Spectroradiometer (MODIS) Land Cover Climate Modeling Grid (MCD12C1), and the Global Roads Inventory Project (GRIP) dataset but found that these variables worsen the accuracy of the model, and these variables were abandoned. A previous study observed a similar issue by incorporating population density. (44)
Most predictor resolutions are 0.01° × 0.01° (∼1 km × 1 km) or 0.5° × 0.625°. Some predictors have a resolution of 0.5° × 0.625° over the nested regions indicated in Figure 2, or 2.0° × 2.5° over the rest of the world. Predictors with lower spatial resolution were gridded to 0.01° × 0.01° resolution with a bilinear interpolation algorithm. The input data span from 1998 to 2019, mostly monthly averages except latitude, longitude, and elevation which are static. All predictors are normalized from different magnitudes and range to distributions with zero mean and unity variance (μ = 0; σ =1) following standard practice. (45)

2.4. Improvement of Loss Function

Neural network models are trained by minimizing a loss function, which represents the error of the neural network and precisely describes what the neural network will minimize. Rather than predicting PM2.5 concentration as is common practice, we modify the loss function to directly include geophysical a priori PM2.5 estimates by predicting the bias in these estimates. Table 2 contains details of the models examined here. A popular loss function for regression is the Mean Squared Error (MSE) loss function L shown in eq 2, which is typically used in the pixel-wise comparison of model estimation and observed datasets. The parameter xi is the input matrix surrounding pixel i, and f(xi) is the model output for pixel i. The parameter yi is the label data in pixel i, i.e., the bias of the geophysical a priori PM2.5 versus ground monitor PM2.5. N is the total number of training datasets input to the model in one training step.

MSE loss function:

L=1N∑i=1N(f(xi)−yi)2
(2)
Few previous studies have customized the loss function for deep learning methods in PM2.5 estimation. (46−48) In this study, we identified shortcomings associated with employing the MSE loss function for training a global CNN PM2.5 model. These deficiencies encompass disregard for regions characterized by low PM2.5 concentrations and the production of unreasonable estimations in areas with limited monitor coverage. To address these limitations, we customize the loss function through the adaptation of value-specific weights and incorporate geophysical a priori PM2.5 estimates inferred from satellite AOD and a chemical transport model.
Table 2. Description of Different Models Used in This Study
Model NameDevelopmentDescription
MSE Model

MSE loss function:

Model trained with the MSE loss function.
adj-MSE Model

Adj-MSE loss function:

Model trained with the adj-MSE loss function.
Standard Model

Adj-GeoMSE loss function:

Model trained with the adj-GeoMSE loss function.
Optimized Model

Adj-GeoMSE loss function:

Model trained with the adj-GeoMSE loss function. An additional geographically weighted average approach is applied if the distance of a pixel to the nearest ground monitor exceeds 150 km.

Optimized:

Biases between geophysical a priori PM2.5 and observed PM2.5 vary regionally, (39) e.g., North America and Asia, which engenders heterogeneous contributions from these regions to the loss function during the training process. Areas with low concentrations typically have small absolute biases that yield weaker contributions to the loss function. To improve the accuracy of the model over regions with low concentrations and promote skill across the full range of concentrations, we modified the MSE loss function as denoted in eq 3 to amplify the weights of loss from those areas with an adjusted coefficient (1+βe−αyi2).

Adjusted MSE loss function (adj-MSE):

L=1N∑i=1N(1+βe−αyi2)(f(xi)−yi)2
(3)
The parameter yi is squared to make the adjusted coefficient symmetric about zero. The coefficients α and β, which are both positive, control the range where the adjusted coefficient is significantly larger than 1 and the maximum value of the adjusted coefficient. The adjusted MSE loss function (adj-MSE) assigns comparatively greater weights to points with lower biases, while gradually transitioning towards a normal MSE loss function as the absolute biases increase. Here α is selected as 0.005 and β as 8 to enhance the contribution of sites with small biases and the coefficient relaxes to 1 at a bias of around 35 μg/m3.
Unrealistic estimation over the Tibetan Plateau, encountered in previous studies utilizing neural networks or other machine learning methods, (22−24) was also observed in the model trained with the MSE loss function (discussed in Section 3.4). To address this issue, we incorporate two regularization terms into the loss function to form an adjusted MSE loss function with geophysical penalty terms (adj-GeoMSE), as depicted in eq 4.

Adjusted MSE loss function with geophysical penalty terms (adj-GeoMSE):

L=1N∑i=1N[(1+βe−αyi2)(f(xi)−yi)2+λ1max(0,−f(xi)−GeoPM2.5,i)+λ2max(0,f(xi)−γGeoPM2.5,i)]
(4)
f(xi) is the estimation from the model in pixel i, and GeoPM2.5,i is the corresponding geophysical a priori PM2.5 concentration. The magnitudes of the two positive parameters, λ1 and λ2, control the strength of the penalty applied, and the parameter γ constrains the range of the second penalty term. λ1, λ2, and γ are set as 10, 0.2, and 3. The first penalty is a natural constraint. When the CNN model gives an estimated bias smaller than −GeoPM2.5,i, it leads to a negative PM2.5 concentration which is unrealistic. Consequently, the first term of the loss function incorporates a positive penalty to address negative concentrations. For the second penalty term, the choice of γ is not self-evident, and it is necessary to rely on empirical results to determine a reasonable γ as described in Supporting Information Section S1. Briefly, the pixel-level distribution of the relative ratio of the biases between monthly geophysical a priori PM2.5 and observed PM2.5 reveals that most relative ratios are concentrated between −1 to 3, which means that although the absolute values of PM2.5 vary greatly across regions, the biases of the geophysical a priori PM2.5 have a defined range that is proportional to geophysical a priori PM2.5 and used to determine γ in the second penalty term. The second penalty term adds a positive penalty when the model gives an estimation that is larger than γGeoPM2.5,i.
To enhance model reliability in remote regions, we employ a geographically weighted average approach when the distance d from the nearest training monitor exceeds 150 km which is informed by the comparison of the deep learning model and geophysical a priori PM2.5 in Section 3.2. At larger distances, the standard CNN model relaxes to the geophysical a priori to produce the optimized PM2.5 estimation which is shown in eq 5.
Optimized⁡PM2.5,i=(1−ωi)PM2.5,std,i+ωiGeoPM2.5,i,⁣whereωi=(max(0,d−150d))2
(5)
where PM2.5,std,i is the PM2.5 estimation of pixel i from the standard CNN model. We refer to this output as optimized as it includes all the optimization steps considered in the study.

2.5. Traditional and Sparse Robustness Tests

We assess the robustness of model performance across diverse distribution densities using multiple k-fold spatial CV approaches. Typically, 10% of monitoring sites are withheld for the spatial CV in PM2.5 estimation. (11,49) However, Figure 1 and previous studies have identified that the distribution of observational sites varies greatly, (3) with North America, Western Europe, and East Asia having much more densely distributed sites than other regions such as Africa and South America. Thus evaluation of performance for sparse monitor conditions is of particular importance but is impeded in normal CV by the lack of sites. We assess model robustness by testing its performance at low and extremely low site densities. Consequently, we randomly withheld different percentages from 10% to 99% of sites for validation, and restricted the other sites to training. We also tested the difference between the model trained with and without a priori information from GEOS-Chem. The model without a priori information from GEOS-Chem is trained with traditional MSE loss function that does not require geophysical a priori.

2.6. Buffer Leave-One-Out (B-LOO) Spatial CV

Spatial autocorrelation can result in biased performance statistics from normal spatial CV by overestimating true model performance. (50) We assess the degree of spatial autocorrelation by constructing a semivariogram of the measured PM2.5 concentration versus distance as shown in eq 6 and a semivariogram of the sum of the normalized training variables in the input matrix versus distance as shown in eq 7.
δPM=∑i=1N(PM2.5,i−PM2.5,i+d)2N
(6)
δTrainingMatrix=∑c=1C∑w=1W∑h=1H∑i=1N(Mi,c,w,h−Mi+d,c,w,h)2N
(7)
δ is the semivariance, and N is the total number of pairs of sites with distance d. PM2.5,i is the measured PM2.5 concentration, and PM2.5,i+d is the measured PM2.5 concentration at distance d from PM2.5,i. Mi,c,w,h is the training matrix, where c is the channel index, w is the width index, and h is the height index. Mi+d,c,w,h is the training matrix at distance d from Mi,c,w,h. We normalized each semivariance matrix by its variance to reduce inter-seasonal variability.
Figure 3 shows the semivariance versus distance relationship. A positive relationship of the semivariance with distance is apparent in both the observed PM2.5 and training matrix indicating strong spatial autocorrelation out to 3,000 km after which semivariance increases and plateaus. This reveals the tendency for nearby sites to have similar PM2.5 concentrations. Larger semivariance of observed PM2.5 in January compared to July reflects the greater spatial heterogenity in winter. Table S1 shows the binned distribution of distances between each site and the nearest site. Around 30% of sites are within 1 km of the nearest site, and around 80% of sites are within 10 km of the nearest site. This proximity implies susceptibility of traditional spatial cross-validation to spatial autocorrelation that could artificially inflate model performance.

Figure 3

Figure 3. Assessment of spatial autocorrelation using normalized semivariance of the observed PM2.5 versus distance (left) and normalized semivariance of training matrix versus distance (right).

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In order to comprehensively evaluate the performance of this model under different spatial dependence conditions and explore the model skill in areas where the station distribution is sparse, we use k-fold buffer leave-one-out (B-LOO) spatial CV. (50) The training datasets are determined by establishing circular buffer zones around randomly selected test sites, thereby excluding any sites within this buffer from the training datasets as shown in Figure 4. Solely those sites lying outside the buffer zones are considered constituents of the training set. Adjusting the radius of the buffer zones enables artificially creating different spatial conditions. The B-LOO CV confers a notable benefit in that it not only mitigates the inherent limitations of naïve model performance evaluation but also facilitates estimating the confidence of the model in its ability to extrapolate (i.e., over unmonitored areas), thus offering advantages over the classical validation approach of normal spatial CV.

Figure 4

Figure 4. Example distribution of buffer zones with a radius of 500 kilometers over the global range (top) and with a radius of 200 kilometers over North America (bottom). Pink shading indicates circular buffer zones in which sites are excluded from training around test sites as part of buffer leave-one-out (B-LOO) spatial cross-validation.

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3. Results and Discussion

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3.1. Performance of the Optimized Model Using Traditional Cross-Validation

Table 3 compares the monthly mean PM2.5 concentration derived from the optimized CNN model with collocated ground-based observations for different regions for time periods during which the region had well-established ground-based observational networks. Also included are R2 values for the traditional 10-fold spatial CV of the MSE CNN model, the optimized model, and hybrid geographically weighted regression (GWR) PM2.5 estimates (39) which are taken as a benchmark here. CNN PM2.5 estimates not only exhibit high consistency with ground-based observations over all regions in all seasons but also generally outperform the traditional statistical method, hybrid GWR. Regionally, the monthly R2 values between the optimized CNN and ground-based PM2.5 over Europe (0.54–0.72) and Asia (0.63–0.77) are higher than those over North America (0.50–0.61), though they are lower compared to the monthly R2 over the global range (0.75–0.87). The relative Root Mean Square Error (rRMSE) exhibits stable values of around 0.3–0.4. The population-weighted average PM2.5 concentrations at ground-based monitor locations exhibit a notable concurrence with the optimized CNN PM2.5 estimates, with the largest difference of 1.6 μg/m3 in January over Asia. Compared with the hybrid GWR PM2.5, our optimized CNN model estimates exhibit higher R2 and lower RMSE values in global and Asia regions and comparable R2 and RMSE values in North America and Europe regions. Given the similarity of input variables employed in both methods, it is reasonable to assert that the CNN possesses a greater capacity to capture information than the hybrid GWR method, thereby enabling superior estimation of PM2.5 concentrations under similar circumstances.
Table 3. Comparison of Annual and Monthly Mean Spatial CV CNN and Monitor-Based OM2.5a
Region and monthOptimized Model R2MSE Model R2Hybrid GWR R2Optimized Model rRMSEHybrid GWR rRMSEOptimized Model slopePopulation-weighted co-monitorb mean PM2.5 (optimized model) [μg/m3]population-weighted monitor means PM2.5 (in situ) [μg/m3]
Globalc annual0.86 [0.83,0.88]0.86 [0.83,0.89]0.84 [0.81,0.86]0.34 [0.33,0.35]0.37 [0.35,0.39]1.00 [0.99,1.00]37.4 [34.7,40.9]36.9 [34.3,40.7]
JAN0.87 [0.86,0.89]0.88 [0.86,0.90]0.86 [0.84,0.88]0.39 [0.38,0.40]0.42 [0.41,0.43]1.00 [1.00,1.00]56.3 [52.5,61.2]55.7 [51.8,60.8]
APR0.83 [0.79,0.85]0.83 [0.79,0.85]0.81 [0.78,0.84]0.38 [0.37,0.39]0.40 [0.39,0.41]1.00 [0.99,1.00]34.7 [32.1,37.5]34.4 [31.6,37.5]
JUL0.75 [0.67,0.80]0.75 [0.69,0.80]0.72 [0.67,0.77]0.42 [0.41,0.45]0.46 [0.44,0.48]0.98 [0.97,0.99]26.2 [24.1,30.0]25.7 [23.6,29.6]
OCT0.81 [0.78,0.84]0.81 [0.79,0.84]0.78 [0.75,0.82]0.42 [0.40,0.44]0.46 [0.45,0.47]0.99 [0.99,1.00]34.1 [32.2,39.8]33.7 [31.1,38.1]
Northd America annual0.57 [0.42,0.73]0.55 [0.39.72]0.57 [0.42,0.73]0.25 [0.23,0.27]0.24 [0.21,0.25]0.84 [0.74,0.95]9.0 [6.5,11.3]9.8 [7.6,12.2]
JAN0.50 [0.27,0.63]0.47 [0.26,0.63]0.51 [0.29,0.64]0.35 [0.30,0.43]0.34 [0.29,0.42]0.78 [0.62,0.88]10.4 [7.6,15.7]11.2 [8.5,16.5]
APR0.54 [0.39,0.68]0.47 [0.34,0.66]0.57 [0.44,0.71]0.30 [0.27,0.34]0.26 [0.24,0.30]0.87 [0.79,0.96]7.4 [5.2,9.6]8.2 [6.2,10.6]
JUL0.61 [0.44,0.78]0.56 [0.36,0.76]0.61 [0.43,0.78]0.29 [0.23,0.43]0.27 [0.21,0.43]0.95 [0.85,1.00]10.5 [7.2,13.1]11.2 [7.9,15.2]
OCT0.51 [0.36,0.68]0.46 [0.32,0.65]0.53 [0.42,0.69]0.31 [0.29,0.36]0.29 [0.25,0.34]0.87 [0.78,0.97]7.6 [5.2,9.8]8.5 [6.6,10.8]
Europee annual0.69 [0.67,0.72]0.69 [0.67,0.70]0.68 [0.66,0.70]0.27 [0.26,0.29]0.27 [0.26,0.29]0.81 [0.78,0.83]15.3 [13.6,17.7]16.4 [14.8,18.7]
JAN0.72 [0.66,0.76]0.71 [0.64,0.76]0.72 [0.67,0.76]0.32 [0.30,0.37]0.33 [0.29,0.38]0.83 [0.75,0.87]20.0 [16.4,26.3]21.3 [17.8,27.7]
APR0.59 [0.58,0.63]0.57 [0.51,0.61]0.59 [0.53,0.64]0.30 [0.28,0.32]0.30 [0.28,0.32]0.80 [0.75,0.85]14.8 [12.2,17.9]15.7 [13.2,18.8]
JUL0.54 [0.40,0.59]0.52 [0.38,0.58]0.53 [0.42,0.58]0.30 [0.28,0.33]0.30 [0.28,0.32]0.78 [0.74,0.83]11.7 [10.3,13.8]12.5 [11.6,14.4]
OCT0.67 [0.58,0.71]0.66 [0.60,0.70]0.67 [0.62,0.71]0.32 [0.30,0.34]0.31 [0.29,0.33]0.86 [0.81,0.91]14.8 [13.2,16.6]15.8 [14.3,17.6]
Asiaf annual0.72 [0.68,0.74]0.71 [0.68,0.74]0.69 [0.65,0.72]0.26 [0.26,0.29]0.27 [0.27,0.28]0.92 [0.91,0.94]48.2 [44.3,52.9]46.8 [42.6,51.9]
JAN0.77 [0.74,0.81]0.78 [0.76,0.82]0.75 [0.72,0.80]0.29 [0.28,0.30]0.31 [0.29,0.31]0.96 [0.96,0.99]74.8 [69.8,81.7]73.2 [68.0,80.5]
APR0.63 [0.60,0.70]0.63 [0.59,0.67]0.62 [0.58,0.66]0.28 [0.27,0.30]0.28 [0.27,0.29]0.91 [0.91,0.92]44.5 [40.5,48.5]43.3 [38.9,47.7]
JUL0.64 [0.56,0.69]0.63 [0.56,0.68]0.59 [0.49,0.65]0.32 [0.30,0.35]0.33 [0.31,0.35]0.93 [0.90,0.96]32.2 [28.9,37.5]30.7 [27.5,36.2]
OCT0.67 [0.63,0.72]0.67 [0.64,0.72]0.61 [0.57,0.64]0.33 [0.32,0.36]0.37 [0.36,0.38]0.91 [0.90,0.93]43.9 [41.3,51.8]42.5 [39.6,50.5]
a

Mean [min, max] values are given.

b

Optimized CNN model estimation in pixels that contain a ground-based monitor.

c

The number of monitor locations for the global region is 10870 over 2015–2019.

d

The number of monitor locations in North America is 2789 from 2001–2019.

e

The number of monitor locations for Europe is 3238 from 2010–2019.

f

The number of monitor locations for Asia is 3471 from 2015–2019.

We also compare the performance of the optimized CNN model versus that of an alternative statistical method (DIMAQ) over global regions in Table 4. Out-of-sample CV results are not available for DIMAQ so within-sample performance is shown for DIMAQ and hybrid GWR. The out-of-sample R2 of our optimized CNN model exceeds the within-sample R2 of the DIMAQ product over the global range (0.86 vs 0.83), South Asia (0.56 vs 0.54), North America (0.57 vs 0.43), and the rest of the world (0.63 vs 0.46). The out-of-sample results of our optimized CNN model are as good as the within-sample hybrid GWR performance over the global range, better over North America (0.57 vs 0.42), tropical Latin America (0.23 vs 0.16), and the rest of the world (0.63 vs 0.54). The in-sample performance of the optimized CNN model exceeds both hybrid GWR and DIMAQ products across all regions.
Table 4. Comparison of Annual Mean Spatial CV for CNN, DIMAQ, and GWR with Monitor-Based PM2.5
RegionsaOut-of-Sample Optimized Model R2 (Annual)In-Sample Optimized Model R2 (Annual)In-Sample DIMAQ Model R2 (Annual)In-Sample GWR Model R2 (Annual)Comparison Year Range
Global0.860.910.830.862015–2019
China0.760.800.770.772015–2019
Southeast Asia0.110.580.310.242015–2019
South Asia0.560.760.540.692015–2019
North America0.570.670.430.422001–2019
Western Europe0.690.770.730.762010–2019
Tropical Latin America0.230.630.280.162015–2019
Rest of World0.630.850.460.542015–2019
a

Region definitions follow the Global Burden of Disease project.

We evaluate the robustness of the model to sparse training data by artificially diminishing the number of ground-based sites to simulate the performance of the model in regions with limited availability of ground-based sites. Figure 5 shows the robustness test results of the model trained with (left) and without (right) incorporating the geophysical a priori PM2.5, and GEOS-Chem outputs as CNN input variables. Excluded variables are listed in Table 1. Exclusion of the geophysical a priori PM2.5 that depends upon GEOS-Chem output changes the loss function to predict total PM2.5 rather than bias in the geophysical a priori estimates. When employing the 10-fold spatial CV with 10% withheld for testing, the R2 of the two models are comparable, and both explain 10%–30% greater variance than the geophysical a priori PM2.5. With progressively greater withheld percentages, the R2 of the CNN model which incorporates the geophysical a priori variables exhibits a gradual decline, yet persistently maintains a superior level in comparison to geophysical a priori PM2.5 except for the North American region under the extreme condition of 99% withheld for testing. In contrast, the R2 of the CNN model which excludes GEOS-Chem information drops rapidly, especially in North America, where the R2 is worse than for geophysical a priori PM2.5 when more than 80% of monitors are withheld for testing. The R2 is lower than geophysical a priori PM2.5 in all regions in the extreme condition of 99% withheld. This evaluation reveals the pivotal role of a physically based model (e.g., GEOS-Chem) in providing geophysical a priori information to the deep learning model to improve performance in regions with few monitors.

Figure 5

Figure 5. Robustness tests indicating R2 of the CNN model as a function of the percentage of monitors withheld for testing. The top panel contains the results of the CNN model including geophysical a priori PM2.5 and GEOS-Chem outputs as input variables. The bottom figure contains the results of the model excluding these from input variables (details in Table 2). The numbers inside of each circle and its size indicate the R2 of annual average PM2.5 compared with the ground-based observations. The color indicates the difference of R2 between the CNN PM2.5 and the geophysical a priori PM2.5 estimates.

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Figure 6 shows density scatter plots comparing the direct PM2.5 observations with spatial cross-validated values from the optimized CNN model over the global domain (2015–2019), Asia (2015–2019), North America (2001–2019), and Europe (2010–2019). The standard CNN model exhibits high consistency with observed data, especially in Asia (R2 = 0.71, slope = 0.93) as well as the global domain (R2 = 0.86, slope = 1.01). Some decline in the slope is found in North America (slope = 0.85) and Europe (slope = 0.79), with overestimation at low concentrations (<2.5 μg/m3 in North America, <5.0 μg/m3 in Europe).

Figure 6

Figure 6. Density scatterplots comparing the optimized CNN model and ground-monitored PM2.5 in different areas. The coefficient of determination (R2), root mean square error (RMSE), reduced major axis linear regression, and the total number are in the top-right corner of each scatter plot. Blue lines indicate the regression line. Black lines are identity lines: y = x.

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Our spatial CV tests exclude from training all years of a test site to isolate spatial evaluation and to avoid the effects of temporal autocorrelation. Had we withheld from training only the test year and allowed data from prior years of a test site to be used for training, the annual R2 for 2015–2019 would have increased globally (from 0.86 to 0.90) and regionally (from 0.42 to 0.49 for North America, from 0.69 to 0.77 or Europe, from 0.71 to 0.78 for Asia), as shown in Table S2, illustrating the need to avoid effects of temporal autocorrelation when evaluating spatial performance.

3.2. Buffer Leave-One-Out Cross-Validation

Figure 7 shows the B-LOO spatial CV results of the optimized CNN, the standard CNN model, the MSE model, the MSE CNN model excluding the GEOS-Chem variables from the input data, and geophysical a priori PM2.5. Table 5 contains the number of training and testing sites for different buffer zone radii. The performance of the CNN model diminishes as the radius increases for two reasons. First, given the 10-fold B-LOO spatial CV implemented here, as the radius increases the number of testing sites remains constant and the number of training sites decreases. Second, as the B-LOO spatial CV excludes the influence of spatial autocorrelation within the buffer radius, an expansion of the buffer size decreases residual spatial autocorrelation.

Figure 7

Figure 7. Global annual R2 and population-weighted mean (PWM) rRMSE for buffer leave-one-out (B-LOO) spatial cross-validation. Solid lines and symbols indicate means of annual values over 2015–2019. Error bars indicate standard deviation of annual values over 2015–2019.

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Table 5. Number of Training and Testing Sites with Different Buffer Radius Settings
Buffer Radius (km)Average Number of Training SitesAverage Number of Testing Sites
097831087
1074321087
5041771087
10020491087
15012991087
2007041087
5002131087
10001431087
The standard CNN model outperforms the geophysical a priori PM2.5 data when the radius is within 150 km, but the R2 drops below that of the geophysical data for larger radii. This finding informs the structure of eq 5, in which the influence from the geophysical a priori PM2.5 begins at 150 km, and the geophysical a priori PM2.5 influence increases as distance increases. The R2 of the MSE model exhibits a faster rate of decline than the standard CNN model as the radius reaches 100 km, again supporting developments to the loss functions. Compared with other models, the R2 of the MSE CNN model excluding GEOS-Chem data exhibits the strongest rate of decline which reaches a similar performance with the geophysical a priori PM2.5 at 50 km radius. At a 1000 km radius, all models except the optimized one exhibit weaker performance than geophysical a priori PM2.5. The comparison of these models demonstrates the importance of introducing an a priori PM2.5 to models in sparsely monitored areas. Meanwhile, all models exhibit similar performance if traditional spatial CV is used (e.g., at buffer radius of 0), highlighting the importance of assessing the influence of spatial autocorrelation when using deep learning to estimate the spatial distribution of PM2.5.
Figure 7 also shows the effect of excluding geophysical a priori PM2.5 from the optimized model when the training monitor distance exceeds 150 km. The standard CNN model exhibits degraded performance at locations with sparse monitoring. This finding highlights the significance of incorporating the geophysical a priori PM2.5 estimates, even in situations where deep learning methods dominate. This result also indicates that our standard deep learning model remains affected by spatial autocorrelation. Overall, the contrasting outcomes of B-LOO CV and traditional spatial CV indicate the value of introducing B-LOO CV to compensate for the weakness of traditional spatial CV methods in evaluating variables with spatial autocorrelation.
To further investigate the performance of models under different spatial conditions, we separate the R2 reduction due to the reduction of training datasets and reduction of spatial autocorrelation. We derive the reduction of R2 caused by the reduction of training datasets by running normal spatial CV with the same number of training datasets as B-LOO CV in different spatial conditions. Figure 8 shows the sources of R2 reduction with different buffer radii for all models. In all models except the optimized model, the reduction of spatial autocorrelation contributes significantly to the overall reduction in R2 across all spatial conditions, with increasing reduction as the buffer radius expands. This finding substantiates the utility of B-LOO CV in quantifying the influence of spatial autocorrelation on model performance. In the optimized model, when the radius exceeds 150 km, the decrease in R2 due to spatial autocorrelation accounts for a small proportion of the decrease in total R2 compared with other models. This implies the capacity of the optimized model to mitigate spatial autocorrelation.

Figure 8

Figure 8. Sources of R2 reduction in buffer leave-one-out (B-LOO) spatial cross-validation. Solid bars represent R2 reduction from the reduction of training dataset numbers, and dashed bars represent R2 reduction from the reduction of spatial autocorrelation.

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3.3. PM2.5 Distribution with the Optimized Model

Figure 9 shows the monthly mean PM2.5 of the optimized CNN model in January and July 2018. Our estimates exhibit coherent seasonal variation with higher global population-weighted concentrations in January (45.5 μg/m3) than July (25.7 μg/m3). The spatial distribution of PM2.5 within Asia exhibits substantial seasonal variation, with wintertime (January) PM2.5 concentrations more than double the summertime (July) concentrations in parts of eastern China and South Asia. The highest PM2.5 concentrations are found over the North China Plain, over the Indo-Gangetic plain in January, and over Pakistan in July. The concentration of PM2.5 in Eastern Europe and northern Italy significantly exceeds that of Western Europe during the wintertime (January), with levels reaching twice the magnitude. Conversely, during summertime (July), the difference in PM2.5 concentrations between the two regions diminishes to approximately 20%, wherein the concentrations in Eastern Europe remain higher than those in Western Europe. Wildfire-induced enhancements exist during the summer (July) across northern and western regions of North America, as well as northeast Asia. Distinct seasonal fluctuations in PM2.5 distribution across Africa are also discernible, with PM2.5 predominantly near the Bodélé Depression in January, and in west Africa and Congo Basin in July. These spatial and seasonal variations exceed the expected model uncertainty (Figure 7) and are consistent with the state-of-science understanding of variabilities in PM2.5 sources and meteorological modulations. (39,51) Inspection of interannual variability also reveals expected features such as the fire in California in November 2018.

Figure 9

Figure 9. Monthly mean PM2.5 estimation of the optimized CNN model in January (top) and July (bottom) 2018. Numbers at the bottom-left are the global population-weighted mean (PWM) PM2.5

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3.4. Effects of Excluding Other Loss Function Modifications

We next examine how model performance would change if specific method developments were excluded. Table 3 shows that although the R2 for the PM2.5 estimates of the MSE CNN model also exhibits high consistency with ground-based observations over all seasons over most regions, the MSE loss function, which is often adopted by most deep learning models for regression tasks, does not perform well in areas with low PM2.5 concentration, e.g., North America and Europe. Had we not customized the loss function by increasing the penalty at low PM2.5 concentration biases, monthly and annual R2 over North America would have degraded by 0.02–0.05, and over Europe would have degraded by 0.01–0.02.
Figure S1 shows the difference of PM2.5 estimates from the MSE model to the optimized CNN model. Pronounced differences are apparent where observation sites are sparse such as northern Africa and the Tibetan plateau. Had we not applied the geophysical penalties in the loss function, the PM2.5 concentration of the MSE CNN model over the Tibetan Plateau would be 40 μg/m3 higher in January and 30 μg/m3 higher in July. Observations from the Tibetan Plateau indicate annual average PM2.5 concentrations below 15 μg/m3. (22−24) Numerous previous investigations employing machine-learning techniques to estimate PM2.5 over the Tibetan Plateau exhibited a prevailing tendency for overestimation. (9,18−21) With the incorporation of geophysical penalty factors to constrain the resultant outputs, the optimized model over the Tibetan Plateau gives the estimation of PM2.5 below 20 μg/m3 in January and around 10 μg/m3 in July. Figure S4 shows R2 values for all models. Skill between the MSE and optimized models remains stable in areas with high PM2.5 concentrations, despite the emphasis on accuracy at low concentration.

3.5. Outlook

In summary, developments of a deep learning model enabled deriving global PM2.5 estimates that exhibit improved performance compared to prior methods. This advancement significantly enhances the quality of PM2.5 exposure estimates across diverse geographical regions. Performance of the deep learning model was improved in regions with few monitors by customizing the loss function to predict the bias versus geophysical a priori PM2.5, by penalizing deviation from the geophysical a priori PM2.5, and by relaxing to the geophysical a priori PM2.5 at large distances from training monitors. Performance was also improved in regions with low concentrations by customizing the loss function to penalize errors at low concentrations. Additionally, the introduction of a more comprehensive method for evaluating deep learning model networks contributes to the provision of a stronger framework for researchers to make informed decisions about model skill in future investigations. The use of B-LOO cross-validation to account for spatial autocorrelation in the assessment of other models is examined to achieve more rigorous evaluation. Further work should examine methods to account for the effects of spatiotemporal autocorrelation on daily PM2.5 inference, which may have an even larger effects on predictive power than on the monthly data examined here.

Data Availability

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The optimized CNN model estimates presented in this work are freely available as a public good via the Washington University Atmospheric Composition Analysis Group website at https://sites.wustl.edu/acag/ or by contacting the authors.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsestair.3c00054.

  • Additional information for loss function adjustment, binned number distribution for the distances between sites, map comparison of MSE model and optimized model, comparison of temporal and spatial cross-validation for the optimized model, and complementary comparison for Table 3 (PDF)

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Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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  • Corresponding Author
  • Authors
    • Chi Li - Department of Energy, Environmental, and Chemical Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, United States;  Orcidhttps://orcid.org/0000-0002-8992-7026
    • Aaron van Donkelaar - Department of Energy, Environmental, and Chemical Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, United States;  Orcidhttps://orcid.org/0000-0002-2998-8521
    • Nathan Jacobs - Department of Computer Science and Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, United States
    • Chenguang Wang - Department of Computer Science and Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, United States
    • Randall V. Martin - Department of Energy, Environmental, and Chemical Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, United States;  Department of Computer Science and Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, United States
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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This work was supported by NASA HAQAST (Grant 80NSSC21K0508), by the NIH (Grants R01ES030616 and R01ES033961), and by internal funds at Washington University.

References

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  • Abstract

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    Figure 1

    Figure 1. Input array and structure of the residual convolutional neural network. The left panel shows the input array. The gridded square indicates the 11 × 11 pixel image of predictor variables cropped around a pixel of interest (blue pixel). The right panel shows the structure of the residual convolutional neural network. Rectangles represent the structure of the residual CNN, with blue for convolutional layers, pink for pooling layers, and orange for the flatten layer. Blue lines represent skip connections. Numbers in each convolutional layer indicate the number of input channels, the number of output channels, the width of the kernel, and the height of the kernel. Numbers in the pooling layer indicate the size of kernels. PM2.5,bias is defined as geophysical a priori PM2.5 minus “true” PM2.5.

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    Figure 2

    Figure 2. Location of ground monitors and corresponding annual average PM2.5 concentration in 2018. Black boxes represent regions used in Table 3 and Figure 6 and correspond to nested regions of the GEOS-Chem simulation.

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    Figure 3

    Figure 3. Assessment of spatial autocorrelation using normalized semivariance of the observed PM2.5 versus distance (left) and normalized semivariance of training matrix versus distance (right).

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    Figure 4

    Figure 4. Example distribution of buffer zones with a radius of 500 kilometers over the global range (top) and with a radius of 200 kilometers over North America (bottom). Pink shading indicates circular buffer zones in which sites are excluded from training around test sites as part of buffer leave-one-out (B-LOO) spatial cross-validation.

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    Figure 5

    Figure 5. Robustness tests indicating R2 of the CNN model as a function of the percentage of monitors withheld for testing. The top panel contains the results of the CNN model including geophysical a priori PM2.5 and GEOS-Chem outputs as input variables. The bottom figure contains the results of the model excluding these from input variables (details in Table 2). The numbers inside of each circle and its size indicate the R2 of annual average PM2.5 compared with the ground-based observations. The color indicates the difference of R2 between the CNN PM2.5 and the geophysical a priori PM2.5 estimates.

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    Figure 6

    Figure 6. Density scatterplots comparing the optimized CNN model and ground-monitored PM2.5 in different areas. The coefficient of determination (R2), root mean square error (RMSE), reduced major axis linear regression, and the total number are in the top-right corner of each scatter plot. Blue lines indicate the regression line. Black lines are identity lines: y = x.

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    Figure 7

    Figure 7. Global annual R2 and population-weighted mean (PWM) rRMSE for buffer leave-one-out (B-LOO) spatial cross-validation. Solid lines and symbols indicate means of annual values over 2015–2019. Error bars indicate standard deviation of annual values over 2015–2019.

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    Figure 8

    Figure 8. Sources of R2 reduction in buffer leave-one-out (B-LOO) spatial cross-validation. Solid bars represent R2 reduction from the reduction of training dataset numbers, and dashed bars represent R2 reduction from the reduction of spatial autocorrelation.

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    Figure 9

    Figure 9. Monthly mean PM2.5 estimation of the optimized CNN model in January (top) and July (bottom) 2018. Numbers at the bottom-left are the global population-weighted mean (PWM) PM2.5

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  • Supporting Information

    Supporting Information

    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsestair.3c00054.

    • Additional information for loss function adjustment, binned number distribution for the distances between sites, map comparison of MSE model and optimized model, comparison of temporal and spatial cross-validation for the optimized model, and complementary comparison for Table 3 (PDF)


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