Local PM_2.5 Hotspot Detector at 300 m Resolution: A Random Forest–Convolutional Neural Network Joint Model Jointly Trained on Satellite Images and Meteorology

Abstract

Satellite-based rapid sweeping screening of localized PM_2.5 hotspots at fine-scale local neighborhood levels is highly desirable. This motivated us to develop a random forest–convolutional neural network–local contrast normalization (RF–CNN–LCN) pipeline that detects local PM_2.5 hotspots at a 300 m resolution using satellite imagery and meteorological information. The RF–CNN joint model in the pipeline uses three meteorological variables and daily 3 m/pixel resolution PlanetScope satellite imagery to generate daily 300 m ground-level PM_2.5 estimates. The downstream LCN processes the estimated PM_2.5 maps to reveal local PM_2.5 hotspots. The RF–CNN joint model achieved a low normalized root mean square error for PM_2.5 of within ~31% and normalized mean absolute error of within ~19% on the holdout samples in both Delhi and Beijing. The RF–CNN–LCN pipeline reasonably predicts urban PM_2.5 local hotspots and coolspots by capturing both the main intra-urban spatial trends in PM_2.5 and the local variations in PM_2.5 with urban landscape, with local hotspots relating to compact urban spatial structures and coolspots being open areas and green spaces. Based on 20 sampled representative neighborhoods in Delhi, our pipeline revealed an annual average 9.2 ± 4.0 μg m⁻³ difference in PM_2.5 between the local hotspots and coolspots within the same community. In some cases, the differences were much larger; for example, at the Indian Gandhi International Airport, the increase was 20.3 μg m⁻³ from the coolest spot (the residential area immediately outside the airport) to the hottest spot (airport runway). This work provides a possible means of automatically identifying local PM_2.5 hotspots at 300 m in heavily polluted megacities and highlights the potential existence of substantial health inequalities in long-term outdoor PM_2.5 exposures even within the same local neighborhoods between local hotspots and coolspots.

1. Introduction

Exposure to fine particulate matter (PM_2.5, with an aerodynamic diameter of 2.5 μm and smaller) has wide-ranging adverse health effects on, for example, cardiovascular, cardiopulmonary and respiratory wellness [1]. Exposure to higher levels of PM_2.5 can lead to increased risks of mortality and loss of life expectancy mostly due to lower respiratory infections and non-communicable diseases, such as ischemic heart disease, stroke, chronic obstructive pulmonary disease, lung cancer, diabetes and cataracts (e.g., [2,3,4,5,6]). A recent study also suggests that a higher historical exposure to PM_2.5 is, in particular, associated with a higher COVID-19 mortality rate [7]. Novel measurement approaches including mobile sampling (e.g., [8,9,10,11,12]) and low-cost air quality sensor networks (e.g., [13,14,15,16,17,18]) have had success in revealing urban air pollution patterns at considerably greater spatial precision than existing rather sparse regulatory air quality monitoring (AQM) stations, which have advanced our understanding of the adverse impacts of highly dynamic and heterogenous air pollutants, such as PM_2.5, at higher spatiotemporal resolutions; however, these two approaches can be further complemented by a satellite-based modeling approach that requires much less manpower for sampling or instrument calibration and maintenance to potentially rapidly screen localized PM_2.5 hotspots over wider spatial areas.

Satellite data have been most commonly used for mapping PM_2.5 at a high spatial resolution. With the help of the recent rapid >advance in satellite sensors and rise in computing power suitable for big data wrangling, a handful of satellite-based methods have succeeded in estimating ambient PM_2.5 concentrations at sub-km levels with reasonably low retrieval uncertainties, such as between 500 m and 1 km (e.g., [19,20,21]) and below 500 m (e.g., [22,23,24,25,26]), with [19,20,21,22,23,24,25] using aerosol optical depth (AOD) while [26] (and this study) using satellite imagery for ambient PM_2.5 retrievals. However, few of the studies in [19,20,21,22,23,24,25,26] took their fine-grain ambient PM_2.5 estimates a step further by adapting them to be an automated PM_2.5 hotspot detector—a missed opportunity to inform decision makers about the main urban PM_2.5 emission sources in a never-before-realizable fashion and to facilitate the effective formulation and implementation of commensurate policy interventions and prioritization of resources for combatting air pollution in megacities. There are a few notable exceptions: for instance, Zhang et al. [25] managed to precisely identify the main PM_2.5 emission sources and their contribution proportions at a 160 m resolution in Wuhan, China, by leveraging the new 160 m AOD data retrieved by the Chinese Gaofen-1 satellite; although only at a 1 km resolution, the work by Bi et al. [15] is worth mentioning in that they demonstrated how massive uncalibrated PM_2.5 measurements from a large-scale PurpleAir low-cost sensor network can be creatively calibrated spatially first, then given lower weights and finally incorporated into a satellite AOD-based PM_2.5 prediction system to help further boost prediction performance and locate the four most destructive wildfire hotspots in 2018 in California. However, the PM_2.5 hotspots identified in these satellite-based studies are all “global” hotspots that have the absolute highest PM_2.5 levels over the entire study region. The “local” hotspots that have the highest PM_2.5 levels only relative to their neighbors at a fine-scale local community level were not studied. The PM_2.5 gradients even between these local hotspots and coolspots within the same local community can still be rather large, which in turn can translate into a huge difference in the risks of mortality associated with PM_2.5 exposure for people (and particularly those potentially vulnerable subgroups) even residing in the same community [3,4,5].

In light of these limitations, we parlayed our previous success in estimating ground-level PM_2.5 concentrations from satellite imagery at a 200 m resolution [26] into a satellite imagery-based local PM_2.5 hotspot detector at a 300 m resolution in this study, with 200 and 300 m being the optimal satellite imagery sizes (determined by the search method in Section 3.3 of [26]) for PM_2.5 modeling for the prediction systems in our previous study [26] and the current one, respectively. Our previous PM_2.5 prediction system [26] is a deep convolutional neural network (CNN)–random forest (RF; [27]) sequential model that is fueled by meteorological conditions and daily 3 m/pixel resolution PlanetScope satellite imagery from Planet [28]. However, this previous CNN–RF sequential model, despite effectively capturing spatial variations, was found to yield higher average PM_2.5 prediction errors than its RF part alone using only meteorological conditions, most likely the result of CNN–RF sequential model being unable to fully use the information in satellite images in the presence of meteorological conditions. To overcome this bottleneck in PM_2.5 prediction performance, this study reformulated the previous CNN–RF sequential model into an RF–CNN joint model where the RF part uses only meteorological data to predict a PM_2.5 baseline map on each day, whereas the CNN part uses PlanetScope satellite imagery of a 300 $\times$ 300 m spatial coverage to fill in the PM_2.5 residuals at a 300 m spatial resolution. The revamped RF–CNN joint model adopts a residual learning ideology [29] that forces the CNN part to most effectively exploit the information in satellite images that is only “orthogonal” to meteorology, thus yielding a greater PM_2.5 prediction performance than both the CNN–RF sequential model and the RF part alone using only meteorological conditions. A local contrast normalization (LCN) algorithm [30] follows downstream to further process the PM_2.5 maps estimated by the RF–CNN joint model so that local PM_2.5 hotspots can be automatically revealed.

We place an emphasis on the megacity Delhi in this study. Delhi is among the most PM_2.5-polluted megacities worldwide according to the World Health Organization (WHO)’s ambient air pollution database update in 2016 [31]. India, as a whole, had ~0.98 million deaths attributable to PM_2.5 in 2019, a large increase of ~6.5 μg m⁻³ in population-weighted annual average PM_2.5 exposure and a ~0.37 million deaths attributable to PM_2.5 since 2010 [32]. Health benefits gained from reductions in PM_2.5 would be much more significant for countries such as India that have the highest PM_2.5 levels [3]. Air quality mapping and hotspot analysis at a fine spatial resolution can put the air quality states in megacities “under the microscope” and help governments and policy makers put the air pollution issues in megacities into a clearer perspective [33], and is, therefore, the right path forward, particularly for regions such as India. Here, we first show that our proposed RF–CNN joint model can achieve equally low PM_2.5 prediction errors at a 300 m spatial resolution for both Beijing and Delhi, which are the study areas of interest in our previous study [26] and the current one, respectively, that have drastically different PM pollution levels and urban spatial structures. We then provide insights into the local PM_2.5 hotspot patterns in Delhi by applying our proposed RF–CNN–LCN pipeline. We demonstrate that for megacities, such as Delhi, which is abundant in PM_2.5 measurements from reference AQM stations, a simpler and scalable subsampling strategy to estimate local PM_2.5 hotspots is plausible and favorable. Finally, we elucidate the local PM_2.5 hotspots and coolspots revealed by the RF–CNN–LCN pipeline in Delhi and the possible disparities of long-term outdoor PM_2.5 exposures and associated mortality risks between people living in the local hotspots and coolspots within the same local communities. This work presents and highlights a prediction system that can be potentially informative about local PM_2.5 hotspots at a 300 m resolution in heavily polluted megacities. This work reveals that there can be a substantial health inequality in long-term outdoor PM_2.5 exposure even within the same fine-scale local neighborhoods between local hotspots and coolspots, suggesting that more attention should be paid to the populations in local community hotspots who can often be shadowed by those in global hotspots when planning actions to control air pollution in megacities.

2. Materials and Methods

2.1. Ground-Level PM_2.5 Data

Daily ground-level PM_2.5 concentrations from 51 available AQM stations in the National Capital Territory (NCT) of Delhi and its satellite cities, including Gurgaon, Faridabad, Noida, Ghaziabad, Baghpat, Sonipat and Bahadurgarh, from 1 January 2018, to 30 June 2020, were acquired to build a high-resolution PM_2.5 hotspot detector for Delhi NCT [34]. Detailed documentation of topographical, climatic and air quality conditions and the local and regional sources that contribute to the air pollution in Delhi can be found in studies such as [35,36,37,38,39]. The current study window was chosen to maximize the total number of available AQM stations, because abundant new AQM stations in the study domain have emerged since February 2018. Figure 1 displays the distribution of these 51 stations. As can be seen in Figure 1, the 51 stations (except for the two stations with the highest and lowest mean PM_2.5, which were reserved for the training set for the sake of good training quality) were randomly divided into a ~50–50% split or more precisely a 24–27 station split as the respective training and test datasets that have roughly comparable summary statistics for ground-truth ambient PM_2.5 concentrations. Specifically, the PM_2.5 of the training set averaged 103.8 μg m⁻³ standard deviation (Std Dev): 81.3 μg m⁻³; range: 0.0–928.3 μg m⁻³), and the test set averaged 105.2 μg m⁻³ (Std Dev: 78.1 μg m⁻³; range: 5.3–985.0 μg m⁻³). The names of these stations along with their corresponding coordinates, categories (training or test) and means of ground-truth ambient PM_2.5 concentrations over the sampling period can be found in

Table 1. The number, name, latitude, longitude, category (training or test), mean of PM_2.5 concentrations, weather station uptime (in %) and number of daily satellite image–stationwide averaged meteorology–PM_2.5 triplets for each of the 51 AQM stations in Delhi. The table is sorted based on each site’s mean PM_2.5 concentrations in ascending order. Note that the uptime of the weather station is different from the uptime of the instrument that measures PM_2.5 at each AQM station.

Number	Sites	Lat	Lon	Category	Mean of PM2.5 (μg m−3)	Weather Station Uptime (in %)	Number of Daily Image–Stationwide Mean Meteorology–PM2.5 Triplets
0	Murthal	29.02721	77.06208	train	62.2	0	392
1	Arya_Nagar	28.67008	76.92541	train	68.8	96	387
2	Pusa_IMD	28.63965	77.14626	test	78.3	81	711
3	Shooting_Range	28.49857	77.26484	train	81.1	100	683
4	Lodhi_Rd	28.59182	77.22731	train	81.8	1	718
5	Aya_Nagar	28.47062	77.10993	test	84.1	3	740
6	Sri_Aurobindo_Marg	28.53132	77.19015	test	86.5	100	572
7	IGI_Airport_T3	28.56278	77.11801	train	86.8	0	733
8	Indirapuram	28.64615	77.3581	train	88.9	97	361
9	Najafgarh	28.57012	76.93374	train	90.8	95	655
10	Knowledge_ParkV	28.55703	77.45365	train	91.7	100	240
11	Patparganj	28.62364	77.28717	test	94.3	99	706
12	Sector116	28.56921	77.39384	test	94.5	100	224
13	Sector1	28.5898	77.3101	test	94.6	100	247
14	Major_Dhyan_Chand_National_Stadium	28.61128	77.23773	test	94.9	100	720
15	Sector62	28.62455	77.35771	train	95.1	3	729
16	Vikas_Sadan	28.45004	77.02634	train	95.1	99	671
17	IHBAS	28.68117	77.30252	train	96.2	100	722
18	Mandir_Marg	28.63643	77.20107	train	98.5	100	778
19	Knowledge_ParkIII	28.47273	77.48199	train	98.9	97	567
20	Sanjay_Nagar	28.68539	77.45383	test	99.3	96	339
21	NISE_Gwal_Pahari	28.42267	77.14893	train	99.6	0	530
22	New_Collectorate	28.97479	77.21335	test	100.1	71	269
23	Sirifort	28.55042	77.21594	test	100.3	97	694
24	Okhla_Phase2	28.53072	77.27121	test	100.8	100	706
25	North_Campus	28.65738	77.15854	test	101.1	4	678
26	R_K_Puram	28.56326	77.18694	test	103.6	100	753
27	Sonia_Vihar	28.71032	77.24945	test	106.4	100	715
28	Loni	28.75728	77.27879	test	106.6	98	351
29	Vivek_Vihar	28.67229	77.31532	train	106.6	100	748
30	Dwarka_Sector_8	28.57099	77.07193	test	107.4	100	744
31	Shadipur	28.65148	77.14731	test	107.9	99	714
32	CRRI_MTR_Rd	28.5512	77.27357	test	108.0	4	734
33	ITO	28.62855	77.24102	test	108.1	0	715
34	Alipur	28.81606	77.15266	test	109.4	97	429
35	Narela	28.8227	77.10191	test	113.2	98	708
36	Sector16A	28.40884	77.30988	train	113.3	99	723
37	NSIT_Dwarka	28.60902	77.03251	test	113.4	100	798
38	Ashok_Vihar	28.69538	77.18163	test	114.3	100	715
39	Punjabi_Bagh	28.67405	77.13102	train	115.1	99	719
40	Sector125	28.54476	77.32313	test	116.9	98	703
41	Nehru_Nagar	28.56786	77.25046	train	117.9	100	714
42	Burari_Crossing	28.72556	77.20111	train	118.8	2	453
43	DTU	28.75005	77.11126	train	119.8	98	700
44	Bawana	28.77618	77.0511	test	123.1	99	557
45	Rohini	28.73251	77.11993	train	124.8	99	690
46	Vasundhara	28.66033	77.35726	train	125.3	99	735
47	Jahangirpuri	28.73278	77.17064	test	129.4	100	697
48	Mundka	28.68449	77.07668	test	130.3	100	584
49	Wazirpur	28.69972	77.1654	train	132.2	99	725
50	Anand_Vihar	28.6469	77.31592	train	136.0	91	672

. The approximately even split between training and test stations may appear to differ from the common practice (e.g., around 75–25%), but it is ideal for this study in that: (1) given that the dataset is large with a total of 51 stations, but only about half of them are more than enough for training our model, increasing the number of holdout stations (for testing) to as high as possible will significantly improve our confidence in the estimation of our model’s spatial predictability on never-before-seen scenes, which is essential to generating both a pollutant concentration prediction map and a pollutant hotspot detection map; (2) more holdout stations means more holdout samples on each sampling day, which gives us more power to fairly examine the model’s spatial predictability at a high daily temporal resolution, which in turn enables us to use only the days on which the model makes the most accurate spatial PM_2.5 predictions (as assessed on the holdout samples) to detect PM_2.5 hotspots, thus yielding a scalable (in both runtime and storage) hotspot detection algorithm. It is worth mentioning that algorithm scalability is very important here; since we are dealing with the computation and the storage of large, high-resolution and high-frequency satellite imagery over more than 2.5 years, it would be much less ideal if we had to rely on such images on all sampling days to uncover potential hotspots. It is also worth highlighting that only stations, but not time periods, were held out for testing in this study. This is because the local hotspot detection only requires spatial predictability, meaning that it is only important that the model can spatially fill in where there are no station data on the historical days.

2.2. Meteorological Data

Meteorological data are a mainstay for our RF–CNN joint model in this paper. Similar to [23,40], ground-based meteorological measurements from weather stations were used for PM_2.5 modeling. We acquired the daily temperature (T), relative humidity (RH) and sea level pressure (SLP) measurements from the available weather stations at the 51 AQM stations from the exact same portal where we obtained the daily ground-level PM_2.5 concentrations [34]. We should mention that SLP and wind speed are interchangeable for the RF–CNN joint model, as including either of them yields similar PM_2.5 prediction performances, while including both does not increase; hence, only one of the two (e.g., SLP) is used. On each individual day, we averaged the daily meteorological measurements from all AQM stations that had any of the T, RH and SLP measurements on that day and then matched all 51 AQM stations with the same stationwide averaged meteorological records (i.e., all 51 AQM stations have the same set of meteorological records on each individual day). The daily meteorological data after stationwide averaging had a completeness of 100% over the study period (the % uptime of the weather station at each of the 51 AQM stations can be found in Table 1). The strategy of stationwide meteorological data averaging and sharing was chosen after considering several potential alternatives: (1) common global gridded meteorological datasets, such as the European Center for Medium-Range Weather Forecasts 5th generation climate reanalysis dataset (ERA5) with a spatial resolution of 0.25° latitude by 0.25° longitude; the Goddard Earth Observing System Data Assimilation System GEOS-5 Forward Processing (GEOS 5-FP) at 0.25° by 0.3125°; and the Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2) at 0.5° by 2/3°, were considered. However, they can be too coarse for Delhi NCT. For instance, the latitudes and longitudes of Delhi vary between (28.413, 28.881) and (76.838, 77.348), respectively. Even with a 0.25° resolution, Delhi NCT would overlap at most around only 4 meteorological grids. More importantly, these analysis data are also generally less accurate than the ground-truth measurements. Resampling these coarse assimilated meteorological data using any of the nearest neighbor (NN) or bilinear or bicubic or cubic spline approaches to match the fine prediction grids (e.g., 300 m), in fact, resulted in a poorer PM_2.5 prediction performance for our RF–CNN joint model in the test set than simply using stationwide averaged meteorological data; (2) the strategy of using NN to resample the daily meteorological measurements from all available AQM stations to the prediction grids (e.g., 300 m) was also considered. This strategy did not increase the RF–CNN joint model’s PM_2.5 prediction performance in the test set, and most importantly, the RF–CNN estimated PM_2.5 maps resulting from this strategy are off, as they resemble a Voronoi diagram where grids that were matched to the same AQM station had the exact same predicted PM_2.5 value, and PM_2.5 values were discontinuous at boundaries of clusters; (3) one can also argue that these ground-based meteorological measurements should be spatially interpolated to fine prediction grids (e.g., 300 m) using approaches such as bilinear, bicubic, cubic spline or inverse distance weighting. We, however, consider this interpolation not necessary (at least for this study). On one hand, the meteorological conditions are rather homogeneous across Delhi with relatively consistent meteorological measurements across stations. The mean T, RH and SLP of the 40 (out of 51) weather stations that had at least 80% uptime (see Table 1) averaged 25.7 °C, 58.5% and 98,686 Pa with Std Devs of 1.2 °C, 5.0% and 622 Pa, respectively. Second, as mentioned in (2), using site-specific meteorological conditions did not outperform using stationwide meteorological data averaging in terms of PM_2.5 prediction for the RF–CNN joint model. Hence, we finally settled on the strategy of stationwide meteorological data averaging and sharing. This strategy holds well both theoretically and empirically. Theoretically, a prediction system using the same meteorological records for all the stations in Delhi on a day can be thought of as generating a single homogeneous baseline map that has the same PM_2.5 prediction across Delhi on that day. The PM_2.5 variation for each location can be filled in later by the prediction system using other sub-km site-specific high-resolution input variables—such as the high-resolution satellite imagery in our study. Empirically, the RF part (of our RF–CNN joint model) alone using stationwide averaged meteorological conditions already yields low PM_2.5 prediction errors, and the spatial variations of PM_2.5 added by the CNN part using satellite imagery further decrease PM_2.5 prediction errors.

2.3. Satellite Imagery

As in [26], we continued using the PlanetScope three-band (red-blue-green, RGB) scene visual product for local PM_2.5 hotspot detection in this study. This satellite product is distributed by the Planet Team [28] and has a ground spatial resolution of 3 m/pixel. In general, the satellite imagery retrieval, filtering and matching in this study followed the procedures outlined in [26], from step 1 of defining areas of interest (AOI) as the 51 N $\times$ N square grid cells with each of the 51 AQM stations located at the geographical center of the square grid; to step 2 of searching and downloading all available images that intersect with our AOI, matching our study date range, and meeting any other potential criteria; and step 3 of weeding out the images that intersect with the AOI but below a certain threshold, and finally matching the remaining images to their corresponding stations’ daily PM_2.5 observations and meteorological conditions. However, two technicalities in total were improved in steps 2 and 3 in this study to enlarge our dataset and to enable us to provide PM_2.5 predictions for as many days as possible. Specifically, unlike our previous study, we no longer constrained ourselves to only the images on uncloudy days by turning off the cloud coverage filter in step 2, and we lowered the AOI intersection threshold from 90% (area-wise) to only 50% in step 3. It should also be noted that the N in step 1 is the spatial resolution of PM_2.5 concentration prediction and hotspot detection that our model offers and was set to 300 m or equivalently 100 pixels, because 300 m was tested to be the resolution at which our prediction system performed best. Details on how to investigate the sensitivity of our model to the satellite imagery size (or spatial coverage) and how to determine the optimal satellite imagery size for PM_2.5 modeling can be found in Section 3.3. of [26]. Example satellite images for each of the 24 training and 27 test AQM stations in Delhi, which show the range of urban land covers that the model is trained and tested on, can be found in Figures S1 and S2, respectively (see Supplementary Materials). Additionally, Videos S1 and S2 show the temporal evolutions of all the images used in the model training and test at an example training site, #18 Mandir Marg, and an example test site, #37 NSIT Dwarka (the training and test sites that have the most samples), in chronological order, respectively. Table 1 shows the number of image–meteorology–PM_2.5 triplets for each of the 51 stations. In total, we obtained 31,568 image–meteorology–PM_2.5 samples, including 15,045 (from the 24 training AQM stations) for training the prediction system and 16,523 (from the 27 holdout AQM stations) for testing.

2.4. RF–CNN Joint Model

While the model in this paper and the one in our previous work [26] both use RF and CNN as building blocks, the formulations of the two are drastically different.

First, the model in [26] is a CNN–RF sequential model, with CNN and RF trained separately and in that particular sequence. Specifically, CNN was first trained on a satellite image to extract satellite image features that best predict PM_2.5, and RF was then trained on the CNN-extracted image features along with meteorological conditions to provide final predictions of PM_2.5. In contrast, the model in this paper, as shown in Figure 2, is an RF–CNN joint model jointly trained on satellite images and high-dimensional embedded meteorological conditions (details in Section 2.4.1.). The joint training of RF and CNN was made possible by adding the RF-predicted PM_2.5 (i.e., the gray dot at the bottom of Figure 2a) and the CNN-predicted PM_2.5 (i.e., the last solid green dot in Figure 2b) together to provide final predictions of PM_2.5 (i.e., the gray-to-green dot at the bottom of Figure 2b). In this way, CNN is forced to predict the residual of RF-predicted PM_2.5 (i.e., true PM_2.5$—$RF-predicted PM_2.5). The decision to switch to a joint model by deploying CNN to predict residuals was made considering the following findings or reasonings: (1) RF alone using meteorological conditions yields low PM_2.5 prediction errors; (2) the previous CNN–RF sequential model was found to yield higher average PM_2.5 prediction errors than RF alone using meteorological conditions. This finding indicates that the CNN–RF sequential model cannot fully use the information in satellite images in the presence of meteorological conditions. The optimization of the CNN–RF sequential model seems to always reach a local (rather than global) optimum solution, despite in which both satellite image and meteorological features being equally important for PM_2.5 prediction, as shown in [26]; (3) therefore, it makes sense to “piggyback” on RF’s low prediction error while forcing CNN to effectively use the information in satellite images that is “orthogonal” to meteorology for PM_2.5 prediction, and hence the current architecture. This RF–CNN joint model is guaranteed to yield lower average PM_2.5 prediction errors than RF alone using meteorological conditions. The RF–CNN joint model is also much easier to train than the CNN–RF sequential model, because the former only requires back-propagation to tune both RF and CNN’s parameters, while the latter requires first back-propagation to tune CNN and then an additional 5-fold cross-validation (CV) to tune RF.

Second, Zheng et al. [26] followed a transfer learning ideology by modifying and (iteratively) training only the several upper layers of a VGG16 network [41] while keeping the remaining lower-level layers’ weights fixed at the original ImageNet weights. In contrast, in this paper, we trained the entire deep CNN architecture (at one go) to best adapt it to our dataset and task. This was made possible by switching from VGG16 to ResNet50 [29]; although over 3 times deeper than VGG16, ResNet50 (with ~23 million parameters) has only ~1/6 of VGG16′s parameters (~138 million parameters). The significantly deeper CNN representations of satellite images along with the more specific optimization of these representations for our own task and dataset guarantee a performance at least as good as the previous VGG16 transfer learning approach.

2.4.1. RF Details

In this first stage, an RF regressor gives its PM_2.5 predictions based on meteorological conditions only. Three distinctive operations involved in this stage are worth emphasizing:

• Instead of directly using the T, RH and SLP meteorological features (as they are) for prediction by RF and CNN, they were first embedded in/mapped to a significantly higher dimension using an unsupervised algorithm called Totally Random Trees Embedding [43], as shown in Figure 2a. Totally Random Trees Embedding can be easily implemented in Scikit-Learn. The idea of this unsupervised algorithm is to first build an RF classifier (by fitting it to only all the meteorology datapoints that you have without using your associated PM_2.5 labels) that aims to separate the original observed meteorology datapoints from the synthetic ones that are generated by sampling from a joint distribution of the observed T, RH and SLP values. Then, this RF classifier transforms each observed meteorology datapoint into the indices of leaf nodes which that datapoint ends up in, expressed in a one-hot encoding format (i.e., for K leaf nodes in each tree in the forest, only the leaf node which the datapoint is sorted into is encoded in 1, while the rest of the K-1 leaf nodes are all encoded in 0). For instance, in this paper, we embedded meteorological data using an RF classifier that consisted of 800 trees, each of which had a max depth of 2 or equivalently at most 2² = 4 leaf nodes. See Figure 2a for the example of a meteorology datapoint embedded by such an RF classifier with the dimension increasing from 3 to at most 3200 (800 trees $\times$ at most 4 leaf nodes = 3200). Additionally, notice the sparse binary nature of the embedded meteorological feature vector; that is, for each tree in the forest, only one of the (at most) 4 leaf nodes is encoded in 1 and the rest all in 0. The intuition behind the high-dimensional embedded meteorological feature vectors is that two similar meteorology datapoints are more likely to lie within the same leaf node of a tree. Embedding meteorological features, however, is not so much to improve RF regressor’s PM_2.5 prediction performance as to improve CNN’s. Embedding meteorological features to a high dimension that rivals the dimension of satellite image features helps CNN cope with the difficulty of combining and effectively using multi-modality data, thus improving its PM_2.5 prediction performance.
• Unlike what is commonly seen in studies that explicitly train an RF using a 5-fold CV, this study only implicitly trained the RF regressor in the tree part (Figure 2a) together with explicitly training the entire CNN using back-propagation. This joint training strategy was possible because we made the tree part’s information flow into the CNN by adding the scaled RF-predicted PM_2.5 to the CNN-predicted PM_2.5 (i.e., the last solid green dot in Figure 2b). Scaling RF-predicted PM_2.5 by a stabilizing factor of ~0.90−0.95 (0.95 was used in this study) is important in that it leaves reasonably more room for CNN to learn to predict PM_2.5 (since RF alone using meteorological conditions can already yield low PM_2.5 prediction errors, as mentioned in Section 2.4.). The optimal hyperparameters for the RF regressor in the tree part were determined to be ~600, 1 and $\sqrt{\mathrm{total} \mathrm{features}}$ for the number of trees in the forest (N); the minimum number of samples required to be at a leaf node (n); and the number of input features to consider when splitting data at a decision node (m), respectively. The optimal values of N and n (the most influential parameter of the three) are consistent with [26], indicating that the RF setting can be universal, regardless of the locations (i.e., hyperparameter tuning is not necessary for RF in the future), although m needs to be switched to $\sqrt{\mathrm{total} \mathrm{features}}$ for a joint model rather than $\mathrm{total} \mathrm{features}$ for a sequential model.
• As discussed in Section 2.3, the meteorological data used in this study were determined to be daily measurements averaged from all available AQM stations on each day (i.e., all AQM stations that have any of the T, RH and SLP measurements on each day), meaning that all 51 AQM stations were matched with the same set of meteorological records on each individual day. The tree part of our prediction system can be thought of as using the same meteorological records to first generate a single homogeneous baseline map that has the same PM_2.5 prediction across Delhi on each day, and the CNN part can be thought of as using the location-specific high-resolution satellite imagery information to then fill in the PM_2.5 variation for each location (e.g., a 300 $\times$ 300 m grid) across Delhi on each day. Hence, in addition to thinking that CNN learns to predict the residual of PM_2.5, readers can also think that it learns to predict the spatial variation of PM_2.5. This also subtly explains why RF alone is not sufficient for detecting hotspots, even though RF alone using meteorological conditions can already yield low PM_2.5 prediction errors. Regardless of how low the RF predictions are, all the RF prediction values on a day are the same, and this is where CNN with satellite imagery information is useful, as it breaks ties and reveals spatial patterns.

2.4.2. CNN Details

With most of the difficult operations involved in the RF–CNN joint model having already been described in Section 2.4.1, the CNN part (see Figure 2b) is fairly standard. Each satellite image of an initial size of 100 (height) $\times$ 100 (width) $\times$ 3 (channel number) is first forward-passed through a ResNet50 architecture whose top layers (including an average pooling, a 1000-dimensional fully connected and a softmax layer) have been replaced by a global max pooling layer, yielding a 2048-dimensional global max-pooled feature vector. This vector, after being concatenated with the ~3200-dimensional meteorology embedding, then proceeds down two identical blocks of dropout (rate = 0.2)—200-way fully connected layer—ReLU activation, before finally going through a fully connected layer of dimension 1 to yield the CNN-predicted residual, which adds the scaled RF-predicted PM_2.5 to provide the final PM_2.5 prediction. The RF regressor and the entire CNN were jointly trained to minimize the mean squared error (MSE) between the final predicted and true PM_2.5 values in the test dataset (i.e., the 27 AQM stations used for testing), using back-propagation with an Adam optimization algorithm with $\alpha =$0.0001, ${\beta }_1=$ 0.01 and ${\beta }_2=$ 0.01 [44] on mini-batches of size 32 of the training dataset (i.e., the 24 AQM stations used for training) within 20 epochs, including early stopping if the model’s performance on the test dataset did not improve in 5 epochs. It is worth mentioning that the model performance is highly susceptible to several settings in the CNN, part including the dropout rates, the number and dimensions of fully connected layers, the Adam setting and the numbers of training and early stopping epochs. These settings were found to be generally not transferable between locations, thus requiring fine tuning when applied to a new location.

2.4.3. RF–CNN Joint Model Evaluation

We evaluated the RF–CNN joint model’s PM_2.5 estimation performance on the test dataset (i.e., the 27 AQM stations used for testing). The evaluation was performed by first forward-passing all the images in the test dataset along with their associated meteorological conditions through the trained RF–CNN joint model and then comparing the model’s final predicted PM_2.5 to the ground truth values based on metrics of spatial Pearson correlation coefficients (r), root mean square error (RMSE), mean absolute error (MAE), normalized RMSE (NRMSE) and normalized MAE (NMAE). Spatial Pearson r is more appropriate than total or temporal Pearson r to unbiasedly evaluate the model’s true spatial predictability (i.e., the only predictability that is of interest to our current application). It is defined as the Pearson r from regressing the mean of the true PM_2.5 over the entire sampling period against the mean of the predicted PM_2.5 over the entire sampling period at each test station [22,45,46,47]. The latter four metrics are defined by Equations (1)–(4). We reported both RMSE (and NRMSE) and MAE (and NMAE) as the errors (and percent errors) of our model, even though our model was trained to minimize only MSE. This is because RMSE is more influenced by outliers than MAE, and by doing this, we ensured that we did not completely ignore the effect of outliers on our model performance, but at the same time, we did not let the performance be misrepresented due to potential outliers either.

$$RMSE=\sqrt{\frac{1}{N}\Vert \mathit{y}-{\widehat{\mathit{y}}\Vert }_2^2}$$

(1)

$$MAE=\frac{1}{N}\Vert \mathit{y}-{\widehat{\mathit{y}}\Vert }_1$$

(2)

$$NRMSE=\frac{RMSE}{mean P{M}_{2.5} conc.in test set}$$

(3)

$$NMAE=\frac{MAE}{mean P{M}_{2.5} conc. in test set}$$

(4)

where $\mathit{y}$, $\widehat{\mathit{y}}$ and N are the true, model-predicted ground-level PM_2.5 concentrations and the number of samples in the test set, respectively.

2.5. Local Contrast Normalization (LCN)

An LCN algorithm [30] was used to further process the PM_2.5 maps estimated by the RF–CNN joint model so that PM_2.5 hotspots can be automatically detected. In this study, PM_2.5 hotspots are defined as the “locally” (i.e., in a N by N pixels neighborhood where N $\gg$ 100 pixels = 300 m) rather than “globally” (i.e., in the whole Delhi NCT region) brightest spots (spots are 100 $\times$ 100 pixels or 300 $\times$ 300 m squares). LCN was originally designed to reduce uneven illumination or shading artifacts in an image by standardizing (i.e., uniformizing the mean and variance of) an image around its local neighborhoods. Readers are encouraged to interact with some LCN examples in [48] to build an understanding that reducing the effect of non-uniform illumination on an image is exactly equivalent to finding local pollutant hotspots around local neighborhoods in a pollutant prediction map. We take the rice images, which can be found in the link above, as an example to illustrate how correcting image uneven illumination is equivalent to finding local hotspots. The rice images on the left and right are before and after the correction of the uneven illumination artifact by LCN, respectively. The rice at the top of the uncorrected image on the left is analogous to both global and local hotspots because it has the brightest pixels not only in the whole image but also with respect to its surrounding black background in its local neighborhood. In contrast, the rice at the bottom of the uncorrected image is a strictly local hotspot (i.e., only local but not global hotspot) because, while it does not have the brightest pixels in the image, it is indeed still much brighter than its surrounding black background in its local neighborhood. It is interesting to note that wherever the rice is in the image, its relative strength to its surrounding black background in its local neighborhood is roughly the same. Therefore, once the uneven illumination in the image has been corrected by the LCN algorithm, that is, once the image has been detrended by standardizing all the pixel values in their local neighborhoods so that all the local patterns (or hotspots) in the image emerge, these revealed local hotspots (i.e., all the rice) in the image on the right have almost the exact same normalized pixel value (or better interpreted as local hotspot strength in local neighborhood). This example intuitively highlights why local hotspots are worth studying: despite strictly local rice hotspots at the bottom of the uncorrected image having comparatively lower pixel values (analogous to lower absolute PM_2.5 concentrations) than global rice hotspots at the top, they are of the same strength as local hotspots in their respective local communities in comparison to their neighbors, because all the rice in the corrected image has the same brightness, indicating that people in strictly local and global hotspots, in reality, can be subject to the same degree of health inequality due to air pollution in comparison to their own neighbors.

The procedure for converting available PM_2.5 prediction maps to a local PM_2.5 hotspot detection map is visualized in Figure 3 and can be summarized by Equation (5). First, the PM_2.5 prediction maps produced by the RF–CNN joint model on N valid days are obtained, each of which is denoted as $f\left(x,y\right)$. Then, for each $f\left(x,y\right)$, an $m_f\left(x,y\right)$ is derived by applying a 2-D Gaussian Smoothing/Blur (with a Std Dev of ${\sigma }_1$ and a neighborhood size default to 8 $\times {\sigma }_1+$ 1) to each $f\left(x,y\right)$, after which the intermediate product $f\left(x,y\right)-m_f\left(x,y\right)$ is obtained. A 2-D Gaussian Smoothing/Blur is a 2-D convolution operation that transforms each pixel’s value to a spatially weighted average of all the values in that center pixel’s neighborhood with a filter whose weights are calculated by a 2-D Gaussian function defined by Equation (6) and whose size is the 2-D Gaussian Smoothing’s neighborhood size. Then, for each $f\left(x,y\right)-m_f\left(x,y\right)$, a ${\sigma }_f\left(x,y\right)$ is derived by taking the square root of the second 2-D Gaussian convolution blurred ${\left[f\left(x,y\right)-m_f\left(x,y\right)\right]}^2$ (similar to the first Gaussian Blur, the second one has a Std Dev of ${\sigma }_2$ and a neighborhood size default to 8 $\times {\sigma }_2+$ 1). After yielding ${\sigma }_f\left(x,y\right)$ for each $f\left(x,y\right)-m_f\left(x,y\right)$, the LCN-normalized-$f\left(x,y\right)$, that is $g\left(x,y\right)$, is obtained by dividing $f\left(x,y\right)-m_f\left(x,y\right)$ by ${\sigma }_f\left(x,y\right)$. Finally, averaging N valid days’ $g\left(x,y\right)$s yields the final local PM_2.5 hotspot detection map. These normalized PM_2.5 values in the hotspot detection map are directly comparable to one another and indicate the intensity of these 300 $\times$ 300 m squares as local PM_2.5 sources in their local neighborhoods. The 300 $\times$ 300 m squares of dark red and dark blue colors at opposite ends of the spectrum are of the most interest, as they indicate extreme local hotspots and coolspots, respectively.

$$g\left(x, y\right)= \frac{f\left(x, y\right) - m_f\left(x, y\right)}{{\sigma }_f\left(x,y\right)}$$

(5)

where $f\left(x,y\right)$ is each of N valid days’ PM_2.5 maps predicted by the RF–CNN joint model; $m_f\left(x,y\right)$ is each $f\left(x,y\right)$’s corresponding mean map estimated by applying a 2-D Gaussian Smoothing/Blur to each $f\left(x,y\right)$; ${\sigma }_f\left(x,y\right)$ is each $f\left(x,y\right)$’s corresponding Std Dev map estimated by applying a series of operations, including square, another 2-D Gaussian Smoothing/Blur and square root to each $f\left(x,y\right)-m_f\left(x,y\right)$; and $g\left(x,y\right)$ is each LCN-normalized-$f\left(x,y\right)$.

$$w\left(x, y\right)= \frac{1}{2\pi {\sigma }^2}exp(-\frac{x^2 + y^2}{2{\sigma }^2})$$

(6)

where $w\left(x,y\right)$ is the weight of the 2-D Gaussian Smoothing filter at $\left(x,y\right)$ in the neighborhood, and $\sigma$ is the Std Dev of 2-D Gaussian Smoothing/Blur. Note that the pixel at the center of the filter (0, 0) receives the highest weight, while its neighboring pixels $\left(x,y\right)$ (i.e., pixels that are $x$ and $y$ pixels away from the center in $x$- and $y$-directions) receive increasingly smaller weights as they move away from the center pixel.

Examining Equation (5) at a high level, one can probably recognize that it is simply an extension of the 1-D standardization formula to 2-D. The two 2-D Gaussian Smoothing operations simply facilitate the estimation of the mean and Std Dev values of each pixel $\left(x,y\right)$ based on that pixel’s (weighted) neighbors. Selecting appropriate ${\sigma }_1$ and ${\sigma }_2$ for the two 2-D Gaussian Smoothing operations is likely the only part that requires expertise when using LCN. In this study, ${\sigma }_1$ and ${\sigma }_2$ were both chosen to be 6 (hence, the neighborhood sizes were both 8 $\times$ 6 $+$ 1 = 49), under which the local hotspot detection map appears to be trustworthy without being highly speckled due an insufficient neighborhood size or having excessive edge effects due to an overly large bandwidth. With ${\sigma }_1$ = ${\sigma }_2$ = 6, $\frac{ The size of neighborhood}{The size of Delhi NCT}$ is ~0.30. We suggest using this ratio as a rule of thumb to initialize the values of ${\sigma }_1$ and ${\sigma }_2$ for new locations.

3. Results

3.1. RF–CNN Joint Model PM_2.5 Prediction Performances

3.1.1. Delhi

Figure 4a–c present the spatial prediction performances of the RF part of the RF–CNN joint model, while Figure 4d–f show the performances of the full RF–CNN joint model on the 24 training and 27 holdout AQM stations in Delhi, respectively. As can be seen in Figure 4a,b, the RF part (of our RF–CNN joint model) alone using the same stationwide averaged T, RH and SLP meteorological conditions for all stations on each day yielded low PM_2.5 spatial prediction errors in the training and more importantly in the test set with an RMSE, MAE, NRMSE and NMAE of 33.44 μg m⁻³, 20.57 μg m⁻³, 31.8% and 19.6%, respectively. Additionally, as demonstrated in Figure 4d,e, the full RF–CNN joint model with the additional CNN part that uses satellite imagery to predict the residual of RF-predicted PM_2.5 further improved the PM_2.5 spatial prediction errors in both training and test sets with an RMSE, MAE, NRMSE and NMAE of 32.69 μg m⁻³, 20.07 μg m⁻³, 31.1% and 19.1%, respectively, in the test set. The RF–CNN joint model also appreciably increased the predictions’ spatial Pearson r over RF (0.48 in Figure 4f vs. 0.19 in Figure 4c), indicating that a reasonable amount of additional information was added by the satellite imagery over meteorology that helped significantly improve the RF–CNN joint model’s spatial predictability. This also explains why, despite the RF–CNN joint model not decreasing RMSE or MAE by a significant margin over RF in Delhi, it still captured the spatial variation in PM_2.5 rather well (as shown in Section 3.3). Our model’s prediction errors rival a state-of-the-art ensemble framework in a recent Delhi PM_2.5 prediction study [47] that reported an RMSE of ~47.2 μg m⁻³ over 2010 to 2016 based on a 10-fold CV of 17,152 samples, but our framework outperforms [47] in terms of the spatial resolution of predictions (300 m vs. 1 km). These results empirically support our model design—the RF part of our prediction system uses the same station-wide averaged meteorological records to first generate a single homogeneous PM_2.5 baseline map across Delhi on each day (which already has low errors on average in comparison to the corresponding “true map”), and then, the CNN part uses high-resolution satellite imagery information at 300 $\times$ 300 m to fill in the PM_2.5 variations across Delhi at a 300 m resolution to complete the estimated PM_2.5 map (which has even lower average errors in comparison to the corresponding “true map”).

3.1.2. Beijing

It is worth pointing out that the two features that our model possesses, which are (1) RF alone using meteorological conditions yields low PM_2.5 prediction errors and (2) the RF–CNN joint model is guaranteed to yield lower average PM_2.5 prediction errors than RF alone using meteorological conditions, are not only applicable to the most polluted megacities, including Delhi. They also hold well for other megacities, such as Beijing, which is the area of interest in our previous study [26] that first presents the possibility of estimating daily ambient PM_2.5 at below 500 m from high-resolution and high-frequency satellite imagery using a deep learning-based model (i.e., CNN–RF sequential model). Beijing is naturally an additional megacity for benchmarking the RF–CNN joint model’s PM_2.5 prediction performance, because (1) the image, meteorological and PM_2.5 data are readily available; more importantly (2), it is in Beijing that the issue of inefficient use of the information in satellite images in the presence of meteorological conditions by the previous CNN–RF sequential model was first found, which directly motivated the formulation of the RF–CNN joint model in this study. It is, therefore, reasonable to show that the reformulated RF–CNN joint model is indeed superior in that it is able to overcome the CNN–RF sequential model’s bottleneck in PM_2.5 prediction performance exactly where the issue was first identified.

For the Beijing experiment, the training and test sets are the exact same ones as in [26], with 13,022 image–meteorology–PM_2.5 samples from 35 ground AQM stations randomly divided into ~80% and ~20% splits for the training (10,400 pairs) and test (2622 pairs) sets, respectively. The settings of the RF–CNN joint model and its Adam optimizer for Beijing are drastically different from those for Delhi. The RF–CNN joint model for Beijing has a stabilizing factor of 0.90; a dropout rate of 0.6; one fully connected vector of dimension 400; ~200 training and ~60 early stopping epochs; and an Adam setting of $\alpha =$0.0001, ${\beta }_1=$ 0.9 (default value) and ${\beta }_2=$ 0.999 (default value), which stands in stark contrast to 0.95; 0.2; two fully connected vectors of dimension 200; ~20 and ~5; and $\alpha =$0.0001, ${\beta }_1=$ 0.01 and ${\beta }_2=$ 0.01 for Delhi. As can be seen in Appendix A Figure A1, by switching from RF alone to the full RF–CNN joint model, the PM_2.5 spatial prediction performances improved significantly over both training (see Figure A1a,d) and more importantly test sets (see Figure A1b,c,e,f) with the RMSE, MAE, NRMSE, NMAE and spatial Pearson r improving from 15.69 to 13.00 μg m⁻³, 8.6 to 7.26 μg m⁻³, 36.7% to 30.4% (a 17.2% relative drop), 20.1% to 17.0% (a 15.4% relative drop) and 0.82 to 0.99, respectively. The previous CNN–RF sequential model achieved only 17.6 μg m⁻³, 10.1 μg m⁻³, 41.2%, 23.7% and 0.91 [26], respectively, on the same test set, which is considerably poorer than the RF–CNN joint model and even RF alone. The comparison among the three model performances over the Beijing dataset perfectly demonstrates the superiority of the RF–CNN joint model and that it can effectively use the information in satellite images that is “orthogonal” to meteorology for greater PM_2.5 prediction over RF, which the previous CNN–RF sequential model failed to do.

3.1.3. Comparison between Delhi and Beijing

It is encouraging to observe that with measurements of only three meteorological variables and satellite imagery as input, the RF–CNN joint model achieved similarly low NRMSE (within ~31%) and NMAE (within ~19%) on the test samples in both Delhi and Beijing that have drastically different levels of PM pollution and urban spatial structures, even though Delhi had a less significant improvement from RF to RF–CNN than Beijing. The most plausible explanation for Delhi’s lesser improvement is that Delhi is the more polluted region of the two, and as a result, its satellite imagery quality is in general far inferior to Beijing (based on our observation) with Delhi’s landscapes most of the time being covered in haze or fog. In other words, there is comparatively less to learn from the images in Delhi. The facts that Delhi’s model and optimizer settings are drastically different from Beijing and that Delhi’s model stopped learning within ~20 epochs, while Beijing lasted around 100 epochs, also support this explanation. The comparison implies that the settings of the RF–CNN joint model and its Adam optimizer for Beijing should be considered as the default when initializing the RF–CNN joint model for new locations.

3.2. A Subsampling Strategy to Detect Hotspots in Delhi

The substantial number of 16,523 samples from a total of 27 holdout stations give us the unique advantage to examine the full RF–CNN joint model’s spatial prediction performance at a daily resolution. The daily performances of the RF–CNN joint model for all available test samples on each available day during the study period as assessed by the daily spatial Pearson r (i.e., the Pearson r from regressing the true PM_2.5 against predicted PM_2.5 at each available test station on one given day), NRMSE and NMAE are illustrated in Figure 5a–c, respectively, in the form of frequency distribution. The r values (excluding the negative ones), NRMSE and NMAE average 0.35 ± 0.22, 27.0 ± 15.1% and 21.0 ± 10.2%, respectively. These average values are, in general, consistent with the results in Figure 4. Figure 5, in general, demonstrates that all days cannot be predicted equally well, but the RF–CNN joint model can indeed perform extraordinarily well on a subset of days. The most interesting long-term persistent PM_2.5 hotspots were supposed to be uncovered, regardless of which days were randomly sampled, as long as the RF–CNN joint model performed exceptionally well on those days. Therefore, it is days like these on which the satellite imagery added the most information to the baseline RF prediction (assessed by Pearson r) and the RF–CNN joint model most accurately predicted PM_2.5 (assessed by NRMSE and NMAE) for the holdout samples that we can take advantage of to reveal the hotspots, thus yielding a scalable (in both runtime and storage) subsampling hotspot detection algorithm.

The days on which the RF–CNN joint model performed extraordinarily well on the available test samples in Delhi are defined as the days on which the Pearson r, NRMSE and NMAE values were all in the best 20% (>0.47, <18.3% and <14.6%, respectively) among all 801 available test days (each of which had at least two test samples), as shown in Figure 5. There are 43 such “exceptional” days, and Figure A2 (in Appendix B) shows that these 43 days are approximately evenly scattered throughout the study period without any obvious bias or pattern except for the apparent lack of samples from June to September due to monsoon season. We also compared the satellite images in the test dataset of these 43 days and of the remaining available test days on which the RF–CNN joint model had suboptimal performances in Appendix C Figure A3. The imagery pixel value frequency distributions for the two groups exhibit no major discrepancy in any of the blue (Figure A3a), green (Figure A3b) or red (Figure A3c) channels, further suggesting that the images on these 43 days are not associated with any specific pattern and qualify as random subsamples for estimating hotspots. The contrast between the performances of RF (see Appendix D Figure A4) and the RF–CNN joint model (see Appendix E Figure A5) on these 43 days is huge. The daily Pearson r, NRMSE and NMAE values for RF alone on these 43 days average 0, 17.3% and 13.7%, as compared to 0.62 (a 0.62 absolute increase), 14.4% (a 16.8% relative improvement) and 11.2% (a 18.2% relative improvement), respectively, for the RF–CNN joint model. It is days like these on which the satellite imagery added the most information to the baseline RF prediction and the RF–CNN joint model most accurately predicted PM_2.5 for the test samples that we can trust to reveal the perennial hotspots. Figure A4 highlights why RF alone is not sufficient for detecting hotspots, even though RF alone using meteorological conditions can already yield low PM_2.5 prediction errors. Regardless of how low the RF predictions are, all the RF prediction values on a day are the same, and this is where CNN with satellite imagery information aids in revealing the spatial patterns. Due to the subsampling strategy, our devised hotspot detection algorithm is scalable in both runtime and storage. It is worth mentioning that algorithm scalability is very important in this case, since we are dealing with the computation and storage of large-scale high-resolution and high-frequency satellite imagery over a long study period.

The RF–CNN-predicted daily PM_2.5 maps of Delhi on the most trustworthy 43 days can be found in Appendix F Figure A6. Averaging these 43 maps yields the averaged PM_2.5 prediction map as shown in Figure 6a. Similar to [25], to cope with the potential influences of severe haze episodes (uniformly high across a region) and excellent diffusion days (uniformly low across a region) on hotspot estimation, a corresponding adjusted averaged PM_2.5 prediction map in Figure 6b was derived by first excluding the top 10% highest and the top 10% lowest values among all pixels over the 43 days and then averaging. By applying the LCN algorithm in Figure 6b, we obtained the corresponding local PM_2.5 hotspot detection map in Figure 6c that is based on the most trustworthy 43 days. These normalized PM_2.5 values in the local hotspot detection map are directly comparable to one another and indicate the intensity of these 300 $\times$ 300 m squares as local PM_2.5 sources in their local neighborhoods. The 300 $\times$ 300 m squares of dark red and dark blue colors at opposite ends of the spectrum are of most interest, as they indicate extreme local hotspots and coolspots, respectively. Figure 6c appears to be highly speckled with widespread extreme local hotspots all over Delhi. This is because the hotspots we attempted to find in this study are local hotspots, whose PM_2.5 values are just higher than their neighbors but not (necessarily) the highest in the whole study region. It is, therefore, reasonable to see hotspots appearing in even the relatively less populated North and West Delhi. We also examined the averaged PM_2.5 prediction map (Figure 6d), the adjusted averaged PM_2.5 prediction map (Figure 6e) and the corresponding local PM_2.5 hotspot detection map (Figure 6f) that were generated based on all available days from January 1, 2018, to June 30, 2020. Seven subregions within Delhi (i.e., North, South, West, East, Central and New Delhi and the airport area) are demarcated in Figure 6e based on the spatial clusters in [47]. The estimated gradients of PM_2.5 concentrations in both Figure 6d and e show that the densely populated East and Central Delhi and airport area are among the subregions that on average have relatively high ambient PM_2.5 concentrations, while the relatively less populated North and West Delhi have on average relatively low ambient PM_2.5 concentrations. These patterns, in general, bear a strong resemblance to the results in [35,47], even though their results are for the periods of 2001–2016 and 2010–2016, respectively. However, we did find New Delhi and South Delhi to be experiencing elevated PM_2.5 levels, as shown in Figure 6e, which was not reported in [47] or [35,47]. Kumar et al. [49], on the other hand, reported similarly elevated PM_2.5 levels in these two subregions and attributed the elevated PM_2.5 levels to heavy traffic at major transport corridors. The PM_2.5 hotspot detection map based on the whole study period (Figure 6f) reveals essentially the same extreme local hotspots as the hotspot detection map based on the most trustworthy 43 days (Figure 6c), which further supports the validity of using a subsampling strategy to detect hotspots. However, the averaged PM_2.5 prediction maps generated from a subsampling strategy in Figure 6a,b with striping artifacts because of the relatively small sample size appear to be less useful in uncovering the spatial gradient of PM_2.5 concentrations. In fact, Figure 6c,f being identical came as no surprise. Note that the predictions would be akin to baseline RF predictions (a flat line) on a large majority of the days when satellite imagery added little information, and the noise in each pixel’s estimation cancels out when averaging over abundant samples, so the critical votes would still depend on those subsampled “exceptional” days. Figure 6c and f being identical offers another insight: for places with limited PM_2.5 data that we are not generally able to proactively find the most trustworthy days from the test set, we can simply let the most trustworthy days reveal themselves by using the whole study period to detect hotspots, although some runtime and storage are sacrificed by doing this. We also want to point out one advantage and one drawback associated with our local hotspot detection LCN algorithm. The advantage is that, regardless of whether an averaged or adjusted averaged PM_2.5 prediction map is used to produce a hotspot detection map, the resulting local hotspot detection maps are identical, implying that LCN is robust to perturbations in PM_2.5 estimations. The apparent flaw is that LCN can cause major edge effects because of zero paddings beyond the study region by 2-D Gaussian Smoothing/Blur in LCN, as can be seen in Figure 6c,f. One solution, however, is to always predict slightly over the boundary of the area of interest so that the area of interest falls outside the edges in the future.

3.3. Case Study: Hottest and Coolest 300 $\times$ 300 m Spots within Each of the 20 Sampled Neighborhoods in Delhi

It is critical to make sense of the messages the RF–CNN–LCN pipeline attempts to convey by examining the patterns of some predicted local hotspots and coolspots, such as those in the 20 sampled representative neighborhoods across Delhi (see their coordinates in Appendix G

Table A1. The latitudes and longitudes of the hottest and coolest spots within each of the 20 sampled neighborhoods, as shown in Figure 6.

Case #	Hottest Spots		Coolest Spots
	Lat	Lon	Lat	Lon
1	28.82872204	77.10700999	28.82350141	77.09460978
2	28.80949079	77.12506275	28.80422361	77.11573631
3	28.80213779	77.07574336	28.80470179	77.08501388
4	28.80554491	77.02971166	28.79971394	77.05725672
5	28.76531395	77.1794628	28.77087418	77.17036198
6	28.75227615	77.14847589	28.74135447	77.15439489
7	28.73269406	77.18799839	28.74647139	77.17292852
8	28.72336389	77.26150048	28.73153257	77.2586055
9	28.70975135	77.09847964	28.72869391	77.09885802
10	28.69026256	76.95380395	28.69554192	76.96311248
11	28.67827673	77.20528242	28.68353818	77.2146013
12	28.67442916	77.10698321	28.67960154	77.1224344
13	28.65632843	77.22323517	28.642799	77.22294971
14	28.6348702	77.03869029	28.64000433	77.05720023
15	28.62106102	77.05683072	28.60776183	77.041234
16	28.60307928	76.99206508	28.6087164	76.97683348
17	28.57328896	77.16935841	28.58150494	77.16339384
18	28.54486672	77.08293893	28.53641738	77.10423034
19	28.5227744	77.27865733	28.54186924	77.26987231
20	28.50720147	77.23848587	28.52062986	77.24489909

) labeled in Figure 7a,b. We conducted the sampling randomly but also considering diversity: (1) at least one sample should be from each of the seven subregions within Delhi, as demarcated in Figure 6e; (2) the sampled neighborhoods (i.e., the rectangles labeled in Figure 7a,b) should come in various sizes, with the rectangles aiming to cover the complete local patterns and preferably but not necessarily at least one dark red and dark blue pixel in the local neighborhoods. The landscapes, the LCN-normalized PM_2.5 values (see Section 2.5 for details) and the mean RF–CNN-predicted PM_2.5 concentrations over the whole study period associated with the hottest and coolest spots (each of which is a 300 $\times$ 300 m grid), respectively, within each of the 20 sampled neighborhoods are displayed in Figure 7c. The mean PM_2.5 concentration estimates over the whole study period are referenced here because they approximate long-term outdoor PM_2.5 exposures, enabling the relation of the PM_2.5 concentrations in Delhi to the corresponding health risks discussed later in this section. The PM_2.5 hotspot detection map based on the most trustworthy 43 days rather than throughout the whole study period is referenced here because the former has more contrast and is, therefore, better for visualization, although both of them reveal essentially the same information about the local hotspots (and coolspots). We want to emphasize that local hotspots can be, but are not necessarily, global hotspots. Zhang et al. [25] defined global hotspots as the pixels that are among the top 5% of the adjusted annual averaged PM_2.5 estimates. We borrow the concept in this study. With a 95th percentile of 98.2 μg m⁻³ in Figure 7a, we can see that cases 1, 3, 4 and 9 that have concentrations below 98.2 μg m⁻³ are strictly local hotspots, meaning that they are only local but not global hotspots. In fact, a large number of the hotspots in West and North Delhi (the subregions that have comparatively low PM_2.5 concentrations) are strictly local hotspots. Similarly, local cool spots only have low PM_2.5 concentrations relative to their neighbors but not necessarily the lowest concentrations in the entire study region. For instance, the coolest spot in case 13 had a PM_2.5 concentration of 95.8 μg m⁻³, which is on-par with the concentrations of the hottest spots in cases 3 and 4 (96.8 μg m⁻³). It is also worth mentioning that the strengths of local hotspots and coolspots are only dependent on their neighbors. For instance, despite the hottest spot in case 15 (Uttam Nagar West subway station) not having the highest PM_2.5 concentrations out of the 20 cases, it is the strongest local hottest spot with the highest normalized PM_2.5 score of 2.62. In a similar vein, although the PM_2.5 concentrations of the coolest spots in cases 3 and 13 differ by 6.3 μg m⁻³, they are both relatively mild to weak coolest spots with similar normalized PM_2.5 scores of −0.93 and −0.86, respectively. We should also point out that the strength of a strictly local hotspot (see case 9 with a normalized PM_2.5 score of 2.06) can be much stronger than the strengths of a large majority of global hotspots (i.e., cases 2, 6, 7, 10, 11, 13, 16, 17, 19 and 20). The contrasts of landscapes between the hottest and coolest spots in Figure 7c indicate that the RF–CNN–LCN pipeline made reasonable and informed predictions for these spots by capturing both the fluctuations of PM_2.5 in microenvironments induced by local built environment features and the main intra-urban spatial trends in PM_2.5. The pipeline made reasonable estimates of the local variations (thanks to the satellite imagery), because Figure 7c illustrates that the hottest spots are mostly associated with scenes of dense buildings, while the coolest spots are typically associated with scenes of green space, water area, open space or considerably less dense buildings. However, obviously, the pipeline did not make the decisions solely based on landscapes, as can be seen from the variations within the hottest and coolest spots. For instance, the hottest spot in case 12 with a much less dense setting in Central Delhi has a higher PM_2.5 concentration than the hottest spot in case 16 with a very dense setting in West Delhi. Similarly, despite the coolest spot in case 11 having an (almost) all green setting, it has a higher PM_2.5 concentration (90.3 μg m⁻³) than the coolest spots in cases 4 and 8 (87.6 and 88.2 μg m⁻³, respectively), which barely have any green in them.

The main reason that we are interested in these local hotspots is because large gradients of long-term average PM_2.5 concentrations can exist even within local neighborhoods/communities between extreme local hotspots and coolspots, as shown in Figure 7c. The gradients average 9.2 ± 4.0 μg m⁻³ over the 20 sampled representative neighborhoods. Among the 20 cases, case 18 (Indian Gandhi International Airport area) had the steepest increase of 20.3 μg m⁻³ from the coolest spot (the residential area immediately outside the airport) to the hottest spot (airport runway), followed by case 12 with an increase of 19.1 μg m⁻³ from park area (coolest spot) to dense school area (hottest spot), to the smallest increase of 4.4 μg m⁻³ in case 13 from a parking lot near New Delhi Railway Station (coolest spot) to a dense commercial area (hottest spot).

With the PM_2.5 prediction values averaged over the whole study period (i.e., from 1 January 2018 to 30 June 2020) approximating long-term outdoor PM_2.5 exposure, we are able to gauge the disparity of risks of death attributable to long-term outdoor PM_2.5 exposure within the same neighborhood. According to Burnett et al. [3], who examined the association between long-term outdoor PM_2.5 exposure and the risk of death by relying on data from 41 cohort studies from 16 countries of outdoor air pollution that covered most of the global concentration range, the association exhibits a near-linear relationship in the high concentration range (e.g., the concentrations in Delhi), and an increase of 10 μg m⁻³ in PM_2.5 was estimated to be associated with an increase in the risk of death of ~6.7% (95% confidence interval (CI)], 4.6% to 9.2%). This translates into an average of a significant 6.2% (95% CI, 4.2% to 8.5%), a maximum 13.6% (95% CI, 9.3% to 18.7%) and a minimum 2.9% (95% CI, 2.0% to 4.0%) difference in the risks of mortality between the hottest and coolest spots within a local community in Delhi based on the 20 sampled neighborhoods. In particular, the four strictly local community hotspots in cases 1, 3, 4 and 9 also had a significant average difference of 5.0% (95% CI, 3.4% to 6.8%). The results reflect that there can be a huge health inequality in the long-term outdoor PM_2.5 exposure even within the same local neighborhood. The results also call for more attention to be paid to the people living in strictly local community hotspots, who can be equally disproportionately affected by air pollution as people in global hotspots in comparison to their respective neighbors but who can often be shadowed by those living in global hotspots when authorities plan actions to control air pollution in megacities. It is, however, critical to emphasize that these roughly estimated differences in the risks of mortality are only the upper limits, as people are generally unlikely to stay in their grids all day.

4. Discussion

Validating local hotspots remains a challenge. Moving forward, it is of paramount importance to corroborate the validity of these local hotspots and coolspots in terms of both their absolute PM_2.5 concentrations and their rankings in neighborhoods by conducting field investigation and ground monitoring with low-cost air quality sensor (AQS) networks. The synergy between satellite PM_2.5 monitoring and low-cost AQS network PM_2.5 monitoring should be explored in future studies. Community air monitoring programs can deploy low-cost AQS under the guidance of high-resolution satellite estimates of PM_2.5 to conduct surveillance in locations that appear to have high concentrations and validate the satellite estimates for those locations at the same time. Low-cost AQS networks can also provide significantly more training samples that cover much more wide-ranging landscapes than reference AQM stations to further improve the model’s generalization/prediction performance, although a downweighting strategy [15] should be followed by assigning a lower weight to the loss function for low-cost AQS samples during the training of our deep learning model in order to reduce the negative impact of the residual errors of calibrated low-cost AQS. The enhanced PM_2.5 prediction model can, in turn, help monitor the health of low-cost AQS networks and report any potential malfunction or drift in calibration in a timely fashion.

This study demonstrates that the RF–CNN joint model can achieve similarly low PM_2.5 prediction errors in both Delhi and Beijing, the two heavily polluted megacities that have drastically different levels of PM pollution. A natural follow-up research question is the following: will this single (in contrast to ensemble-based [22,47]) ambient PM_2.5 prediction framework perform equally well at 300 m in lightly polluted megacities that have relatively limited PM_2.5 data (e.g., Los Angeles with only a few Federal Reference Method monitors that most commonly sample only once in 3, 6 or even 12 days)? A multitasking [50] variation of the original RF–CNN joint model could be a solution to the issue of PM_2.5 data limitation in these lightly polluted megacities. The architecture of this multitasking RF–CNN joint model is displayed in Appendix H Figure A7 with a detailed description and explanation in Appendix H. In summary, the multitasking RF–CNN joint model derives from the original RF–CNN joint model by simply growing additional branch(es) from the root of the 5248-way concatenated vector in the CNN part in order to learn to predict additional air pollutants that are highly relevant to PM_2.5 (such as PM₁₀) as side tasks in addition to its main PM_2.5 prediction task. Take PM₁₀ as an example, by learning to predict PM₁₀ through its PM₁₀ side task branch, the upstream of the CNN part (i.e., from the satellite imagery input to global max-pooled feature vector) learns more about the structure of the satellite imagery and consequently how to more effectively extract the satellite imagery feature vector that can be more informative about PM pollution, which in turn improves the model’s performance in its main task of predicting PM_2.5. Therefore, multitasking is essentially a data augmentation technique, with the limited PM_2.5–image training pairs being augmented by the datasets of PM_2.5′s highly relevant air pollutants, such as PM₁₀. With the local PM_2.5 hotspot detection maps based on the whole study period and the subsampled most trustworthy days revealing essentially the same information about local hotspots and coolspots, as shown in Section 3.2, LCN shows promise of identifying local PM_2.5 hotspots even for places where PM_2.5 data can be somewhat limited (such as in lightly polluted megacities) that we are not generally able to proactively find the most trustworthy days from the test set. This is because via LCN, the most trustworthy days can reveal themselves when using the whole study period to detect local hotspots. A lingering research question along the same vein, however, is as follows: will LCN still make reasonable predictions about local PM_2.5 hotspots at 300 m in low PM_2.5 concentration environments with no prevalent local point sources or in environments whose air quality regimes are dominated by large particles (i.e., the antithesis of Delhi)? Benchmarking the PM_2.5 prediction performances of the RF–CNN joint model and its multitasking variation and examining LCN at 300 m in low PM_2.5 concentration environments with comparatively limited regulatory monitoring PM_2.5 data and local PM_2.5 point sources and in different air quality regimes are critical in future studies.

While the RF–CNN joint model can achieve reasonably low PM_2.5 prediction errors with only three meteorological variables and satellite imagery as input, it might be worthwhile to explore additional variables that RF can use to generate an improved PM_2.5 baseline map on each day in future studies, although we speculate that the improvement will not be significant. Benefiting from our RF–CNN–LCN pipeline and the established association between long-term outdoor PM_2.5 exposure and the risk of death in the high concentration range [3], we identified and analyzed local major PM_2.5 sources (i.e., local hotspots) and local background areas (i.e., local coolspots) at a 300 m resolution, based on which we conveniently gauged the potential maximum disparity in risks of death attributable to long-term outdoor PM_2.5 exposure within Delhi local neighborhoods. The finding of the possible existence of huge health inequality in fine-scale local neighborhoods in this study can be a prelude to more rigorous future studies that will investigate the precise health implications of long-term PM_2.5 exposure at a fine-grain community level using the air quality analytic products resulting from our RF–CNN–LCN pipeline.

5. Conclusions

The RF–CNN–LCN pipeline presented in this study can be potentially informative about local PM_2.5 hotspots at a 300 m resolution in heavily polluted megacities—thanks to (1) the RF–CNN joint model in the pipeline that was proven to achieve a low NRMSE for PM_2.5 of within ~31% and an NMAE of within ~19% for the holdout samples at a 300 m spatial resolution in both Delhi and Beijing and (2) the ability of LCN in the pipeline to reasonably reveal local major PM_2.5 sources by further processing the RF–CNN-estimated PM_2.5 maps. We placed emphasis on analyzing the local PM_2.5 hotspot patterns in Delhi as an example in this study to showcase the effectiveness of the RF–CNN–LCN pipeline. The pipeline revealed an annual average 9.2 ± 4.0 μg m⁻³ difference in PM_2.5 between the local hotspots and coolspots within the same community in Delhi, based on 20 sampled representative neighborhoods across Delhi. In some cases, the differences were much larger; for example, at the Indian Gandhi International Airport, the increase was 20.3 μg m⁻³ from the coolest spot (the residential area immediately outside the airport) to the hottest spot (airport runway). The results imply that substantial health inequalities in long-term outdoor PM_2.5 exposure can potentially exist even within the same local communities between local hotspots and coolspots. This implication could be a wake-up call for governments and policy makers who might have only paid attention to the health impacts of outdoor air pollution on the populations in global hotspots but not those in community-level local hotspots when designing policy interventions to control air pollution in megacities. Future studies should explore the synergy between satellite PM_2.5 monitoring and low-cost AQS network PM_2.5 monitoring, examine the RF–CNN–LCN pipeline in low PM_2.5 concentration environments with comparatively limited regulatory monitoring PM_2.5 data and local PM_2.5 point sources and shed light on the precise health implications of long-term PM_2.5 exposure at a fine-grain community level using novel air quality analytic products at high spatial resolutions (such as those produced by our RF–CNN–LCN pipeline).