The ground-based observations in Hebei were acquired from the China National Environmental Monitoring Center (http://106.37.208.233:20035/), which published hourly concentrations of SO2, NO2, CO, O3, PM2.5, and PM10 from 53 monitoring stations over Hebei in 2013. This dataset was built and maintained by the Ministry of Environmental Protection in China and is used as the official dataset for national air-quality management. The ground-based stations are primarily located in urban centers because they are designed to assess population exposures in the densest areas.

In the HB-EI inventory, we estimated the anthropogenic emissions of Hebei Province in 2013 as follows: 1.4 Tg SO2, 2.0 Tg NOx, 1.5 Tg VOCs, 0.5 Tg NH3, 16.8 Tg CO, 827.2 Tg CO2, 2.7 Tg TSP, 1.3 Tg PM10, 0.9 Tg PM2.5, 0.1 Tg BC, and 0.2 Tg OC. The magnitudes of emissions in MEIC were scaled to match HB-EI by emission source; therefore, the discrepancies between MEIC and HB-EI were primarily attributed to the differences in spatial distributions. The MEIC inventory represented a mixture of data sources from downscaled province-level emissions and point sources (i.e., power plants), in which 25 % SO2, NOx, and CO2 emissions were identified as point sources (Fig. 2a). Conversely, more than 70 % emissions in the HB-EI inventory were inventoried as point sources (Fig. 2b), and the remaining emissions were constrained by road- and county-level activities.

The discrepancy in emission shares of point sources varied by pollutant between MEIC and HB-EI. For pollutants that dominated emissions by industrial combustion and production (e.g., CO2, SO2, and NOx), HB-EI presented a much larger share of point source emissions than MEIC, while for the pollutants mainly emitted from diffuse sources (e.g., VOCs, NH3, BC, and OC), the two datasets presented similar contributions from point sources. These findings suggested that the nonlinearities in CO2 emissions and spatial proxy covariance identified in early studies (e.g., Gurney et al., 2009; Rayner et al., 2010; Oda and Maksyutov, 2011; Wang et al., 2013; Asefi-Najafabady et al., 2014) may have diverged for different air pollutants.

Table 2 shows the comparison between the gridded emissions of the bottom-up inventory (HB-EI) and the proxy-based inventory (MEIC) over the Hebei region at different resolutions. Following the method established by Rayner et al. (2010), three metrics were adopted for comparison: (1) spatial correlation (R), which quantifies the correspondence of spatial patterns; (2) summed absolute difference (SAD), which is the sum of the absolute difference for the whole domain; and (3) relative summed absolute difference (RSAD), which is calculated as the SAD divided by total emissions over the domain. For the pollutants of which emissions are dominated by point sources, the two gridded inventories agreed well at coarse resolutions (grid size larger than 0.25∘), while the differences tended to increase when grid size decreased, indicating more spatial biases involved in proxy-based inventories at high spatial resolutions. For example, the resolutions of 0.05 and 0.1∘ produced normalized bias (RSAD) as large as 80–100 %, results that were much higher than the uncertainties in total emissions (e.g., 20–40 % for SO2 and NOx). For the pollutants of which emissions are dominated by nonpoint sources (e.g., NH3), the two inventories agreed well regardless of spatial resolution because they shared the same spatial proxies.

Figure 3 compares the spatial distributions of gridded emissions using NOx as an example. Figure 3a–d presents NOx emission distributions in HB-EI at different spatial resolutions, and Fig. 3e–h presents the differences between the two inventories. At high resolutions (0.05 and 0.1∘), MEIC tended to overestimate emissions in urban centers but underestimate emissions in rural areas, leading to unrealistically higher urban–rural emission gradients. Following economic development and air quality control progress in China, polluted industries have tended to move away from urban centers in large cities (see Fig. 4 for the two largest cities in Hebei), resulting in the divergence of polluting industries from dense population distributions. Therefore, the use of population distribution to allocate emissions tended to overestimate the urban–rural gradients of emissions. At coarse resolutions of 0.5 and 1.0∘, relative differences between the two inventories were smaller because the large grid covered both urban and rural regions and smoothed emission distributions.

To elucidate the variations in urban and rural areas, we analyzed the relationships between emission fluxes of NOx and demographic trends at multiple resolutions, as shown in Fig. 5. In HB-EI, 32 % of emissions were attributed to the top 25 % of the populated dense grids, as shown by the line of HB-EI-NOx. Emission fluxes gradually declined, moving from the dense urban grids to the less dense suburban and rural grids, while emission fluxes in MEIC declined relatively sharply compared to HB-EI. This trend occurred because the proxy-based downscaling method tended to over-allocate industrial emissions to urban areas, such that 42 % of NOx emissions was distributed to populated grids in the upper quartile, 10 % higher than HB-EI, which resulted in larger urban–rural gradients. This pattern was evident at the finer scales given that the NOx emission fluxes from the 10 % most densely populated grids were 46–140 % higher than those of HB-EI at 0.05 and 0.1∘. At coarse resolutions, the urban and rural areas were aggregated with evenly distributed emissions. Therefore, both HB-EI-NOx and MEIC-NOx approached the 1 : 1 line at 0.5 and 1.0∘ and exhibited similar emission flux patterns that were not influenced by spatial allocation biases.

Urban-scale models have emerged in response to a critical need for fine-scale modeling. However, the proxy-based downscaling method over-allocates emissions to urban centers, producing artificial emission hotspots that can result in biases in high-resolution models. When estimated as population-weighted exposures, the health risks induced by air pollution may also be overestimated due to the collocation of gridded emissions with dense populations. We evaluate how uncertainties in fine-scale gridded emissions influence air pollution modeling in the next section.

The uncertainties in gridded emission inventories induced by the proxy-based method can affect the biases of chemical transport modeling. This bias propagation was quantified by comparing performance of the WRF-CMAQ model with the MEIC (S1) and HB-EI (S2) emission inputs. The comparison was conducted at 36, 12, and 4 km resolutions, which roughly corresponded to the 0.5–0.05∘ grid sizes discussed above.

For the densest urban areas, the finer-scale simulations predicted higher concentrations of air pollutants due to concentrated emissions (Fig. 6). This enhancement led to better agreement with the observations, as demonstrated by the S2 simulation moving from 36 to 4 km. Higher concentrations modeled at finer scales were also observed in the S1 simulation, but S1 tended to introduce higher positive biases rather than better performances. This tendency was likely due to the over-allocated urban emissions produced by the proxy-based downscaling method. Compared to bottom-up inventories, the use of proxy-based emissions produced similar modeling results, with biases of 3–13 % in predicting surface concentrations of different pollutants at 36 km resolution. At 12 and 4 km, the major pollutants modeled by proxy-based inventories were overestimated by 28–114 % and O3 was underestimated by 17 % due to the enhanced titration effect caused by concentrated NOx emissions. The finer-scale modeling using proxy-based emissions introduced additional 8–73 % biases compared with bottom-up inventories. This finding suggested that urban-scale modeling efforts at ∼ 10 km cannot achieve corresponding accuracies until factory-level inventories are used. Regarding the emission spatial biases (see Sect. 3.2), the proxy-based downscaled emissions were appropriate for modeling at the global and regional scales (e.g., 0.25–0.5∘ or 36 km in this case study), while they could cause larger biases for finer resolutions on the urban scale.

Figure S1 in the Supplement presents the spatial distribution of modeled surface concentrations for primary pollutants. The S1 simulation predicted higher NO2 and SO2 in the south-central part of the province but lower concentrations in the southwest. The densest cities in Hebei are located in the former region, and the industrial district along the Taihang Shan is located in the latter. The proxy-based downscaling method allocated more emissions to the populated regions, resulting in higher estimates of air pollution levels in the densest cities. Compared to bottom-up emissions, the modeling surface concentrations of air pollutants in urban areas were approximately 20–50 % higher for the 36 km domain and were much higher at 12 and 4 km (see Fig. 7). The bias level was influenced by the size of cities. The cities with large populations and industries tended to experience rapid urbanization, with people gathering in the urban centers and polluted industries moving outward. The modeling discrepancies of the two largest cities in Hebei (i.e., Tangshan and Shijiazhuang) were as large as 100–200 %. The small cities presented scattered distributions for both populations and industries and exhibited smaller differences when using population to distribute emissions.

Figure S2 in the Supplement presents the spatial distribution of modeled PM2.5 and O3 concentrations. The S1 simulation tended to predict an 18–55 % higher PM2.5 in the densely populated regions but a 30–110 % lower PM2.5 in the less dense regions. The differences were slightly smaller than those found in the primary pollutants because of the nonlinear particle formation processes and long-range regional transport. For O3, the enhanced titration by NO due to concentrated emissions resulted in negative biases. The S1 simulation predicted 12–30 % lower O3 in the dense regions but 16–35 % higher O3 in the less dense regions. When estimated as population-weighted exposures and averaged within the areas with a population density over 600 km-2 (see Fig. 7), the PM2.5 exposures tended to be 10–20 % higher, whereas the O3 exposures tended to be 10–15 % lower. In the urban centers, the population exposures to PM2.5 and O3 were biased at rates as high as 50–100 %. The overestimated exposures of PM2.5 associated with the underestimated exposures of O3 suggested that more effort is needed to evaluate air pollution health risks on the urban scale. The uncertainties in gridded emissions comprised important uncertainties in health risk assessment.

The proxy-based spatial allocation method assumed linear correlations between emission intensities and spatial proxy densities within a given district. To investigate the sensitivity of the assumption to spatial proxies, we evaluated the spatial correlations between the gridded emissions of HB-EI and different spatial proxies (see Fig. 8). We concluded that the spatial correlation was enhanced significantly with increasing grid size, which was not sensitive to spatial proxy type. The grid size of 0.25∘ roughly corresponded to the correlation coefficient of 0.5. At coarse resolutions (grid size larger than 0.25∘), good spatial correlations were found for different proxies across all pollutants. However, the correlation worsened when the spatial resolutions grew, except for pollutants dominated by nonpoint sources that were correlated with their allocating proxies (e.g., NH3 vs. rural population). Due to the discrepancies in emission source composition, the air pollutants presented different distribution patterns (see Fig. 8). Compared to nonpoint source emissions (e.g., NH3, VOCs, OC), the pollutants dominated by point sources (e.g., TSP, CO2, SO2) showed relatively poor correlations with spatial proxies. This result was not very sensitive to spatial proxy type. For example, changing allocators caused the correlation coefficient to vary only between 0.07 and 0.18 for TSP at 0.05∘. This pattern arose because point sources have been increasingly sited away from urban areas, a phenomenon that was difficult to represent by spatial proxy distribution. In contrast, the pollutant distributions of nonpoint sources were sensitive to spatial proxies at resolutions finer than 0.25∘ because the pollutants allocated with one proxy were clearly correlated with this proxy but uncorrelated with other proxies on fine scales. However, all the proxies tended to present similar spatial distributions on large scales, demonstrated by the correlation coefficient of almost 1 at resolutions coarser than 0.25∘. The findings above suggest that the underlying assumption inherent in the proxy-based emission allocation process is potentially valid on a coarse scale but is highly suspect on scales finer than 0.25∘.

We evaluated the spatial correlations of HB-EI with different proxies by sector, as shown in Fig. 9. NOx is shown as an example (the results for other pollutants are similar). Because the locations of point sources were decoupled from spatial proxies at fine resolutions, power plant and industrial emissions presented poor correlations (R2 < 0.2) with various spatial proxies when grid size was smaller than 0.5∘. The decoupling effect was weakened when grids were aggregated to 0.5∘ or higher, and consistent spatial patterns were found between emissions from point sources and different spatial proxies. The residential and transportation emissions were sensitive to proxy selections on finer scales, which were affected by the allocating proxies used by the two sectors. When grids were aggregated to 0.25∘ or higher, these nonpoint source emissions showed consistent spatial distributions regardless of spatial proxies. For total emissions, the variation of spatial correlation between gridded emissions and proxies was narrowed for grids larger than 0.25∘. Therefore, the proxy-based downscaling method tended to introduce large errors on scales finer than 0.25∘, where local patterns in the distributed point sources dominated over diffuse nonpoint sources, which have not yet been reproduced by any spatial proxy on finer scales.

The findings above imply that spatial proxies should be used with caution. When building regional and global gridded emissions (typically larger than 0.25∘), the two proxies of total population and nighttime light performed slightly better than the other proxies did. These two proxies correlated well with gridded emissions, while other proxies such as urban population, rural population, and road network had several limitations. Urban population tended to over-allocate emissions to urban areas. Rural population had poor spatial correlation with gridded emissions. The spatial distribution patterns of road networks were not suitable for emission allocation except for those from vehicles. When mapping emissions at higher resolutions (e.g., finer than 0.25∘), the proxies of total population and nighttime light were poorly correlated with gridded emissions dominated by point sources, and the spatial distributions of nonpoint source emissions were very sensitive to spatial proxies. In this case, the bottom-up method must be used instead of the proxy-based method to improve the spatial representation of emission distributions.

The bottom-up method estimated emissions for each individual facility as a point source to improve the accuracy of inventory. The point source estimates constituted the main difference between MEIC and HB-EI, demonstrated by the discrepancy in point source shares (Fig. 2). Compared to MEIC, the distinct improvement of HB-EI was to treat all facilities from the industry sector as point sources in addition to a minor improvement in province-to-county emission allocation. These changes produced better agreements with in situ observations when used for urban-scale modeling. At 4 km resolution, the bottom-up inventory of HB-EI reduced biases by 8–73 % in predicting the surface concentrations of different air pollutants. To evaluate the sensitivity of fine-scale modeling to point source estimates, we conducted a sensitivity analysis by slightly reducing the contributions of point sources, an analysis denoted by S3 (see Sect. 2.2.2). The extent to which fine-scale modeling influenced the modeling performance highlighted the implications for point source estimates and the role high-resolution emission mapping played in fine-scale modeling.

For S3, we converted small industrial boilers (≤ 24.5 MW) in HB-EI to nonpoint sources for a sensitivity test by aggregating the emissions into provincial totals and then distributing them into grid cells like MEIC. The emission shares of point sources were reduced by ∼ 20 % for almost all pollutants (Table 3). The modeling biases that used this adjusted inventory (S3) fell between those from the MEIC-based simulation (S1) and HB-EI-based simulation (S2). The normalized mean biases of the criterion pollutants were approximately 5–15 % higher than those produced by S2 due to the inclusion of ∼ 20 % fewer point sources, whereas they were 18–90 % lower than those produced by S1 due to the inclusion of ∼ 50 % more point sources. This difference suggested that the spatial biases tended to decline significantly as more point sources were included. The improvement of modeling biases roughly corresponded to the increased contributions of point sources to emissions.