Resolution dependence of uncertainties in gridded emission inventories: a case study in Hebei, China

This study describes the construction and evaluation of a high-resolution bottom-up inventory of air pollutant emissions for Hebei Province in northern China. The authors compare the performance of a mesoscale chemical transport model (WRF/CMAQ) using their new inventory, which is built from local data, with CTM runs that use a proxy-based national inventory as a model prior. Their results show nicely that uncertainties in model output are influenced by the spatial resolution of the model grids, and the degree to which the inventory priors rely on spatial downscaling to generate gridded emissions at local scales. The authors have isolated the contributions of different elements in the prior inventories, which allowed them to quantify uncertainties in the spatial distribution of emissions, as well uncertainties produced by aggregating emissions to coarser spatial grids. There findings that the proxy-based inventory produced large biases in estimated pollution concentrations at high resolution in urban areas is novel, and should be of interest to the broad readership of ACP. Their results are a valuable confirmation that urban-scale modeling of emissions and pollutant concentrations requires high-resolution local activity data to accurately capture the spatial patterns of pollution. Abstract. Gridded emission inventories are essential inputs for chemical transport models and climate models. Spatial proxies are applied to allocate emissions from regional totals to spatially resolved grids when the exact locations of emissions are absent, with additional uncertainties arising due to the spatial mismatch between the locations of emissions and 15 spatial proxies. In this study, we investigate the impact of spatial proxies on the accuracy of gridded emission inventories at different spatial resolutions by comparing gridded emissions developed from different spatial proxies (proxy-based inventory) with a highly spatially disaggregated bottom-up emission inventory developed from the extensive use of locations of emitting facilities (bottom-up inventory) in Hebei Province, China. We find that proxy-based inventories are generally comparable to bottom-up inventories for grid sizes larger than 0.25º because spatial errors are largely diminished at coarse 20 resolutions. However, for gridded emissions with finer resolutions, large positive biases in urban centers and negative biases in suburban and rural regions are identified in proxy-based inventories and are then propagated into significant biases in urban-scale chemical transport modeling. Compared to bottom-up inventories, the use of proxy-based emissions exhibits similar modeling results, with biases varying from 3%–13% in predicting surface concentrations of different pollutants at 36 km resolution and an additional 8%–73% at 4 km resolution. The resolution dependence of uncertainties in proxy-based 25 gridded inventories can be explained by the decoupling of emission facility locations from spatial surrogates, especially because industry facilities tend to be located away from urban centers. This distance results in a divergence between emission distributions and the allocation of proxies on smaller grids. The decoupling effects are weakened when the grid size increases to cover both urban and rural regions. We conclude that proxy-based inventories are of sufficient quality to support regional and global models (larger than 0.25º in this case study); however, to support urban-scale models with accurate 30 emission inputs, bottom-up inventories incorporating the exact locations of emitting facilities should be developed instead of proxy-based inventories.

: There is a reference to Zheng et al 2014 (e) but I don't see that on the table.

Response:
The reference to Zheng et al 2014 (e) is labeled on the subsector of on-road emissions in Table 1.

Introduction
Gridded emission inventories have emerged as a critical component of atmospheric chemistry and climate models. The importance of these inventories has been driven by the advent of regional chemical transport models at different spatial 35 scales. As the key inputs, spatial representations of emission estimates containing errors can be propagated into modeled concentrations, affecting subsequent studies based on those chemical transport models.
Gridded emission inventories can be developed using two methods: bottom-up estimates and proxy-based estimates with downscaling techniques. Bottom-up estimates rely on massive spatial information such as point sources, detailed censuses, and traffic statistics. For large point sources, emissions can be estimated for each individual facility and then mapped at high 40 resolutions (e.g., Zhao et al., 2008;. For on-road emissions, high-resolution mapping can be achieved using road-specific traffic count data at spatial scales ranging from 500 m to 10 km (e.g., Gately et al., 2013Gately et al., , 2015McDonald et al., 2014). The above bottom-up inventory methods rely on mass data inputs, which are accurate but difficult to extend through all sectors and regions. For example, Gurney et al. (2009) developed the Vulcan inventory to quantify fossil fuel CO2 emissions for the contiguous U.S. at a resolution of 10 km. This data product was built upon the best available data 45 sources through all sectors throughout the U.S., including point, nonpoint and airport datasets with additional emission monitoring data from individual facilities.
The proxy-based method relies on spatial proxies to build emission inventories in gridded form. Because they require relatively less data, proxy-based approaches are widely used for developing gridded emission inventories. Proxies such as population and nighttime lights have been used to derive gridded emissions (e.g., Raupach et al., 2010;Oda et al., 2011;50 Wang et al., 2013), which are implicitly assumed to be resolution-independent at sizes ranging from district level to grid cells. However, this correlation is likely sensitive to fine-scale spatial resolutions, which introduce uncertainties in highresolution emission mapping. Gurney et al. (2009) highlighted the spatial biases inherent in a population-based gridded emission inventory due to the decoupling of emissions and population at 0.1°. Oda et al. (2011) presented the uncertainties in a nighttime light-based inventory due to the saturation errors in nighttime light data at 1 km. Gately et al. (2013Gately et al. ( , 2015 found 55 that the spatial correlation between the per-mile CO2 emissions of motor vehicles and population density changed from positive to negative when population density increased (cut-off point of approximately 2000 persons km -2 ). The above studies suggest that nonlinearities exist between emissions and spatial proxies at fine scales. The downscaling method with fixed correlation can involve large uncertainties in proxy-based gridded emissions, especially at high resolutions.
The uncertainties in proxy-based gridded emission inventories are sensitive to spatial resolution. Recent efforts suggest that 60 uncertainties is unknown. This paper aims to investigate how resolutions influence uncertainties in gridded emission inventories of air pollutants and the subsequent atmospheric chemistry modeling. The spatial resolution dependence of uncertainties in gridded emission inventory is quantified using multi-resolution emission inventories, a chemical transport model, and in situ measurements.
We use Hebei Province in China, where a detailed bottom-up emission inventory is available. We first develop gridded 70 emission inventories for Hebei at the resolution of 1 km using proxy-based and bottom-up methods and then compare the two datasets at multiple aggregated spatial resolutions. The Community Multi-scale Air Quality model (CMAQ) is driven by the two gridded emission datasets to explore how uncertainties affect the performance in predicting the surface concentrations of different air pollutants.

Bottom-up inventory
We used the bottom-up method to develop a high-resolution emission inventory for Hebei Province in 2013 (denoted by HB-EI). The emission sources were subdivided into more than 700 sector/fuel (or product)/technology combinations of source categories and aggregated into five sectors (power, industry, residential, transportation, and agriculture). Each source 80 category was classified as point, nonpoint or mobile, with a different emission accounting method applied to each category.
Point sources were stationary emitting sources inventoried at a facility level. The power and industry sectors were treated as point sources, from which the emissions were calculated using the following: where i represents the emitting facility, s represents air pollutants (i.e., SO2, NOx, VOCs, NH3, CO, CO2, PM2.5, BC, OC, 85 PM10 and TSP (particulate matter with aerodynamic diameter of 100 μm or less)), A is the activity rate, EF is the unabated emission factor, n represents an air pollution control device, and ηi,n,s is the removal efficiency of pollutant s by control device n installed at facility i. The point sources were located according to their latitudinal and longitudinal coordinates. The locations of large point sources were checked and corrected by visual inspection in Google Maps. Large point sources included power and heating plants, large industrial boilers (≥ 24.5 MW), and manufacturing factories of coke, iron, steel, 90 cement and flat glass. These sites constituted 90% of the energy demand from all the point sources. For the other point sources, the coordinates of registered addresses were used directly. Nonpoint or area sources were stationary emitting sources inventoried at a province level, from which emissions exit from diffuse sources without identifiable stacks. The residential, non-road transportation and agriculture sectors were estimated as nonpoint sources using the following: 95 , , , = , × , , × , , , × ∑ ( , , , × (1 − , )), where j represents sector, k represents fuel or product, m represents technology, X is the fraction of activity rates contributed by a specific technology, C is the penetration of a specific pollution-control technology, and the other parameters are the same as in Eq. (1). The nonpoint sources were allocated to a 30″ × 30″ grid in two steps. First, the provincial emission totals were distributed to each county based on county-level activity statistics. For example, we used the residential coal and 100 biofuel use of each county to allocate residential emissions. Second, county emissions were allocated to grids based on spatial proxies, such as urban or rural extents (Schneider et al., 2009) and population (Oak Ridge National Laboratory, 2013).
The parameters used in nonpoint source emission distributions are summarized in Table 1.
Mobile sources referred to the on-road transportation sector, which were estimated using the method established by Zheng et al. (2014). The county-specific vehicle activity and emission factors were simulated and multiplied to calculate county-level 105 vehicle emissions. County emissions were downscaled to a 30″ × 30″ grid using a GIS road atlas and traffic flow statistics specific to different vehicle and road types (Zheng et al., 2014).

Proxy-based inventory
We used the data from the Multi-resolution Emission Inventory for China (MEIC) as the proxy-based estimate. MEIC is a technology-based emission model framework developed by Tsinghua University (http://www.meicmodel.org). This model 110 was built on the foundation laid by the same group responsible for the present study (e.g., Zhang et al., 2007Zhang et al., , 2009Lei et al., 2011), with high-resolution mapping of emissions for power plants  and on-road vehicles (Zheng et al., 2014).
The emission source categorization in MEIC is the same as that in HB-EI. Emissions of power plants were estimated for each unit using Eq. (1). The on-road transportation sector was estimated following the method established by Zheng et al. 115 (2014) as the bottom-up inventory. The industrial, residential, non-road transportation and agricultural sectors were estimated as nonpoint sources using Eq. (2) with activity rates and emission factors at the provincial level. Emission totals from nonpoint sources were allocated to grid cells using different spatial proxies. The proxies used for MEIC are also presented in Table 1 and compared with HB-EI. For example, in MEIC, the residential sector used county population to split provincial emissions by county instead of residential energy consumption used in HB-EI. 120 In this work, we used Hebei emissions from 2013 from MEIC v1.2 and scaled the emission magnitude to match the HB-EI inventory by source category. This approach can support the magnitude-independent comparison to reflect the discrepancies in the spatial distribution of gridded emissions. Multi-resolution gridded emissions aggregated from the 30″ × 30″ grids were used to assess the resolution dependence of uncertainties in the gridded emission inventory.

Model configuration
The WRF/CMAQ system was used to evaluate emission inventories and assess how uncertainties in gridded emission inventory influenced atmospheric chemical modeling. CMAQ v5.0.1 (http://www.cmascenter.org/cmaq/) was applied in this work, which was driven by assimilated meteorological fields from the Weather Research and Forecasting model v3.5.1 (http://www.wrf-model.org/). The model configurations were determined following the method established in our previous 130 work . We used the updated carbon bond gas-phase mechanism with updated toluene mechanism (Whitten et al., 2010), aerosol module 6 (AERO6) and ISORROPIA v2.1 inorganic chemistry (Fountoukis and Nenes, 2007).
The aqueous-phase chemistry method used in this study was the updated mechanism of the Regional Acid Deposition Model (Walcek and Taylor, 1986;Chang et al., 1987). Photolytic rates were calculated in line using simulated aerosol and ozone concentrations. The ACM methodology was adopted in the cloud module to compute convective mixing for aerosols. The 135 above configurations were evaluated in Zheng et al. (2015).
Anthropogenic emissions outside Hebei Province were taken from MEIC for China (http://www.meicmodel.org) and MIX for the other Asian countries . Emission inputs were processed on simulation domains from their native resolutions (30 s × 30 s for MEIC and 0.25° × 0.25° for MIX). Other emissions, such as biomass burning, sea salt and biogenic VOCs, were taken from various models and datasets following the method established by Zheng et al. (2015). 140 The boundary and initial conditions were processed from the GEOS-Chem model output (Bey et al., 2001) using the tool developed by Henderson et al. (2014).

Simulation design
Two full-year simulations of 2013 were conducted using MEIC (denoted by S1) and HB-EI (denoted by S2), both at triplenested domains (36, 12 and 4 km), with the finest resolution focusing on Hebei Province (Fig. 1). We also conducted a 145 sensitivity simulation (denoted by S3) for Jan, Apr, Jul and Oct using the adjusted HB-EI emissions by changing ~20% point sources into nonpoint source estimates to assess the influence of highly spatially resolved emission sources on atmospheric chemistry modeling. We aggregated the emissions from small industrial boilers (≤ 24.5 MW) into provincial totals and then distributed the totals onto grid cells using the same spatial proxies as those used in the industrial sector in MEIC.
The model performances were evaluated against ground-based measurements. We compared the annual daily mean of 150 simulation and observation for the criteria air pollutants and calculated mean bias (MB) and normalized mean bias (NMB) to evaluate modeling results.

In situ measurements
The ground-based observations in Hebei were acquired from the China National Environmental Monitoring Center in China and is used as the official data 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.

Emission inventories: bottom-up versus proxy-based 160
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 165 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 were constrained by road-and countylevel 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 170 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. This finding suggested that the nonlinearities in CO2 emissions and spatial proxy covariance identified in early studies (e.g., Gurney et al., 2009;Oda et al., 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. 180

Resolution dependence of uncertainties in the gridded emission inventory 175
For the pollutants of which emissions are dominated from point sources, the two gridded inventories agreed well at coarse resolutions (grid size larger than 0.25º ), 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 non-point sources (e.g., Figure 3 compares the spatial distributions of gridded emissions using NOx as an example. Figure 3(a-d) presents NOx emission distributions in HB-EI at different spatial resolutions, and Fig. 3(e-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 190 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 largest two cities in Hebei), resulting in the divergence 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. 195 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 200 emissions to urban areas, such that 42% of NOx emissions were distributed to populated grids in the upper quartile, 10% higher than HB-EI, resulting 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 205 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 210 fine-scale gridded emissions influence air pollution modeling in the next section.

Resolution dependence of biases in air pollution modeling
The uncertainties in gridded emission inventory induced by the proxy-based method can affect the biases of chemical transport modeling. The bias propagation was quantified by comparing performance of the WRF-CMAQ model with the MEIC (S1) and HB-EI (S2) emission input. The comparison was conducted at 36 km, 12 km and 4 km resolutions, which 215 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 km 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 220 urban emissions produced by the proxy-based downscaling method. Compared to bottom-up inventories, the use of proxybased emissions produced similar modeling results, with biases of 3%-13% in predicting surface concentrations of different pollutants at 36 km resolution. At 12 km 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 225 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 at the urban scale. Figure S1 presents the spatial distribution of modeled surface concentrations for primary pollutants. The S1 simulation 230 predicted higher NO2 and SO2 in the south-central province but lower concentrations in the southwest. The densest cities in Hebei are located in the former region, and the industrial district along Taihang Mountain is located in the latter. The proxybased 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 km and 4 km (see Fig. 7). The 235 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. 240 Figure S2 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 30%-110% lower 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 in the less dense regions. When 245 estimated as population-weighed exposures and averaged within the areas with population density over 600 per 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 at the urban scale. The uncertainties in gridded emissions comprised important uncertainties in health risk 250 assessment.

Sensitivity to different proxies
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 255 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 the increasing of 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 260 allocating proxies (e.g., NH3 vs. rural population). Due to the discrepancies of emission source compositions, 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 265 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 at fine scales. However, all the proxies tended to present similar spatial distributions at large scales, demonstrated by the correlation coefficient of almost 1 at resolutions coarser than 0.25°. The above findings suggest that the underlying 270 assumption inherent in the proxy-based emission allocation process is potentially valid at a coarse scale but is highly suspect at 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 (R 2 <0.2) with various spatial 275 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 at 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 280 between gridded emissions and proxies was narrowed for grids larger than 0.25°. Therefore, the proxy-based downscaling method tended to introduce large errors at 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 at finer scales.
The above findings 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 285 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 network were not suitable for emission allocation except 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 290 dominated by point sources, and the spatial distributions of nonpoint sources 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.

Sensitivity to point sources
The bottom-up method estimated emissions for each individual facility as a point source to improve the accuracy of 295 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. For S3, we converted small industrial boilers (≤ 24.5 MW) in HB-EI to nonpoint sources for sensitivity test, by aggregating 305 the emissions into provincial totals and then distributing them onto 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 criteria 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 310 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.
In this study, we assessed the resolution dependence of uncertainties in gridded emission inventories, using Hebei, China as a case. The inherent uncertainties involved in emission distributions caused systematic biases in both the emission flux 315 patterns and subsequent chemical transport modeling. In the case of Hebei, China, the proxy-based downscaling method tended to over-allocate emissions to the urban center. For example, the NOx emission fluxes from the 10% most densely populated grids tended to be overestimated by 46%-140% at 0.1° and 0.05° in this case study. This effect was demonstrated by the modeling performance of the CMAQ model, in which the modeling biases of different pollutants using proxy-based inventory were 8%-73% higher than using bottom-up inventories at fine scale (12 km and 4 km). The modeling biases 320 induced by uncertainties in gridded emissions caused population exposures of PM2.5 to be overestimated and O3 to be underestimated in urban areas.
In the proxy-based inventory, the inherent assumption of spatial correlation between emissions and allocating proxies was highly suspect at an urban scale (grid sizes smaller than 0.25° in this case study). This lack of validity was caused by polluted industries increasingly moving away from urban centers, a phenomenon that resulted in a decoupling of emissions 325 from spatial proxies at finer scales. The gridded emissions at a coarse scale tended to aggregate urban, suburban and rural areas; smooth emission distributions; and weaken the decoupling effect. Extensive use of point sources could improve the accuracy of gridded emissions, demonstrated by the improvement of modeling performance as the contribution of point sources increased. We concluded that proxy-based inventories are capable of supporting regional and global models (larger than 0.25º in this case study); however, to support urban-scale models with accurate emission inputs, bottom-up inventories 330 with exact locations of emitting facilities should be developed instead.