We improved the exponentially modified Gaussian method (Beirle et al., 2011) to quantify the multi-year average NOx emissions obtained from OMI NO2 observations for sources located in a polluted background (Liu et al., 2016a). In this work, we adapted the fitting functions of Liu et al. (2016a) to calculate the NOx emissions for individual cities and power plants, including adjustments to meet the requirements of the trend analysis.

Consistently with our previous study (Liu et al., 2016a), we used the OMI tropospheric NO2 (DOMINO) v2.0 product (Boersma et al., 2011) together with the ECMWF ERA interim reanalysis (Dee et al., 2011) to perform the analysis. We calculated the mean NO2 tropospheric vertical column densities (TVCDs) for calm wind speeds below 2 m s-1 and eight different wind direction sectors, by following the approach in Beirle et al. (2011), and for weak-wind conditions (below 3 m s-1), by following the recommendations in Lu et al. (2015), from 2005 to 2015. We used only non-winter data (from March to November) in order to avoid larger uncertainties because of larger solar zenith angles and variable surface albedo (snow). In addition, the longer NOx lifetimes in winter resulted in a less direct relationship between NOx emissions and satellite NO2 observations.

Emissions were derived in a two-step approach in Liu et al. (2016a). The first step was to use NO2 patterns under calm wind conditions as a proxy for the spatial distribution of NOx emissions and determine the effective atmospheric NOx lifetime from the change of spatial patterns measured at higher wind speeds. The second step was to derive emissions from the NO2 mass integrated around the source of interest divided by the corresponding lifetime.

To perform a trend analysis, we adjusted the method as follows: we based the estimation on NO2 columns around the source of interest averaged over 3 years, in agreement with previous studies (e.g., Fioletov et al., 2011; Lu et al., 2015), and then the total NOx mass was integrated over the mean TVCDs at weak-wind speeds (below 3 m s-1) instead of calm winds (below 2 m s-1) to balance the need for increasing the number of observations and minimizing interferences by advection. Notably, we were not able to derive valid lifetimes on the basis of the 3-year average NO2 columns; instead, we fitted the lifetimes on the basis of multiple-year data (the entire study period) because of the lack of sufficient observations for different wind sectors within a 3-year period. Therefore, the NOx emissions for each 3-year period were calculated by dividing the corresponding total NOx mass by the multiple-year average lifetime. In this way, the temporal variations in NOx emissions were merely dependent on the changes in the total NOx mass, excluding background pollution, assuming that the lifetimes did not change over time. However, we wanted to include the fit over the lifetime in this study to make the comparison of top-down and bottom-up estimates more straightforward. Subsequently, we included mountainous sites, which were defined as sites where the absolute difference in elevation between ECMWF and GTOPO data (available at https://lta.cr.usgs.gov/GTOPO30; rescaled to 0.05∘) was larger than 250 m, in the following analysis. Our previous findings (Sect. 2.6 in Liu et al., 2016a) have indicated that appropriate wind fields, which are required for accurate lifetime calculations, may not always be achieved from the ECMWF simulation over mountainous regions. However, depending on changes in the total NOx mass, the fitted emission trends are not as sensitive as the fitted lifetimes to wind fields; thus, we did not exclude mountainous sites from the trend analysis. The fitting results with poor performance (i.e., R<0.9, lower bound of confidence interval CI < 0, CI width for lifetime > 10 h, CI width for the NO2 mass > 0.8 × mass) were discarded, in accordance with the criteria in Sect. 2.2 of Liu et al. (2016a).

We selected the Huolin power plant (site no. 2; 45.5∘ N, 119.7∘ E), which is located in Holingol, a county-level city of Inner Mongolia, China (shown in Fig. 1), to demonstrate our approach. The Huolin power plant has a total capacity of 2400 MW and dominates the NOx emissions from the city of Holingol, contributing over 80 % of the total emissions estimated by using the Multi-resolution Emission Inventory for China (see Sect. 2.2), which is a bottom-up emission inventory. Figure 2a displays the 3-year average NO2 TVCDs around the power plant under weak-wind conditions from 2005 to 2015. For simplicity, the 3-year period is represented by the middle year with an asterisk (e.g., 2006∗ denotes the period from 2005 to 2007). A significant increase in TVCDs was observed from 2006∗ to 2010∗, which was followed by a subsequent decrease. Figure 2b presents the fitted background and NOx emissions. The fitted NOx emissions showed an increase of up to a factor of 4 from 2006∗ to 2010∗ and a decrease of 30 % from 2011∗ to 2014∗, whereas the fitted background was steady and showed a standard deviation of less than 10 % from 2006∗ to 2014∗. The growth of the fitted NOx emissions in the early stage was found to be consistent with the construction of new electric-generating units, with the total capacity increasing from 300 to 2400 MW from 2005 to 2009. Subsequently, the fitted NOx emissions remained steady from 2010∗ to 2012∗, when no new electric-generating units were placed into service, and finally decreased after the installation of selective catalytic reduction (SCR) equipment at the power plants. This decrease in emissions indicated the effectiveness of SCR equipment for decreasing emissions.

We used bottom-up information to pre-select promising sites and to perform a comparison with the fitted top-down emission trends. We selected bottom-up emission inventories widely used in the community, in which multi-year gridded estimates are provided (more than 3 years of data available from 2005 to 2015). We finally included Emission Database for Global Atmospheric Research version 4.3 (EDGAR v4.3; available for 1970–2010; Crippa et al. 2016), Regional Emission inventory in Asia version 2.1 (REAS v2.1; available for 2000–2008; Kurokawa et al., 2013), and the Multi-resolution Emission Inventory for China (MEIC; http://www.meicmodel.org) compiled by Tsinghua University. The analysis was focused on the MEIC inventory that are available for the whole period. Vehicle population and coal consumption at the city level were derived from the China Statistical Yearbook for Regional Economy (NBS: CSYRE, 2004–2014) and the China Environment Yearbook (NBS: CEY, 2004–2015), respectively. We derived the information for the coordinates, unit capacities, and technologies for individual power plants from the unit-based China coal-fired Power plant Emissions Database (CPED) (Liu et al., 2015) integrated in MEIC.

We calculated the NOx emissions from cities and power plants from 2005 to 2015. Only emissions for non-winter seasons were considered, in accordance with the emissions included for the top-down estimates, except for EDGAR in which only annual emissions are available. The gridded bottom-up inventories were integrated over a 40 km ×40 km metropolitan area for which the proposed top-down method was sensitive to calculate the total urban emissions (Liu et al., 2016a). Emissions for individual power plants are derived from CPED and the power plant sector of REAS directly (emissions from individual point sources are not available in EDGAR). Notably, the emissions uncertainties associated with power plants derived from CPED were much lower (30 %) than those for cities (50–200 %) because the former was calculated directly from unit-level information whereas the latter was derived by downscaling regional-based emission data to finer grids using spatial proxies and integrating emissions from corresponding grids.

We selected large cities and power plants in China as the pre-selected sites for which bottom-up emission information was derived from the MEIC and CPED inventories, respectively. China classifies its administrative divisions into five practical levels (from large to small): province, prefecture, county, township and village. Only prefecture-level cities were selected for analysis in this study. Power plants with NOx emission rates greater than 10 Gg yr-1 were selected for emission fitting. Figure 1 illustrates all investigated sites where the fit results showed good performance. Among over 200 pre-selected cities, 48 cities (including 14 mountainous sites) were fitted with good performance (see the definition in Sect. 2.1). While among over 100 pre-selected power plants, more than half were excluded from the fit procedure because they are located in a radius of 100 km around prefecture-level city centers, on the basis of a visual inspection of satellite imagery from Google Earth. Only seven power plants (including three mountainous sites) were fitted with good performance. Detailed information on the sites is tabulated in Table S1 of the Supplement.

The trends in the fitted NOx emissions for 48 cities from 2006∗ to 2014∗ are shown in Fig. 3a, with an average growth trend of 52 % prior to 2011∗ for all investigated cities and a declining trend of 21 % from 2011∗ to 2014∗. The NOx emissions over urban areas essentially represent a marker for combustion-related emissions, including coal combustion for power generation and industrial processes and oil combustion for transportation. Figure 3b further summarizes the statistical data of industrial coal consumption (open squares) and vehicle population (proxy of oil consumption, solid squares), which are available for only 28 cities. Not surprisingly, the fitted emission trends for the 28 cities (circles) were consistent with those for the overall 48 cities. The observed sharp growth of 47 % in NOx emissions during the period of 2006∗–2011∗ was attributed to the growth of 75 and 158 % in coal consumption and vehicle population, respectively. Coal consumption and vehicle population continued to rise and increased by 8 and 26 % from 2011∗ to 2014∗, respectively; however, a subsequent decline in NOx emissions was observed. We further divided these NOx emissions by coal consumption and vehicle population because their respective temporal variations can be treated as an approximation of the average emission factor trends in the industrial (including power) and transportation sectors, on the basis of the assumption that contributions of NOx emissions from corresponding sectors are constant over time. The ratio of emissions to coal consumption and vehicle population has diminished over time and decreased by 37 and 65 % from 2011∗ to 2014∗, respectively. This declining trend was greater than the fluctuations in contributions of NOx emissions from the corresponding sectors (ranging from 1 to 24 % for individual cities) and indicated the effectiveness of emission control measures.

The time series between fitted emissions and bottom-up inventories are generally consistent in Fig. 3b. The changes in NOx emissions from 2005 to 2015 according to sector for the investigated cities on the basis of MEIC estimates are summarized in Fig. 3a and indicate the driving force underlying the emission changes. In agreement with previous findings (Liu et al., 2016b), power plants are the primary component responsible for the decline in NOx, and the associated bottom-up NOx emissions decreased by 59 % between 2011 and 2015. This finding was further supported by the power plant emission trends shown afterwards in Sect. 3.3. The decrease in both fitted and bottom-up emissions has accelerated since 2013 because of the implementation of air pollution prevention and control action plans (the State Council of China, 2013). Such plans require the deployment of denitration devices for coal-fired boilers and cement precalciners, and the requirements are not limited to power plants, as observed in earlier policies. By 2015, 92 % of the power plant boilers and cement precalciner kilns in China had installed denitration devices. In addition, low-efficiency small coal-fired boilers and even complete factories have been phased out. Iron, steel, and cement factories with an overall production capacity of 86, 44, and 263 Gg were shut down in China from 2013 to 2015. Additionally, Chinese cities have pursued a reduction in coal consumption through the gradual transformation of the energy system from coal to renewable energy and natural gas. For instance, Beijing has outlined plans for “coal-free zones” that ban coal usage, and these plans required the replacement of all coal-fired boilers with natural gas in inner suburban districts by 2015 (Clean Air Action Plan 2013–2017, Beijing Municipal Government, 2013). Accordingly, China reached peak coal consumption in 2013, and a decline of 4 % in coal consumption for the investigated cities was observed between 2013 and 2014 (Fig. 3b). Moreover, Chinese cities have been required to meet more stringent vehicle emission standards. For instance, Euro IV emission standards were widely implemented in 2015, and the NOx emission factor is only 2.6 % of the Euro 0 standard for gasoline vehicles (Huo et al., 2012). Because of the notable success of emission control induced by stricter emission standards, the contributions of high-emitting old vehicles (Euro 0 in most cases) to overall emissions are becoming increasingly significant. Reports have indicated that Euro 0 vehicles accounted for more than 50 % of the total vehicle emissions in China in 2009 (MEP, 2010). Thus, China has marked high-emitting vehicles with yellow labels, implemented traffic restrictions and subsidized scrappage programs for these vehicles (Wu et al., 2017). A total of 15 million yellow-label vehicles were scrapped between 2013 and 2015. Significant progress in controlling vehicle emissions has also been observed with improvements in vehicular fuel combustion efficiency and license registration control policies, which allocate quotas for new vehicles through public auction or lottery. Note that all bottom-up inventories show a lower increase rate around the year 2010, compared to the fitted emissions (Fig. 3b). This is most likely caused by the spatial allocation approach adopted in bottom-up inventories, which tends to diminish regional diversity and may consequently result in smaller emission growth (see further discussion in Sect. 3.2).

The fitted results allowed for a closer examination of the trends and causes of emission changes at the individual city level instead of at a regional level, as performed in previous studies (e.g., Liu et al., 2016b). Figure 4 compares the fitted and bottom-up emissions for selected cities, which can be considered in three broad categories: mega cities with large amount of vehicle emissions (Guanzhou and Shanghai in Fig. 4a and b), cities with power plants as the dominant emission source (Wuhai and Huainan in Fig. 4c and d), and cities with industrial plants as the dominant emission source (Karamay and Jiayuguan in Fig. 4e and f).

Figure 4a and b show that megacities reached the emission peak prior to the average timeline shown in Fig. 3. Here, we discuss in detail the temporal variations in Guangzhou, the largest city in South China. The early decline in emissions was primarily related to the stricter regulations on vehicles, which was the only source that showed decreasing emissions, as indicated by the bottom-up inventory. Guangzhou implemented Euro III emission standards for all light-duty vehicles and heavy-duty diesel vehicles in 2006, which was 2 years earlier than the national requirement. Traffic restrictions for motorcycles and trucks and for yellow-label vehicles have also been implemented since 2007 and 2008, respectively. In addition, alternative fuels in buses and taxis have also been promoted in Guangzhou, and 75 and 94 % of these vehicles, respectively, were using liquefied petroleum gas by 2009 (Zhang et al., 2013). The early decline before 2010 in Shanghai shown in Fig. 4b is attributable to similarly strict regulations for vehicle emissions that were implemented before the national schedule. In addition, Guangzhou has gradually phased out the high-pollution iron and steel industry since 2008; however, such emission reductions were not well presented by the bottom-up inventory. In line with the national denitration procedure, coal-fired power plants have remained a significant contributor to emission reductions since 2011. The bottom-up NOx emissions from power plants in Guangzhou decreased by over 50 % between 2011 and 2015, because of the wider deployment of denitration devices at power plants.

The interannual trends of NOx emissions for the cities of Wuhai and Huainan are displayed in Fig. 4c and d, and power plants were the dominant source of NOx emissions. Not surprisingly, the top-down and bottom-up information was more consistent than the information for the other two categories, because of the better quality of emission estimates for the power sector. The fitted emissions decreased with the decline in emissions from power plants around 2012, and this finding was related to the deployment of denitration devices.

Emission variations for cities for which the industrial sector was the dominant emission source are shown in Fig. 4e and f, which indicate significant inconsistencies in the top-down and bottom-up information, even for the total amount. Cities belonging to this category were usually medium and small cities. For instance, the city of Jiayuguan (Fig. 4f) has a total population of 0.2 million, a vehicle population of 0.03 million and a large-sized industrial enterprise (Jiuquan Iron & Steel (Group) Co., Ltd). Industrial activities are the most likely contributor to the recent deceleration and even decline in total emissions, because of the small human and vehicle populations and the limited amount of power plant emissions (light blue line) in the city. To meet the demands of the air pollution prevention and control action plan (the State Council of China, 2013), the iron and steel enterprises have been required to regulate their emissions since 2013. Additionally, the city is required to meet stricter vehicle emission standards and retire aged vehicles. However, the bottom-up inventory for the city of Jiayuguan was consistent with this analysis for only the transportation sector and not the industrial sector as shown in Fig. 4f. The bottom-up transportation emissions experienced a decline of 10 % and a sharp increase of 20 % in the vehicle population between 2013 and 2015. In addition, the NOx emissions from the industrial sector were fairly steady and showed a decrease of only 2 % between 2013 and 2015 and account for a small share (20 %) of the total emissions. For industrial emissions, MEIC first downscaled provincial totals to counties using industrial GDP, and then allocate county emissions to grids with population density. Thus, uncertainty of emissions from the industrial sector is larger than that from power plants. Such changes in the industrial sector most probably represent the regional average level and do not represent the levels for a city with a large-sized iron and steel enterprise, because of the uncertainty of downscaling approaches adopted in the bottom-up inventory.

Although we used bottom-up inventories to interpret the changes in NOx emission, certain notable discrepancies occurred between the fitted emissions and the bottom-up inventories. We further explored the reasons for these inconsistencies in cities by examining the differences in trends between top-down and bottom-up estimates at different spatial scales. Figure 5 presents the temporal variations at provincial and city scales from 2006∗ to 2014∗ for the top-down and bottom-up data sets. The top-down information at the provincial level (Fig. 5a) was the 3-year average OMI NO2 column densities for non-background regions, where the average annual NO2 column densities were larger than 1×1015 molec cm-2 or the average NO2 column densities for summer exceeded those for winter in Liu et al. (2016b), and the top-down estimates (Fig. 5c) at the city level were derived from this study. The bottom-up emissions were calculated by summing the emissions of the corresponding grids belonging to individual provinces (Fig. 5b) or cities (Fig. 5d, see Sect. 2.2). Not surprisingly, the comparison of the two independent data sets showed that the trends at both the provincial and city levels were generally consistent, with both levels experiencing a sharp rise before 2012∗ (2011∗ in Fig. 5c) and a continuous decline thereafter. However, a closer examination of the magnitude of relative changes showed that the differences were scale dependent. The provincial-level comparison showed a growth trend of 40 % ± 26 % and 34 % ± 21 % from 2006∗ to 2012∗ and a subsequent declining trend of 9 % ± 4 % and 14 % ± 6 % from 2012∗ to 2014∗ for the top-down and bottom-up data sets, respectively, and indicated the acceptable accuracy of provincial totals in bottom-up estimates. However, the city-level comparison exhibited a large discrepancy in the magnitude of change rates. For instance, the top-down growth rates reached 45 % ± 46 % in the period from 2006∗ to 2012∗, whereas the bottom-up rates were only 25 % ± 27 % for the same period.

We expect that the scale dependence of the differences shown in Fig. 5 may be explained by the spatial allocation approach adopted in bottom-up inventories. Current gridded bottom-up emission inventories rely heavily on spatial proxies because rare emissions, excluding the emissions from stacks of large point sources, can be directly measured. A variety of spatial proxies, such as population density, road density, and satellite-observed nightlights, are used to geographically distribute emission totals from a large scale down to the scale of geographic grids of various sizes. Several studies (e.g., Hogue et al., 2016) have indicated that such a spatial distribution approach using proxy data introduces significant uncertainties because emissions can be misallocated spatially and temporally. Although the MEIC inventory has substantially improved its accuracy, such as by using the high-resolution power plant database CPED (Liu et al., 2015), a lack of data has led to the inclusion of other types of point sources (such as industrial boilers) as areal sources of emissions. For example, the MEIC first downscales provincial industrial emission totals to county totals according to industrial GDP values and then distributes county emissions to grids according to the population density. However, industrial facility locations are likely to be decoupled from spatial proxies, because polluted facilities are often required to be located in rural areas with smaller GDP and populations (Zheng et al., 2017), and this decoupling may have resulted in the underestimation of emissions from steel and iron factories shown in Fig. 4f. In addition, the spatial distribution of proxies cannot easily represent the emission changes caused by anti-leapfrogging policies implemented in cities ahead of the national schedule, such as the previously discussed new vehicle emission standards in Guangzhou. Thus, regional diversity may have been diminished and consequently resulted in the small standard deviation over cities shown in Fig. 5d.

The correlation coefficients of the pair-wise trends between the fitted NOx emissions and the bottom-up inventory for the period 2006∗ to 2014∗ are illustrated in Fig. 6. The correlation coefficient of the time series of NOx emissions showed remarkable diversity for cities and reached over 0.9 for Urumqi (no. 9 in Fig. 6) and dropped to less than -0.7 for Jinzhou (no. 5 in Fig. 6), probably because of the high uncertainties of the bottom-up inventories for cities. Notably, the negative correlation coefficients do not necessarily correspond to a strong inverse linear relationship and may suggest inconsistency over only one or two periods (Fig. 4b). Additionally, the negative correlation coefficients were always observed when the time series of fitted emissions experienced a minor fluctuation without a significant trend, as demonstrated in Fig. 6b by cities with a correlation coefficient less than -0.4.

The trends in fitted NOx emissions for seven power plants from 2006∗ to 2014∗ are shown in Fig. 7. The changes in the total NOx mass and derived NOx emissions were consistent with the addition of new units in individual power plants until the installation of denitration devices. The dramatic growth in NOx emissions (red line) prior to 2010∗, which reached 89 % on average for all power plants investigated in this study, was driven by increases in the capacity of 84 % for the corresponding power plants (gray bar). However, the subsequent decline in NOx emissions could not be explained by the simultaneous changes in total unit capacities, which increased by 3 % from 2010∗ to 2014∗, but suggests a good agreement with the wider deployment of denitration devices, such as SCR equipment. The installation of SCR devices generally ensures a NOx removal efficiency of 80–85 % (Forzatti et al., 2001). However, the denitration devices used in Chinese power plants usually do not meet this standard efficiency, because of the non-optimal use of catalysts and reductants. The average removal efficiency of SCR equipment for 2014 was only 60 % on the basis of statistics from the CPED. In this way, the increasing penetration of SCR equipment (up to 73 %, blue line) corresponded to a decrease of approximately 40 % (i.e., 73 % × 60 %) in NOx emissions, a result consistent with the changes in fitted emissions. The fitted emissions were further compared with the bottom-up emission estimates, and both values shared a similar trend. The significant decline of 40 ± 22 % (mean ± standard deviation) in fitted NOx emissions for individual power plants from 2010∗ to 2014∗ was generally consistent with the simultaneous decline in bottom-up estimates of 22±29 %. However, a minor difference in the peak year of emissions was detected for a few power plants, and was most probably caused by uncertainty in the fitted emissions related to the lack of interannual variations in NOx lifetimes.

China has implemented the new emission standards for thermal power plants (Ministry of Environmental Protection of China (MEP), 2011) in 2012, requiring power plants, particularly large plants, to install denitration devices, such as SCR equipment, to control their NOx emissions. The deployment of denitration devices (shown in Fig. 7) was consistent with this new policy, and the national average penetration of SCR equipment grew from 18 to 86 % between 2011 and 2015 (China Electricity Council, 2012–2016). Given that the overall capacity of the power plants investigated in this study was equivalent to only 2 % of the total national capacity, we may not be able to conclude that the temporal variations in NOx emissions derived from the seven power plants reflect the emissions from large power plants at the national level. While for the investigated power plants, the derived emissions were consistent with the bottom-up emissions and the time series of the two estimates were well correlated, even for mountainous sites where the absolute values of the emission estimates differed significantly (Fig. 6a). The good consistency increased our confidence that the fitted emission trends accurately represented the real-world emission variations, because the uncertainty of the bottom-up emission inventory for power plants is fairly low (Liu et al., 2015).

The fitted NOx emissions were compared with the bottom-up emission estimates (Sect. 2.2) for all 48 cities and seven power plants in Fig. 8, and their correlations were consistent with the average emission estimates for multiple years shown in previous work (Liu et al., 2016a). In general, the comparisons indicated consistency among non-mountainous sites, which presented a higher correlation coefficient for power plants (blue symbols in Fig. 8a, r=0.89) than cities (blue symbols in Fig. 8b, r=0.81). The results for the mountainous sites showed higher scatter for both power plants (red symbols in Fig. 8a, r=0.79) and cities (red symbols in Fig. 8b, r=0.44), thus confirming that those top-down estimates had higher uncertainties because of inaccurate ECMWF wind fields for mountainous sites (Liu et al., 2016a). The comparable correlation among the results presented here and in the previous study by Liu et al. (2016a) increased our confidence in the accuracy of the fitted results.

We estimated the uncertainty of the fitted NOx emissions and their trends by using a method analogous to that in Liu et al. (2016a) because of the consistency in methodology between the two studies. The uncertainty analysis was performed on the basis of the fit performance and according to sensitivity studies that have investigated the dependencies on a priori settings, which are detailed in the supplement of Liu et al. (2016a). The major sources of errors contributing to the overall uncertainties included (a) fit error, (b) choice of fit intervals, (c) tropospheric NO2 VCDs and the NOx / NO2 ratio, (d) choice of wind fields and (e) lifetime variations. The uncertainties arising from (a) to (c) were consistent with those reported in Liu et al. (2016a). Here, we briefly discuss the impact of (d) and (e).

(d) Choice of wind fields. The NO2 trends observed under weak-wind conditions may vary from those under all-wind conditions (Lu et al., 2015), because higher wind speeds are expected to cause longer NOx lifetimes because of the faster dilution of NOx (Valin et al., 2013). A change in the weak-wind conditions by all-wind conditions affects the resulting total mass by approximately 10 % on average.

(e) Lifetime variations. We use multiple-year average lifetimes and 3-year average NO2 masses to calculate NOx emissions trends in this study. The variations in total NO2 mass do not necessarily correlate linearly with NOx emissions, because of potential changes in the NOx lifetimes related to variations in meteorology and NOx chemistry. However, the temporal variations in lifetimes corresponding to the 3-year moving averages of TVCDs are reduced significantly, as supported by the similar decreases in the 3-year mean NOx emissions and OMI NO2 observations over urban areas in the US (Lu et al., 2015). In addition, we could not unambiguously relate the variability of fitted NOx lifetimes to NO2 levels (Liu et al., 2016a).

The method was applied to the period prior to the row anomaly (the 3-year period from 2005 to 2007), which had a larger number of observations than the other periods. The method was successful for 19 sites, and the fitted lifetimes were not sensitive to the NO2 changes within the studied period, with the lifetimes increasing by only 9 % when the average NO2 increased by ∼ 20 % compared with the multiple-year level. The uncertainties caused by lifetime variations were estimated to be 10 %, and this value was applied to all considered sources.

The total uncertainty was defined as the root of the quadratic sum of the aforementioned contributions, which were assumed to be independent. We estimated that the total uncertainties of the fitted NOx emissions were within 66–99 % for all investigated sites. Notably, this estimate is rather conservative because of the assumption that all the contributors to uncertainties are independent. In addition, the uncertainty in emission trends was significantly lower than that of emissions because the errors from the choice of fit intervals, wind fields, tropospheric columns, and NOx / NO2 ratios were generally compensated for in the assessment of trends.