2.1 The GEOS-Chem model and its adjoint

We updated the GEOS-Chem global 3-D chemical transport model (version 8.2.1) to simulate the emission, transport, chemistry, and deposition of NMVOCs, as well as the resulting formaldehyde and glyoxal column concentrations for the year 2007. The use of an older version of the GEOS-Chem forward model was necessary because, at the time of our study, the GEOS-Chem adjoint (version 34) was based on this older version. However, we updated the NMVOC chemical schemes (described below) and corrected several model errors in both our forward model and its adjoint by following the progress of the forward model up to version 10.1. GEOS-Chem was driven by the assimilated meteorological data from the NASA Goddard Earth Observing System (GEOS-5) (Bey et al., 2001). To drive our simulations, the horizontal resolution of GEOS-5 data was downgraded from its native 2/3^∘ longitude × 1/2^∘ latitude to 5^∘ longitude × 4^∘ latitude. The number of vertical levels was reduced from 72 to 47 by merging layers in the stratosphere. The lower 2 km of the atmosphere was resolved by 14 levels. The temporal resolution of GEOS-5 data into GEOS-Chem is 3 h for atmospheric variables and 1 h for surface variables.

We updated the dicarbonyl chemical mechanism in GEOS-Chem developed by Fu et al. (2008), which in turn was originally adapted from the Master Chemical Mechanism (MCM) version 3.1 (Jenkin et al., 1997; Saunders et al., 2003). Table S1 in the Supplement lists the yields of formaldehyde and glyoxal from the OH oxidation of NMVOC precursors in our updated chemical mechanism. The lumped NMVOC precursors of formaldehyde in our mechanism included ethane, propane, ≥C₄ alkanes, ethene, ≥C₃ alkenes, benzene, toluene, xylenes, isoprene, monoterpenes, acetone, hydroxyacetone, methylgloxal, glycolaldehyde, acetaldehyde, 2-methyl-3-bute-nol, methyl ethyl ketone, methanol, and ethanol (lumped into ≥C₄ alkanes). The lumped NMVOC precursors of glyoxal in our mechanism included ethene, ethyne, benzene, toluene, xylenes, isoprene, monoterpenes, glycolaldehyde, and 2-methyl-3-bute-2-nol (MBO). Hereinafter we focused our discussion on these NMVOC precursors only, as their emissions may be constrained by formaldehyde and glyoxal observations.

The OH oxidation of isoprene is a major source of both formaldehyde and glyoxal over China (Fu et al., 2007, 2008; Myriokefalitakis et al., 2008). We replaced the isoprene photochemical scheme with that used in GEOS-Chem v10.1, which included updates from Paulot et al. (2009a, b) and Mao et al. (2013). In this updated scheme, oxidation of isoprene by OH under high-NO_x conditions produces formaldehyde and glyoxal at yields of 0.436 molecules per carbon and 0.0255 molecules per carbon, respectively (Table S1), mainly via the RO₂ + NO pathways. Under low-NO_x conditions, oxidation of isoprene by OH produces formaldehyde and glyoxal at yields of 0.38 molecules per carbon and 0.073 molecules per carbon, respectively (Table S1), via both RO₂ + HO₂ and RO₂ isomerization reactions. Li et al. (2016) implemented this same isoprene photochemical scheme in a box model and compared the productions of formaldehyde and glyoxal from isoprene oxidation with those in the MCM version 3.3.1 (Jenkin et al., 2015). They showed that the production pathways and yields of formaldehyde and glyoxal were similar in the two schemes under the high-NO_x conditions typical of eastern China.

We updated the molar yields of glyoxal from the OH oxidations of benzene (33.3 %), toluene (26.2 %), and xylenes (21.0 %) following the latest literature (Arey et al., 2009; Nishino et al., 2010). These new molar yields were higher than those used in Fu et al. (2008) (which were based on averaged yields in the literature: 25.2 % for benzene, 16.2 % for toluene, and 15.6 % for xylenes) but still lower than those used by Chan Miller et al. (2016) (75 % for benzene, 70 % for toluene, and 36 % for xylenes), which were taken from the aromatic chemical scheme in MCM version 3.2 (Jenkin et al., 2003; Bloss et al., 2005). In MCM version 3.2, more than half of the glyoxal from aromatics oxidation was produced during second- and later-generation photochemistry, but such productions are with limited experimental support and uncertain (Bloss et al., 2005).

Formaldehyde and glyoxal in the GEOS-Chem model were both removed by photolysis, as well as dry and wet deposition (Fu et al., 2008). We updated the Henry's law constant for glyoxal from $\mathrm{3.6}\times {\mathrm{10}}^{\mathrm{5}}\times \exp [\mathrm{7.2}\times {\mathrm{10}}^{\mathrm{3}}\times (\mathrm{1}/T-\mathrm{1}/\mathrm{298}\left)\right]$ (Fu et al., 2008) to $\mathrm{4.19}\times {\mathrm{10}}^{\mathrm{5}}\times \exp \left[\right(\mathrm{62.2}\times {\mathrm{10}}^{\mathrm{3}}/R)\times (\mathrm{1}/T-\mathrm{1}/\mathrm{298}\left)\right]$ (Ip et al., 2009) and added the dry deposition of formaldehyde, glyoxal, methylglyoxal, and glycolaldehyde on leaves (Mao et al., 2013). In addition, we assumed that glyoxal was reactively taken up by wet aerosols and cloud droplets with an uptake coefficient $\mathit{\gamma }=\mathrm{2.9}\times {\mathrm{10}}^{-\mathrm{3}}$ (Liggio et al., 2005; Fu et al., 2008). All other physical and chemical processes in our forward model were as described in Fu et al. (2008).

For the forward model described above, we developed the adjoint by modifying the standard GEOS-Chem adjoint (version 34) (Henze et al., 2007). We used the Kinetic PreProcessor (KPP) (Daescu et al., 2003; Sandu et al., 2003) to construct the adjoint of the updated photochemical mechanism. Adjoint algorithms were updated to include the emission and deposition processes of formaldehyde and glyoxal precursors. The aqueous uptake rate of glyoxal by wet aerosols was a function of the ambient glyoxal concentration and the total wet aerosol surface area (Fu et al., 2008). We linearized this uptake process in the backward integrations by using the archived wet aerosol surface areas from the forward simulations.

We verified the adjoint model mathematically in two ways. Firstly, we used the adjoint model to calculate the sensitivities of global glyoxal and formaldehyde burdens to biogenic isoprene and anthropogenic xylene emissions, respectively, and found that the results reproduced the calculated sensitivities from the forward model (Fig. S1 in the Supplement). Secondly, we used a set of bottom-up NMVOC emission inventories (Sect. 2.2) to drive the forward model and took the resulting global tropospheric formaldehyde and glyoxal column concentrations as pseudo observations. We then used the pseudo observations of formaldehyde and glyoxal to successfully optimize back to the bottom-up NMVOC emission estimates over high-emission areas from an initial guess that was 5 times larger (Fig. S2). These experiments demonstrated the usefulness of the adjoint model for the inversion of NMVOC emissions.

2.2 A priori emission estimates of Chinese NMVOCs

As a starting point for our inversion, we compiled the a priori Chinese NMVOC emission estimates from recent bottom-up emission inventories. Table 1 summarizes the annual total of these a priori emission estimates and their associated uncertainties.

Table 1Inversion experiments to constrain Chinese NMVOC emissions.

^a From Li et al. (2017). ^b From Guenther et al. (2006). ^c Compiled from the emissions estimated by van der Werf et al. (2010) plus a scaling of the emissions estimated by Huang et al. (2012). See text (Sect. 2.2) for details.

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The a priori biogenic NMVOC emissions from China and from the rest of the world were calculated with the MEGAN v2.0 algorithm (Guenther et al., 2006) and dependent on temperature, shortwave radiation, and monthly mean leaf area index. Previous top-down studies suggested that MEGAN overestimates global biogenic methanol by a factor of 2 to 3 (Stavrakou et al., 2011; Wells et al., 2012). We scaled our global biogenic methanol emissions to the value (100 Tg yr⁻¹) reported by Stavrakou et al. (2011) to be the a priori in this study. The contributions of Chinese biogenic ethanol to formaldehyde are expected to be low due to its small emissions (Guenther et al., 2012); thus the Chinese biogenic ethanol emissions were neglected in this study. The resulting annual total biogenic NMVOC emissions over China for the year 2007 were 17.3 Tg yr⁻¹, including 7.5 Tg yr⁻¹ of isoprene, 4.6 Tg yr⁻¹ of methanol, and 5.2 Tg yr⁻¹ of other species (including monoterpenes, ethene, acetone, ≥C₃ alkenes, and MBO). Previous estimates of Chinese biogenic isoprene emissions ranged from 5.8 to 9.9 Tg yr⁻¹ (Guenther et al., 2006; Sindelarova et al., 2014; Stavrakou et al., 2014, 2015, 2017). Based on this range, we estimated the uncertainty of the a priori biogenic emissions over China to be ±55 %.

The a priori emissions for Chinese anthropogenic NMVOCs were from the Multi-resolution Emission Inventory for China inventory (MEIC, http://meicmodel.org, last access: December, 2014) (Li et al., 2014, 2017), which was developed at $\mathrm{0.25}{}^{\circ }\times \mathrm{0.25}{}^{\circ }$ resolution for the year 2010. The MEIC inventory, including emissions from industry, transportation, power generation, and residential activities, was compiled using monthly Chinese provincial activity data and a combination of Chinese and western emission factors. The estimated Chinese annual anthropogenic emission of NMVOCs was 18.8 Tg yr⁻¹, including 63 % from industries, 26 % from residential activities, 10 % from transportation, and 1 % from power generation. The estimated annual Chinese anthropogenic emission of aromatics was 5.4 Tg yr⁻¹, including 73 % from industries, 15 % from residential activities, 9 % from transportation, and 3 % from power generation. Previous estimates of Chinese anthropogenic NMVOC emissions for the years 2005 to 2012 ranged from 12.7 to 35.5 Tg yr⁻¹, with aromatics emissions ranging from 2.4 to 13.4 Tg yr⁻¹ (Bo et al., 2008; Q. Zhang et al., 2009; Cao et al., 2011; Liu et al., 2012; Kurokawa et al., 2013; Li et al., 2014, 2017; Stavrakou et al., 2015; Wu et al., 2016; Huang et al., 2017; Granier et al., 2017). We therefore estimated the uncertainty for the a priori Chinese anthropogenic NMVOC emission estimates to be a factor of 2. As such, we did not scale the MEIC Chinese NMVOC emissions to the year 2007 because the uncertainty in the emission estimates was much larger than the differences in emissions between the years 2007 and 2010 (Chinese anthropogenic NMVOC emissions increased 14 % from 2006 to 2010 according to Li et al., 2017). The spatial distribution of Chinese anthropogenic NO_x emissions was from the MEIC inventory for the year 2010 (Li et al., 2017) but scaled to the year 2007 levels using top-down constraints from the GOME-2A NO₂ observations (Mijling et al., 2013). Anthropogenic NMVOC emissions for the rest of Asia were from Li et al. (2017) for the year 2010. Anthropogenic emissions for Europe, the US, and the rest of the world were from the European Monitoring and Evaluation Programme inventory (Vestreng, 2003), the U.S. EPA 2005 National Emission Inventory (https://www.epa.gov/air-emissions-inventories/national-emissions-inventory-nei, last access: December, 2012), and the EDGAR inventory (version 2.0) (Olivier et al., 1999), respectively, and scaled to the year 2007 using CO₂ emissions (van Donkelaar et al., 2008).

Post-harvest, in-field burning of crop residue has been recognized as a large seasonal source of NMVOCs in China (Fu et al., 2007; Huang et al., 2012; Liu et al., 2015; Stavrakou et al., 2016). These emissions from crop residue fires have been severely underestimated in inventories based on burned area observations from satellites, such as the Global Fire Emissions Database version 3 (GFED3; van der Werf et al., 2010). The recent Global Fire Emissions Database version 4 (GFED4s; van der Werf et al., 2017) included small fires by scaling burned area with satellite fire pixel observations, but the resulting Chinese NMVOC emission estimate from biomass burning (0.91 Tg yr⁻¹) was still much lower than the bottom-up inventory by Huang et al. (2012). Huang et al. (2012) estimated the Chinese CO emission from crop residue burning to be 4.0 Tg yr⁻¹, based on MODIS daily thermal anomalies, Chinese provincial burned biomass data, and emission factors from Akagi et al. (2011). We scaled this CO flux using speciated NMVOC emission factors from crop residue burning from the literature (Hays et al., 2002; Akagi et al., 2011) and then multiplied the resulting NMVOC flux estimate by 2. The reason for doubling the scaled NMVOC flux was that the emission factors for many NMVOC species were not measured, such that the sum of the speciated NMVOC emission factors was only half of the total NMVOC emission factor (Akagi et al., 2011). This difference may partially explain why the formaldehyde inversion study by Stavrakou et al. (2016) found that Huang et al. (2012) underestimated the NMVOC fluxes from crop fires over the NCP in June by at least a factor of 2.

Our resulting a priori estimate for annual Chinese NMVOC emissions from biomass burning was 2.27 Tg yr⁻¹, including 1.80 Tg yr⁻¹ from crop residue burning (obtained by scaling Huang et al., 2012, as described above) and 0.47 Tg yr⁻¹ from other types of biomass burning activities from GFED3 (van der Werf et al., 2010). Previous estimates of Chinese NMVOC emissions from biomass burning for the years 2000 to 2012 ranged widely from 0.47 to 5.1 Tg yr⁻¹ (Fu et al., 2007; van der Werf et al., 2010, 2017; Wiedinmyer et al., 2011; Huang et al., 2012; Liu et al., 2015; Stavrakou et al., 2015, 2016). We therefore estimated the uncertainty of the a priori Chinese biomass burning NMVOC flux to be a factor of 3. Biomass burning emissions from the rest of the world were from GFED3 (van der Werf et al., 2010).

Figure 1Spatial distributions of annual NMVOC emissions from China. (a–d) The a priori annual NMVOC emission estimates from (a) biomass burning, (b) anthropogenic, (c) biogenic, and (d) total sources. (e–h) The average of our four sets of top-down estimates of annual NMVOC emissions. Annual Chinese total emission estimates are shown in the inset in units of Tg yr⁻¹. The uncertainties of the a priori emission estimates and the range of top-down emission estimates are shown in parentheses. (i–l) Scale factors for our averaged top-down estimates relative to the a priori estimates.

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Figure 1a–d show the spatial distribution of the a priori Chinese NMVOC emissions from biomass burning, anthropogenic, biogenic, and total sources, respectively. Biomass burning emissions were highest over the NCP and southwest China, reflecting the strong emissions from crop residue burning over the NCP in June and over southwest China during February to April. Chinese anthropogenic and biogenic NMVOC sources were both stronger in the east than in the west, reflecting the colocation of dense population and vegetation in the east. The highest biogenic NMVOC emissions were over southern China due to the combined modulation by vegetation densities, temperature, and sunlight. Anthropogenic NMVOC fluxes exceeded 10³ kg km⁻² yr⁻¹ throughout industrialized and densely populated eastern China, with the highest fluxes over the NCP and around the Yangtze River Delta area.

Figure 2Estimates of monthly Chinese NMVOC emissions. For each month, the bars from left to right represent the a priori emission estimates and the a posteriori emission estimates from IE-1, IE-2, IE-3, and IE-4. Color keys for NMVOC species are shown in the inset, with the suffixes of “bb”, “an”, and “bg” indicating emissions from biomass burning, anthropogenic, and biogenic activities, respectively.

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Figure 2 shows the seasonal variation in the a priori Chinese NMVOC emissions. The a priori anthropogenic NMVOC fluxes were larger during the cold months and lower during the warm months, driven by the seasonal strengths of industrial and residential activities (Li et al., 2017). The a priori biogenic NMVOC fluxes showed the opposite seasonal pattern, with 65 % of the total annual flux emitted in summer (June to August). The a priori biomass burning NMVOC source was relatively small, except when it peaked due to post-harvest burning over the NCP in June and over southwest China in spring. As a result, the a priori Chinese NMVOC emissions were predominantly anthropogenic in winter but mainly biogenic in summer. During the transition seasons of spring and fall, the anthropogenic, biogenic, and biomass burning contributions were comparable.

2.3 Formaldehyde and glyoxal column concentrations observed by GOME-2A and OMI

We used the monthly mean tropospheric formaldehyde and glyoxal column concentrations retrieved from the GOME-2A instrument and the OMI for the year 2007 to constrain Chinese NMVOC sources. The four sets of satellite retrievals used in this study are briefly described below; further technical details are summarized in Table S2.

The native GOME-2A pixel vertical column densities (VCDs) of formaldehyde and glyoxal were retrieved by De Smedt et al. (2012) and Lerot et al. (2010), respectively. Pixel slant column densities (SCDs) of formaldehyde and glyoxal were retrieved in the 328.5–346 and 435–460 nm windows, respectively, using the DOAS technique (Platt et al., 1979). Previous glyoxal SCD retrievals often showed biases over remote tropical oceans due to absorption from liquid water (Wittrock et al., 2006; Vrekoussis et al., 2010). This bias was corrected in Lerot et al. (2010) by explicitly accounting for liquid water absorption during the DOAS fitting. Pixel SCDs were then converted into VCDs using air mass factors (AMFs), which were calculated using the linearized discrete ordinate radiative transfer (LIDORT) model (Spurr, 2008) and trace gas profiles simulated by the IMAGES v2 model (Stavrakou et al., 2009b). The native pixel VCDs were gridded to daily means at $\mathrm{0.25}{}^{\circ }\times \mathrm{0.25}{}^{\circ }$ resolution (De Smedt et al., 2012; Lerot et al., 2010). We further averaged the daily means to monthly means at 5^∘ longitude × 4^∘ latitude resolution. The retrieval errors of the spatially and temporally averaged VCDs were estimated to be 30 %–40 % for formaldehyde and 40 % for glyoxal due to a combination of errors associated with the SCD retrievals, the reference sector correction, the a priori profile, and the AMFs (De Smedt et al., 2012; Lerot et al., 2010).

The OMI native pixel VCDs of formaldehyde and glyoxal were retrieved by González Abad et al. (2015) and Chan Miller et al. (2014), respectively. Pixel SCDs were retrieved by directly fitting the absorption spectra in the 328.5–356.5 nm (formaldehyde) and 435–461 nm (glyoxal) windows (Chance, 1998; Chan Miller et al., 2014). Pixel SCDs were then converted to VCDs using AMF calculated with a linearized vector discrete ordinate radiative transfer model, VLIDORT (Spurr, 2006), and trace gas profiles simulated by the GEOS-Chem model (González Abad et al., 2015). Liquid water absorption was also explicitly calculated for the glyoxal retrieval (Chan Miller et al., 2014). The typical uncertainties of OMI-observed pixel VCDs over polluted areas were estimated to be 30 % to 45 % for formaldehyde and 100 % for glyoxal (González Abad et al., 2015; Chan Miller et al., 2014). The native pixel VCDs were averaged to monthly means at 5^∘ longitude × 4^∘ latitude resolution. For glyoxal, we further removed VCDs with signal-to-uncertainty ratios of less than 100 %. We assumed the retrieval uncertainty of monthly mean OMI formaldehyde and glyoxal VCDs at $\mathrm{4}{}^{\circ }\times \mathrm{5}{}^{\circ }$ resolution to be 40 % and 100 %, respectively.

To remove global systematic biases in the satellite observations, we aligned the observed monthly mean VCDs over remote reference areas to those simulated by the GEOS-Chem model (sampled at satellite overpass time) using the a priori NMVOC emissions. The remote Pacific (140–160^∘ W, 90^∘ S–90^∘ N) was chosen as the reference area for formaldehyde (Palmer et al., 2003, 2006; Fu et al., 2007; González Abad et al., 2015). The Sahara desert (20–30^∘ N, 10^∘ W–30^∘ E), where the interference from liquid water absorption was minimal, was chosen as the reference area for glyoxal (Chan Miller et al., 2014). The justification for performing the alignment was twofold. Firstly, the formaldehyde and glyoxal VCDs over these remote reference areas were small and well simulated by the model (Fu et al., 2007; Chan Miller et al., 2014). The removed biases over the remote areas were less than 20 % and 10 % of the typical formaldehyde ($>\mathrm{4}\times {\mathrm{10}}^{\mathrm{15}}$ molecule cm⁻²) and glyoxal ($>\mathrm{2}\times {\mathrm{10}}^{\mathrm{14}}$ molecule cm⁻²) monthly mean VCDs observed over eastern China, respectively. More importantly, our inversion was performed over China only, assuming that the a priori NMVOC emissions for the rest of the world were unbiased. As will be seen in Sects. 3 and 4, the optimization of NMVOC sources was predominantly driven by local formaldehyde and glyoxal enhancements produced by relatively short-lived NMVOCs.

2.4 Inversion experiments using the GEOS-Chem adjoint

We used the GEOS-Chem model to perform Bayesian inversions on Chinese NMVOC emissions, using satellite observations of formaldehyde and glyoxal over China and the a priori emission estimates as constraints. The inversion minimized a cost function, J(x), over China (Rodgers, 2000).

The first and second terms on the right-hand side of Eq. (1) represented the penalty error and the prediction error, respectively. x, which we sought to optimize, was the vector of scale factors (for each NMVOC species from each emission sector and for each grid) applied to the a priori emissions. x_a was a unit vector applied to the a priori NMVOC emission estimates. y was the vector of satellite-observed monthly mean VCDs of the targeted tracer (formaldehyde and/or glyoxal). F(x) was the vector of VCDs of the targeted tracer simulated by the forward model F. S_o was the a priori emission error covariance matrix, which we assumed to be diagonal. The observation error covariance matrix in Eq. (1), S_o, was difficult to quantify, as it included contributions not only from the satellite retrieval but also from the model representation of chemistry and transport. Zhu et al. (2016) and Chan Miller et al. (2017) compared vertical profiles of GEOS-Chem-simulated formaldehyde and glyoxal over the southeast US in summer against aircraft measurements. They reported that the simulated formaldehyde mixing ratios showed only a small bias (−3 % ±2 %) in the lower troposphere but were lower than the observations by 41 % in the free troposphere, likely due to insufficient deep convection in the model (Zhu et al., 2016). The simulated glyoxal mixing ratios were within 20 % of the observations in the mixed layer, but they were too low in the upper troposphere by more than a factor of 2, also likely due to insufficient model vertical transport (Chan Miller et al., 2017). It should be noted that these errors assessed by Zhu et al. (2016) and Chan Miller et al. (2017) likely also included the errors associated with precursor emissions. Nevertheless, based on these assessments, we estimated the model errors for formaldehyde and glyoxal VCDs to be ±80 % and ±100 %, respectively. Adding these estimated model errors in quadrature to the satellite retrieval errors (Sect. 2.3), we estimated the observation error (S_o) of formaldehyde and glyoxal to be about ±90 % and ±150 %, respectively.

The optimization of Eq. (1) was dependent on the relative weighting of the penalty error (S_o) and the prediction error (S_o), which were often incompletely represented. In addition, we found that due to the mathematical formulation of Eq. (1), the cost function J(x) was heavily weighted by grids in which the a priori estimates were too high, such that the optimization was less effective at increasing emissions where the a priori emissions were too low. These issues were empirically addressed in inversion studies by the introduction of a regularization factor, γ, to adjust the relative weight of the penalty error. Henze et al. (2009) used the L curve method (Hansen, 1998) to find an optimal γ value, which minimized the total cost function while balancing the prediction term and the penalty term. We followed that methodology and found a γ value of 0.01 for July, which we applied to all warmer months (March to October). An optimized γ value of 0.1 was found for January and applied to colder months.

Table 1 lists our inversion experiments. Figure S3 illustrates our protocol for the inversion experiments. We experimented with four different sets of satellite retrievals as constraints, with the goal of bracketing the possible range of top-down estimates for Chinese NMVOC emissions. The first two experiments (IE-1 and IE-2) constrained emissions using the formaldehyde and glyoxal VCDs observations from GOME-2A and OMI, respectively. Several studies showed that GOME-2A formaldehyde VCDs may be low by a factor of 1.3 to 1.7 (Lee et al., 2015; Zhu et al., 2016; Wang et al., 2017). As an upper bound constraint, we conducted a third inversion experiment (IE-3) constrained by 1.7 times the GOME-2A formaldehyde VCDs. We conducted a fourth inversion experiment (IE-4) constrained by OMI glyoxal VCDs alone to explore the impacts of glyoxal observations on the inversions.

4.1 A posteriori formaldehyde and glyoxal VCDs from inversion experiments

The qualitative analyses in Sect. 3 showed that the GOME-2A and OMI retrievals of formaldehyde and glyoxal VCDs provided disparate, and apparently contradictory, information on seasonal Chinese NMVOC emissions. Therefore, our four inversion experiments using different satellite observations as constraints represented the range of probable top-down estimates given current satellite observations. Here we first examined how the inversion experiments optimized the a posteriori formaldehyde and glyoxal VCDs and the resulting effects on the top-down monthly Chinese NMVOC emission estimates. Figure S7 shows the changes in the normalized cost functions over China in the four inversion experiments. Relative to their respective initial cost function values, the optimized cost function values were reduced by 8 % to 75 % for all four experiments. The unusually modest 8 % reduction occurred in the optimization in IE-3 for April. In that case, the initial cost function value was small; i.e., the a priori formaldehyde VCDs were already in good agreement with 1.7 times the GOME-2A formaldehyde VCDs (Fig. 3 and Table S5). Figure 2 shows the top-down monthly Chinese NMVOC emission estimates from the four inversion experiments and compares them against the a priori emission estimates. Figure S6 compares the a priori and a posteriori emission estimates for anthropogenic glyoxal precursors.

Figures 3 to 6 show the a posteriori simulated monthly mean formaldehyde and glyoxal VCDs from the GOME-2A formaldehyde and glyoxal inversion experiment (IE-1). Overall, IE-1 greatly improved the agreement between the a posteriori VCDs and the GOME-2A observations for both formaldehyde (Table S4) and glyoxal (Table S6) over eastern China for most months. The optimization was especially effective in optimizing the spatial pattern of the a posteriori formaldehyde VCDs, such that the a posteriori R against the GOME-2A formaldehyde VCDs exceeded 0.85 over eastern China for all 12 months (Table S4). Relative to the a priori VCDs, the a posteriori VCDs of formaldehyde and glyoxal both decreased over the NCP in winter and increased over eastern China between May and September. During the transition months of April and October, the a posteriori formaldehyde VCDs decreased relative to the a priori, while the a posteriori glyoxal VCDs increased relative to the a priori. Figures 2 and S6 illustrated how these changes in a posteriori formaldehyde and glyoxal VCDs affected the top-down monthly NMVOC emission estimates. For IE-1, the estimated emissions of all NMVOC species were reduced in winter but enhanced between May and September. In April and October, however, IE-1 decreased the total NMVOC emissions while preferentially increasing the emissions of anthropogenic glyoxal precursors.

Figures 7 to 10 show the a posteriori monthly mean formaldehyde and glyoxal VCDs from the OMI formaldehyde and glyoxal inversion experiment (IE-2). IE-2 was effective in reducing the a posteriori formaldehyde VCDs over eastern China year-round to better agree with the OMI formaldehyde observations (Table S7). However, IE-2 increased the a posteriori glyoxal VCDs only slightly and was less effective in bringing agreement with the OMI glyoxal observations (Table S8). Figure 2 shows that the a posteriori NMVOC emission estimates from IE-2 were lower than the a priori estimates for all months. This was due to a combination of factors at work in the inversion. The low formaldehyde observations from OMI in all months drove a large reduction in the emissions of NMVOCs that produced only formaldehyde (≥C₄ alkanes and ≥C₃ alkenes from anthropogenic activities, as well as primary formaldehyde from biomass burning). At the same time, the relatively high glyoxal observations from OMI drove an increase in the emissions of NMVOCs that produced mainly glyoxal (ethene, ethyne, and aromatics from anthropogenic activities, as well as primary glyoxal from biomass burning). For precursors that produced large amounts of both formaldehyde and glyoxal (most importantly biogenic isoprene), the inversion reduced the top-down emissions as the formaldehyde observations had more weight in the cost function than the glyoxal observations due to the lower observational errors in the formaldehyde VCDs. These findings showed the importance of well-characterized retrievals with reliable error estimates in inversion studies.

Figures 3 and 4 showed the a posteriori formaldehyde VCDs from the inversion experiment IE-3, which was constrained by the GOME-2A-observed formaldehyde VCDs scaled by a factor of 1.7. The a posteriori formaldehyde VCDs in IE-3 increased further over eastern China during the warmer months relative to IE-1, especially over the NCP and central China in summer. In December and January, the scaled-up GOME-2A observations over eastern China were still lower than the simulated formaldehyde VCDs using the a priori emissions, leading to a reduction in the a posteriori formaldehyde VCDs over eastern China (Table S5). Figure 2 shows that the top-down monthly emission estimates for all NMVOC species were lower than the a priori in November, December, January, and February and higher than the a priori for the warmer months. Consequently, although no observations of glyoxal were used as constraints in IE-3, the a posteriori glyoxal VCDs also decreased in winter and increased in summer, which was in better agreement with the GOME-2A observations (Figs. 5 and 6). This is consistent with our analyses in Sect. 3: the constraints exerted by the GOME-2A formaldehyde and glyoxal observations were consistent in winter and in summer, when the NMVOC emissions were dominated by anthropogenic and biogenic sources, respectively. However, IE-3 had almost no effects on the a posteriori glyoxal VCDs and the top-down emission estimates of anthropogenic glyoxal precursors in April and October. This demonstrated the necessity of glyoxal observations in constraining the emissions of NMVOC species that preferentially produced glyoxal, including most importantly the aromatics.

The impacts of satellite glyoxal observations on constraining Chinese glyoxal precursor emission estimates were further demonstrated in IE-4. Figures 9 and 10 show that the a posteriori glyoxal VCDs from IE-4 were in better agreement with the OMI glyoxal observations for all months (Table S8). Figures 2 and S6 show that this increase in the a posteriori glyoxal VCDs in IE-4 was achieved by substantially increasing the emission estimates of anthropogenic glyoxal precursors for all months. In summer, the emissions of biogenic isoprene (precursor to both glyoxal and formaldehyde) also increased. As a result, the a posteriori formaldehyde VCDs in IE-4 increased in summer but remained similar to the a priori simulation for the other months (Figs. 7 and 8, Table S7).

Figure S4 also compared the model a posteriori formaldehyde VCDs in 2007 against the GOME-2 observations, the model a priori formaldehyde VCDs, and the MAX-DOAS measurements (during 2010–2016) at Xianghe at GOME-2 crossing time. Compared to the a priori, our a posteriori formaldehyde VCDs were in better agreement with the seasonal variation in the MAX-DOAS measurements (R values increased from 0.81 for the a priori to 0.95 for IE-1 and 0.93 for IE-3). During the warm months (May to September), the monthly a posteriori formaldehyde VCDs from IE-1 and IE-3 bracketed the interannual variation in monthly formaldehyde VCDs measured by MAX-DOAS. For the rest of the year, both the GOME-2A observations and the a posteriori formaldehyde VCDs were systematically biased low relative to the MAX-DOAS measurements. As discussed before, these biases could not be fully accounted for by the interannual variability in the local formaldehyde VCDs and were thus likely due to sampling or retrieval difference between the MAX-DOAS and the satellite.

Figure 11Comparison of estimates of annual Chinese NMVOC emissions from (a) anthropogenic, (b) biogenic, (c) biomass burning, and (d) total sources. For each panel, the bars from left to right are the a priori estimates and the a posteriori estimates from IE-1, IE-2, IE-3, and IE-4. Annual total NMVOC emissions are shown in black numbers on top of each bar. The red dashed boxes and red numbers in (a) indicate annual emissions of anthropogenic glyoxal precursors. The green dashed boxes and green numbers in (a) indicate annual emissions of anthropogenic aromatics. The grey dashed boxes and grey numbers in (b) indicate annual biogenic isoprene emissions. The orange dashed boxes and orange numbers in (b) indicate annual biogenic methanol emissions. Color keys to NMVOC species are shown at the bottom, with suffixes of “an”, “bg”, and “bb” indicating anthropogenic source, biogenic source, and biomass burning source, respectively.

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4.2 Top-down estimates of Chinese NMVOC emissions from inversion experiments

Table 1 and Fig. 11 show the top-down estimates for Chinese annual NMVOC emissions from the four inversion experiments and compare them against the a priori. Our annual total top-down estimates for Chinese NMVOCs ranged from 30.7 to 49.5 Tg yr⁻¹, compared to the 38.3 Tg yr⁻¹ of the a priori. The highest top-down estimate was from IE-3, constrained by 1.7 times the GOME-2A formaldehyde VCD observations. The lowest top-down estimate was from IE-2, mainly driven by the relatively low formaldehyde observations from OMI.

Anthropogenic sources constituted 44 %–53 % of the total top-down NMVOC emissions. The lowest total top-down anthropogenic emission estimate was from IE-2 (16.4 Tg yr⁻¹). All four inversion experiments consistently showed larger annual emissions of anthropogenic glyoxal precursors than the a priori (Fig. 11). In particular, our top-down estimates for anthropogenic aromatics ranged from 5.5 to 7.9 Tg yr⁻¹, consistently larger than the a priori of 5.4 Tg yr⁻¹ (Li et al., 2017). The highest top-down anthropogenic glyoxal precursors (including aromatics, ethyne, ethane, and glyoxal) emission estimate was from IE-4 (12.3 Tg yr⁻¹), which reflected the strong impacts of the OMI glyoxal observations on constraining anthropogenic NMVOC emissions.

The top-down estimates for biogenic NMVOC emissions from IE-1, IE-3, and IE-4 ranged between 20.0 and 22.8 Tg yr⁻¹ (top-down biogenic isoprene emission estimates between 9.8 and 11.7 Tg yr⁻¹), which were significantly larger than the a priori. As a result, the contrast between the NMVOC emissions in summer and those in winter was greatly enhanced in the top-down estimates in these three inversion experiments, relative to the a priori (Fig. 2). The exception was IE-2, which estimated the biogenic NMVOC emissions to be 12.2 Tg yr⁻¹ (including 5.4 Tg yr⁻¹ of isoprene). The top-down estimate for biomass burning NMVOC emissions from the four inversion experiments was between 2.08 and 3.13 Tg yr⁻¹, with the largest top-down estimate driven by the scaled-up GOME-2A formaldehyde VCDs (IE-3).

Figure 12Spatial distributions of the optimized scale factors for annual Chinese NMVOC emissions, relative to the a priori emission estimates, for the four inversion experiments.

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Figure 12 shows the spatial distribution of the scale factors for the Chinese annual NMVOC emissions from each of the four inversion experiments relative to the a priori emission estimates. The use of GOME-2A formaldehyde and glyoxal observations as constraints in IE-1 led to a domain-wide increase in biogenic NMVOC emissions, except in the northeast. IE-1 also found an increase in biomass burning emissions over the NCP in June. In contrast, anthropogenic NMVOC emissions were slightly reduced over northeast, north, and southwest China. In IE-3, the annual NMVOC emissions over eastern China increased for all three sources, due to constraints exerted by the scaled-up GOME-2A formaldehyde VCDs. The optimized emission scale factors from IE-2 and IE-4 were of opposite signs. Using only OMI glyoxal observations as constraints in IE-4 led to a domain-wide increase in NMVOC emissions from all sectors. However, when constraints of the relatively low OMI formaldehyde observations were added in IE-2, the top-down NMVOC emission estimates decreased across the domain.

As discussed previously, our four inversion experiments using different satellite retrievals as constraints represented the range of probable top-down estimates given by currently available satellite observations. To represent the difference between these top-down estimates relative to the a priori, we averaged the top-down estimates from the four inversion experiments. Our averaged top-down estimate for Chinese total annual NMVOC emissions was 41.9 Tg yr⁻¹, including 20.2 Tg yr⁻¹, 19.2 Tg yr⁻¹, and 2.48 Tg yr⁻¹ from anthropogenic, biogenic, and biomass burning sources, respectively. Our average emission estimate for anthropogenic aromatic emissions was 6.5 Tg yr⁻¹, which was 20 % larger than the a priori estimate of Li et al. (2017).

Figure 1 shows the spatial distributions of our averaged top-down Chinese NMVOC emissions and the scale factors relative to the a priori estimate. Our averaged top-down estimates for Chinese NMVOC emissions were spatially consistent with the a priori estimate, but the total fluxes were larger than the a priori estimate throughout eastern China by 10 % to 30 %. In particular, we found a 40 % increase in the biomass burning emissions over the NCP. We also found a 10 %–30 % increase in the anthropogenic NMVOC emissions in coastal eastern China. Large increases in the biogenic emissions were found near the northwestern border of China and along the northeast-to-southwest division line of vegetation density. This potentially indicated an underestimation of biogenic NMVOC emissions from semiarid ecosystems in the MEGAN inventory.

Table 2Comparison of annual Chinese NMVOC emission estimates for the years 2000 to 2014.

^a These emission estimates included some NMVOC species that were not precursors to formaldehyde or glyoxal and therefore not included in this work. See color keys in Fig. 2 for NMVOC species whose emissions were included in this work. ^b Used SCIAMACHY-observed glyoxal VCDs as constraints. ^c Used GOME-2A-observed and OMI-observed formaldehyde VCDs as constraints. ^d Consisted of emissions from open burning of crop residues and from biofuel burning. ^e Calculated by the GEOS-Chem model using GEOS-5 meteorological data. ^f Average of top-down estimates from four inversion experiments. ^g Only anthropogenic emissions of reactive alkenes, formaldehyde, and xylenes from northeastern, northern, central, and southern China were included.

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