CAMx version 5.3 (ENVIRON, 2010) with the Carbon Bond version 2005 (CB05) chemical mechanism was used to simulate a SIP modeling episode developed by TCEQ for the HGB O3 attainment demonstration (Fig. 1) from 13 August to 15 September 2006, coinciding with the intensive measurement campaign TexAQS 2006. The meteorology fields were modeled by the NCAR/Penn State (National Center for Atmospheric Research/Pennsylvania State University) Mesoscale Model, Version 5, release 3.7.3 (MM5v.3.7.3) (Grell et al., 1994), and the boundary conditions were taken from the Model for Ozone and Related Chemical Tracers (MOZART) global model (ENVIRON, 2008). The base case emission inventory for HGB SIP modeling was provided by TCEQ (TCEQ, 2010). Lightning and aviation NOx emissions were added into the base emission inventory. The lightning NOx emission is developed based on the measured National Lightning Detection Network (NLDN) data with intra-cloud flashes assumed to be 3 times the cloud-to-ground flashes and 500 mol NO emissions per flash (Kaynak et al., 2008); and the aviation NOx emissions, obtained from the Emission Database for Global Atmospheric Research (EDGAR), were placed at the model height of 9 km. The soil NOx emission was doubled from its base value because the Yienger and Levy method (YL95) (Yienger and Levy, 1995) has been found to underpredict soil NOx by around a factor of 2 over the United States (Hudman et al., 2010). More details about the model inputs and configurations, the emission inventory development, and evaluations of model meteorological inputs can be found in Tang et al. (2013).

The photolysis rate calculations in CAMx include two steps (ENVIRON, 2010). First, a Tropospheric Ultraviolet and Visible (TUV) Radiation Model developed by NCAR is used to generate a multi-dimensional table of clear-sky photolysis rates (Madronich, 1987; NCAR, 2011) as inputs for the CAMx model as shown in Eq. (1).

Clear-sky photolysis rates (s-1) are calculated as J=∫λ1λ2σ(λ)φ(λ)F(λ)dλ, where σ(λ) (m2 molecule-1) is the absorption cross section, λ is the wavelength (μm), ϕ(λ) is the quantum yield (moleculesphoton-1), and F(λ) is the actinic flux (photonsm-2s-1µm-1).

Second, the tabular clear-sky photolysis rates are interpolated into each grid cell in the modeling domain and adjusted based on cloud information generated by the meteorology model in standard operational procedure, as shown in Eqs. (2) and (3). Below the cloud, photolysis rates are adjusted as (Chang et al., 1987) Jbelow=Jclear[1+fc(1.6trccos⁡(θ)-1)]. Above the cloud, photolysis rates are modified as Jabove=Jclear[1+fccos⁡(θ)(1-trc)], where fc is the cloud fraction for a grid cell, trc is cloud transmissivity at each model grid layer, and θ is the solar zenith angle.

In CAMx, trc is calculated using Eq. (4) (Stephens, 1978), trc=5-e-τc4+3τc(1-β), where τc is the cloud optical depth simulated in the model and β is the scattering phase-function asymmetry factor assumed to be 0.86 (Chang et al., 1987). The fc in each grid cell is predicted by the MM5 model.

GOES-observed cloud properties recover fc and broadband trc, which can be used directly in Eqs. (2) and (3) to adjust photolysis rates below and above the clouds, bypassing the need for estimating those values in the model. Within the cloud, the photolysis rates are adjusted via the interpolation of calculated values between satellite-retrieved cloud top and model-estimated cloud base. GOES is capable of measuring cloud properties with spatial resolution down to 1 km and temporal resolution down to an hour or less (Haines et al., 2004), ensuring the sufficient spatial and temporal data coverage for the modeling episode. In this study, hourly GOES observations with integrated 12 km cloud properties from sub-pixels have been used. However, due to the satellite data availability, satellite-retrieved fc and broadband trcmay not be available in the early morning and late afternoon. In such cases, the fc and trc generated by standard operational procedures in CAMx will be used. More details regarding satellite retrievals of fc and trc can be found in Pour-Biazar et al. (2007).

As in Tang et al. (2013), an inversion region inside the 12 km model domain is designed for both region-based and sector-based DKF inversions, including five urban areas – HGB, DFW, BPA, NE Texas, and Austin and San Antonio – surrounded by a north rural area (N rural) and a south rural area (S rural) (Fig. 1).

Six separate NOx emission sectors – area, nonroad mobile, on-road mobile, biogenic, electric generating units (EGU) and non-EGU point sources – are provided by TCEQ. Lightning and aviation NOx emission sectors were developed in Tang et al. (2013) and added into base emission inventory as independent, elevated sources (Table 1). Area sources, including small-scale industry and residential sources such as oil and gas production, gas stations, and restaurants contribute 10 % of total emissions in the entire inversion region and 25 % in NE Texas in the base inventory. Nonroad sources – including construction equipment, locomotives, and commercial marine – contribute 14 % overall. Mobile source emissions by on-road vehicles contribute 27 % of total NOx emissions and dominate in the cities such as HGB and DFW. The biogenic NOx source is from soil emissions, which contribute 16 % of total NOx emissions but dominate in remote regions. Lightning and aviation sources contribute 8 and 6 % to the total emission, respectively. Non-EGU point sources such as refineries, big boilers, and flares contribute 40 % of NOx emissions in BPA and 21 % in HGB, the two regions with most of the petrochemical industries. EGU point emissions are from major power plants with the hourly NOx emissions measured by continuous emissions monitoring (CEM) systems, which are considered the most accurate NOx emission source in the bottom-up emission inventory. Thus, in this study, EGU NOx emissions are assumed to be correct and are not adjusted by DKF inversions.

NO2 sensitivities to NOx emission in each emission sector used in the following sector-based DKF inversions are calculated through the decoupled direct method (DDM, Fig. 5). The biogenic, lightning, and non-EGU point sources have their own spatial patterns that differ from the other emission sectors. For example, the aviation source shows strong sensitivity centered from the DFW and HGB regions and slowly spreading elsewhere. The sensitivities from the area, nonroad, and on-road sources have similar spatial patterns concentrated in urban areas due to strong anthropogenic activities, while the on-road source can be distinguished by the strong highway emissions. Previous studies (Rodgers, 2000; Curci et al., 2010) indicated that the inversion results would be ill-conditioned to estimate strongly overlapped sources. Therefore, in this study, the area and nonroad sources are grouped as a single sector in the DKF inversions.

Two DKF inversion approaches, region-based and sector-based, are applied in this study to create top-down NOx emissions for Texas. The procedure of incorporating the DKF method into the CAMx-DDM model was described in detail in Tang et al. (2013).

The DKF inversion process (Prinn, 2000), driven by the difference between the measured NO2 (CNO2observed) and the modeled NO2 (CNO2predicted), seeks the optimal emission perturbation factors (x^) (a posteriori) by adjusting NOx emissions in each designated emission region or sector iteratively until each a priori emission perturbation factor (x-) converges within a prescribed criterion, 0.01. x^NOx=xNOx-+PNOx-ST(SPNOx-ST+ROMI)-1(CNO2observed-CNO2predicted-SxNOx-) S in Eq. (2), calculated via DDM in this study, is the first-order semi-normalized sensitivity matrix of NO2 concentrations to either region-based or sector-based NOx emissions. The uncertainty value in the measurement error covariance matrix (R) for the OMI-observed NO2 is set to 30 % (Bucsela et al., 2013) for all diagonal elements. The uncertainties adopted from Hanna et al. (2001) provide the values for each of the diagonal elements in the emission error covariance matrix (P). A value of 100 % is assigned to each emission region, as well as to the area, nonroad, aviation, on-road, and biogenic emission sectors, but a value of 50 % is assigned to the non-EGU point emission sector. The uncertainty of lightning NOx emissions was estimated in recent studies, ranging from 30 % (Martin et al., 2007) to 60 % (Schumann and Huntrieser, 2007) on a global scale; thus, the uncertainty value in the lightning sector is set to 50 % here. The off-diagonal elements in P are set to zero since each emission component is assumed to be independent.

The GOES-retrieved cloud fractions and broadband transmissivity as described in Sect. 2.2 are used to adjust the photolysis rates in CAMx. To investigate the impact from GOES-derived photolysis rates, the differences of modeled ground-level NO2 photolysis rate (JNO2), NO2, and O3 between CAMx modeling with and without the GOES-retrieved cloud fractions and transmissivity are calculated.

Using GOES-observed clouds corrects the cloud underprediction issue in the current meteorological models (Pour-Biazar et al., 2007; Guenther et al., 2012; ENVIRON, 2012), making JNO2 decreases over most of the domain in this study. While on average there is a domain-wide reduction in JNO2, the impact on O3 production is not uniform (Figs. 2 and 3), mostly paired with the NOx emission distributions. The general impact of using GOES observations is that, where the JNO2 decreases, modeled NO2 increases, and O3 decreases (Figs. 2 and 3), indicating that slower photochemical activity inhibits O3 formation and thus consumes less NO2, and vice versa. However, an exception occurs at places close to the Houston Ship Channel, showing that, although the JNO2 decreases, modeled NO2 still decreases (Fig. 3b) and O3 slightly increases (Fig. 3c). This is probably caused by the availability of other pathways for consuming NOx in the VOC-rich environment, and the inhibition of NO regeneration due to reduction in photochemical activity. The largest discrepancy of 80 ppb in modeled O3 occurs at 13:00 on 2 September 2006 over the DFW region during the modeling period. At that time, GOES-based modeling showed up to 6 times higher JNO2 (reaching approximately 36 s-1), and 10 ppb lower NO2 in this region (Fig. 2). However, the differences in modeled JNO2, NO2, and O3 are much more moderate on a monthly 8 h (10:00–18:00) averaged basis, reaching only up to 3 s-1 for JNO2, 0.6 ppb for NO2, and 3 ppb for O3, with largest discrepancies in the HGB region (Fig. 3). For the changes in O3 sensitivities, approximately 6 % less JNO2 on a domain-wide makes modeled O3 overall less sensitive to NOx emissions (Fig. 3d) and more sensitive to VOC emissions (Fig. 3e).

The modeled daily 8 h (10:00–18:00 LT) NO2 and O3 using either satellite-derived or base model photolysis rates are evaluated by AQS-measured data for the entire modeling period. The positive changes in spatiotemporal correlation (R2) and negative changes in normalized mean bias (NMB) and normalized mean error (NME) indicate that satellite-derived photolysis rates improved model performance (Fig. 4). For O3 simulations (Fig. 4 right), the difference in R2 increases 1 % on average and reaches up to 7 % on 26 August, while the differences in NMBs and NMEs decrease 1 % on average and reach up to 10 % on 11 September, suggesting the satellite-corrected photolysis rates improve the model performance in simulating ground O3. However, NMB and NME for NO2 simulations (Fig. 4 left) do not improve despite an increase in R2, probably because other uncertainties in the model and measurements may have a larger impact on NO2 performance.

A controlled pseudodata test was performed in Tang et al. (2013) to test the applicability of the DKF inversion to adjust the NOx emission in each inversion region with the CAMx-DDM model. This showed that the DKF method adjusted the perturbed NOx emission in each region accurately back to its base case. In this study, a similar controlled pseudodata test is conducted to test the applicability of the sector-based DKF inversion with CAMx-DDM.

The pseudodata test for the sector-based DKF inversion is conducted on 10 modeling days (13 August to 22 August), but the modeling results from the first 3 days are discarded to eliminate the model initialization error. A 7-day (16 August to 22 August) averaged modeled NO2 VCD at 13:00–14:00 LT with the base case NOx emission inventory is treated as a pseudo-observation, and the one using perturbed NOx emissions in six emission sectors with known perturbation factors ranging from 0.5 to 2.0 (Fig. 6) is used as an a priori case. As described in Sect. 2.3, the area and nonroad emission sources are considered as one sector (ARNR), and EGU point source is excluded from the inversion. The emission uncertainties are set to 50 % for the non-EGU and lightning sectors and to 100 % for the others. The measurement error for the pseudo-observation is set to 30 %.

The pseudodata test results (Fig. 6 top) show that the a posteriori modeled NO2 closely matches the base case modeled value, indicating the DKF inversion is capable of correcting the perturbed NOx emissions in each emission sector. The sensitivity analysis results (Fig. 6 bottom) illustrate that the inversions are insensitive to both emission and observation error covariance matrices for the pseudocases.

The a priori NOx emission inventory used in this study is based on the TCEQ base case emission inventory with added lightning and aviation and doubled soil NOx emissions (Tang et al., 2013). The reaction rate constant of the reaction NO2+ OH in CB05 chemical mechanism is reduced by 25 % based on Mollner et al. (2010); this tends to increase NOx lifetime and transport to rural regions.

To evaluate the extent to which the addition of lightning and aviation NOx closes the gap between observed and modeled NO2 in the upper troposphere noticed by Napelenok et al. (2008), the modeled NO2 vertical profile is compared with INTEX-NA DC-8-measured NO2 profiles from the ground to the free troposphere. The comparison (Fig. 7 left) shows that CAMx with the a priori emission inventory strongly overestimates NO2 near the ground, reasonably agrees with DC-8 NO2 measurements from 1 to 5 km, slightly overestimates NO2 from 6 to 9 km, and slightly underestimates NO2 from 10 to 15 km. The modeled NO2 profile is further evaluated by the P-3-measured NO2 from ground to 5 km (Fig. 7 right), showing the same pattern of the overestimated surface NO2 and good agreement with aircraft observations from 1 to 5 km. The injection of the aviation NOx into a single model layer at altitude 6 to 9 km rather than more broadly distributed vertically probably causes the overestimation of modeled NO2 compared to DC-8 at that altitude (ENVIRON, 2013). A low bias of modeled NO2, approximately 40 ppt, exists in the upper troposphere, from 10 to 15 km altitude, which is the CAMx model top layer. Similar low bias of the modeled NO2 in the upper troposphere compared to the DC-8 measurement also has been found in Allen et al. (2012). Because the low bias in the upper troposphere may arise from model uncertainties other than those associated with emissions (Henderson et al., 2011, 2012), we follow the adjustment approach of Napelenok et al. (2008) and add 40 ppt NO2 homogeneously to the top layer (10–15 km) of the model results when computing the CAMx NO2 VCDs.

Although the revised CB05 chemical mechanism and artificially added upper-tropospheric NO2 increase modeled NO2 VCDs in the inversion region by an average of 13 % (Supplement, Sect. 2), CAMx-modeled NO2 VCDs remain an average of 2 × 1014 moleculescm-2 less than OMI observations in rural regions (Fig. 8c).

The DKF inversions with OMI NO2 are performed to constrain NOx emissions in each designated emission region and emission sector. To ensure sufficient spatial coverage, a monthly averaged OMI NO2 VCD (13 August to 15 September) is calculated and paired with the corresponding modeled NO2 VCD at satellite passing time (13:00–14:00 LT). The DKF inversions are then conducted with 2116 data points covering every grid cell in the inversion region, and the hourly a priori NOx emissions are adjusted iteratively until the inversion process converges.