The core meteorological and chemical forecast model is the regional online chemical transport model (CTM) WRF-Chem v3.4.1 (www2.acd.ucar.edu/wrf-chem). The model domain is a one-way nest with an outer domain of 12 km resolution covering western North America and an inner domain of 3 km resolution focused on the city of Denver, CO (Fig. 1). The 3 km resolution domain is 660 km by 840 km. The model has 30 vertical levels between the surface and an upper boundary of 100 mb and 10 levels within the boundary layer (∼ 1.5 km). Simulations of meteorology in the outer domain are initialized and constrained at the lateral boundary by North American Regional Reanalysis (NARR) data from National Centers for Environmental Prediction (NCEP). The NARR data have a native horizontal resolution of 32 km with 45 pressure levels and 3 h temporal resolution. We use the global chemical model output from MOZART to initialize the chemical simulation in the outer domain and to provide the chemical boundary condition. After a spin-up time of 4 days for the outer domain, the inner domain simulation is initialized and constrained through one-way nesting in both meteorology and chemistry.

Anthropogenic emissions for WRF-Chem are from the National Emissions Inventory (NEI) 2011 version 1 at native 4 × 4 km2 resolution. The NEI 2011 provides hourly-varying emissions for a typical weekday in summertime. The emissions do not vary from day to day. Biogenic emissions are calculated online with the simulation results by the Model of Emissions of Gases and Aerosols from Nature (MEGAN). Fire emissions are not included. We use the widely used regional acid deposition model version 2 (RADM2) as the gas-phase chemical mechanism (Stockwell et al., 1990). There are 59 species and 157 reactions to represent both inorganic and organic chemical reactions under tropospheric conditions. It includes the chemical losses of NOx through reaction with OH radical to form nitric acid, and other NOx sinks such as peroxyacyl nitrates and alkyl nitrate.

WRF-Chem/DART is a regional multivariate data assimilation system developed by the National Center for Atmospheric Research (NCAR) to analyze meteorological variables and chemical variables simultaneously (Mizzi et al., 2016). We use the ensemble adjustment Kalman filter (EAKF) in DART to analyze the states with an ensemble size of 30. Details of the EAKF algorithm and its implementation in DART are documented in Anderson, 2001; Anderson and Collins, 2007; and Anderson et al., 2009. In this study the system is extended to assimilate synthetic TEMPO NO2 column observations. As emissions are not prognostic variables of the forecast model, we implement a state augmentation approach to include emissions in the state variables (Aksoy et al., 2006). The chemical state variables include the NO2 concentration and NOx emissions. Based on the settings used in meteorology data assimilation, the meteorological state variables are U, V, W, T, QVAPOR, QCLOUD, QRAIN, QICE, and QSNOW. MU and PH are used in vertical coordinate transforms. T2, Q2, U10, V10, and PSFC are used for surface data assimilation forward operators. Definitions of these variables are taken from Romine et al. (2013) and are given in the Appendix. Adaptive spatially and temporally varying inflation is applied to the prior state to assist in maintaining the ensemble spread. We summarize the DART configuration details in Table 2.

We generate the initial chemical ensemble by adding the perturbations to the mean state of the fine domain forecast. In the ensemble method the generated ensemble should represent the error statistics of the initial guess of the model state (Evensen, 2003). The correlation between perturbations of chemical state variables is modeled by a simple isotropic exponential decay function with a characteristic correlation length of 50 km. For the meteorology ensemble, random perturbations were added to each member by sampling the NCEP background error covariance using the WRF Data Assimilation System (WRFDA; http://www2.mmm.ucar.edu/wrf/users/wrfda) (Barker et al., 2012). The options used for the WRFDA settings are summarized in Table 3. The parameter cv_option indicates the background error options in WRFDA. With a cv_option = 3, we use the NCEP background error covariance, which is estimated in grid space by what has become known as the National Meteorological Center (NMC) method. The statistics are estimated with the differences of 24 and 48 h global forecast system (GFS) forecasts with T170 resolution, valid at the same time for 357 cases, distributed over a period of 1 year. The parameter je_factor is the ensemble covariance weighting factor. This factor controls the weighting component of ensemble and static covariances. The ensemble member lateral boundary condition perturbations are generated in a similar manner to the initial ensemble using the fixed-covariance perturbation technique. The boundary condition for the analysis time is adjusted to match the analysis from DART. The tendencies for the later times in the forecast are adjusted to match the change in the boundary condition for the analysis time.

By including emissions in the ensemble state vector, emissions are estimated as hourly evolving parameters. Estimation of time-evolving emissions using data assimilation was first presented for carbon flux estimation (Kang et al., 2011, 2012). Such an approach provides emission information beyond an average for a specific time period. NOx emissions within cities show significant variation within the urban core and between the urban core and the surrounding suburbs. The observed columns show strong spatial variation dominated by an emission hotspot that results from the combination of spatial patterns in emissions and the short chemical lifetime. The goal of this work is to constrain hourly evolving emissions at the native model resolution. Here we start with a simple case in which the emission error is a constant fraction at all times of the day with the prior emissions set as 70 % of the true emissions and we investigate the ability of assimilation to recover the original emissions.

A challenge for updating the emissions in the augmented state vector is the absence of an emission forecast model to evolve the emission variables forward in time. The bottom-up inventory to be optimized provides hourly-resolved emissions for each model grid point. Instead of treating the emission variables of each hour at a specific location as independent parameters, we update the emission scaling factors at each assimilation cycle. In our emission update scheme, the TEMPO NO2 observations at time i are assimilated to generate a scaling factor for emissions at time i-1. In this way, the model–observation difference in the NO2 column will correct the emission of an hour ago instead of the current emission. This approach is reasonable because errors in NO2 concentration result from errors in previous emissions. Considering the short NO2 lifetime of 3 h in summer daytime, emissions from the previous hour have a large contribution to the NO2 total mass at the current time. For a given model grid point, we define the true (ei-1t), prior (ei-1prior), and posterior (ei-1post) emissions at time i-1. Since we start the assimilation with 70 % of the true emissions, we have emprior=0.7emt for any time m. After assimilating observations at time i, we compute the scaling factor (Si-1) for emissions at time i-1 as follows: Si-1=ei-1post/ei-1prior. Then we update the prior emissions at time i as eiprior=Si-1×eiprior. This prescription enables us to derive spatial 2-D emission scaling factors, which play the role of emission forecast models.

Assimilated observations include meteorological observations and NO2 column retrievals from the TEMPO observing system simulation experiments (OSSE). For meteorological observations, we assimilated synthetic observations of temperature, wind, and humidity from the NCEP Meteorological Assimilation Data Ingest System (MADIS) (https://madis.noaa.gov/). MADIS is a meteorological observational database and data delivery system that provides observations that cover the globe. MADIS ingests data from NOAA data sources and non-NOAA providers, decodes the data, and then encodes all of the observational data into a common format with uniform observational units and time stamps. For wind observations, the assimilated observation types include standard aviation routine weather reports (METAR), wind profilers, aircraft-based observations (ACARS), national mesonet data, and satellite data. Among these, the mesonet wind data are the most abundant, with ∼ 1000 observations located in the mapping domain in Fig. 2. The observation errors are the default values from the DART facility that are defined based on NCEP statistics (Romine et al., 2013).

The Geostationary Coastal and Air Pollution Events (GEO-CAPE) mission (Fishman et al., 2012) aims at improving our understanding of both coastal ecosystems and air quality from regional to continental scales. As the first phase of the GEO-CAPE implementation, TEMPO (Zoogman et al., 2017), launch date circa 2019, will provide hourly measurements of NO2, HCHO, tropospheric ozone, aerosols, and cloud parameters during the daytime. TEMPO will measure solar backscattered light in the UV–visual spectral range. Implemented on a geostationary platform, TEMPO retrievals will achieve hourly observations of NO2 vertical column density (VCD) at a native spatial resolution of 2 × 4.5 km during the daylight period. TEMPO's high spatiotemporal resolution will allow a more detailed assessment of emission inventories, e.g., urban-scale and large power plant NO2 emissions and mobile emissions that show significant spatial and temporal variations due to urban transit patterns, than is possible with existing LEO observations.

As TEMPO has not been launched yet, we generate synthetic TEMPO NO2 observations by simulating the instrument's observing characteristics. We carried out a model run, i.e., a forward integration of WRF-Chem for the period from 2 July to 7 July 2014 with NO2 emissions specified by NEI 2011 (true). In the NO2 retrieval algorithm, a layer-dependent box-air-mass factor (BAMF) represents the sensitivity of the retrieved NO2 in a specific layer to the true value in the atmosphere. The BAMF of NO2, as an optically thin absorber, is a vector and determines the measurement sensitivity to NO2 molecules at 35 pressure levels. In the calculation of BAMFs, we follow the latest version of the NASA standard product retrieval (level 2, version 2.1, collection 3) algorithm (Bucsela et al., 2013) assuming the TEMPO measurement has similar characteristics to the Ozone Monitoring Instrument (OMI). We assume clear-sky conditions for all observing scenes. Cloudy-sky scenes affect only the number of observations available as the cloudy scenes are usually discarded in the data filtering process. Without running a radiative transfer code, the elements of the BAMF vector are computed as a function of solar zenith angle (SZA), viewing zenith angle (VZA), relative azimuth angle (RAA), terrain reflectivity (Rt), terrain pressure (Pt), atmospheric pressure level (p), and the NO2 profile (Bucsela et al., 2013). The viewing parameters are computed by simulating the viewing geometry based on the location of ground pixels in relation to the observing instrument. The geometry-related parameters (SZA, VZA, and RAA) are computed hourly for each TEMPO observation using Matlab functions sun_position.m and geodetic2aer.m with inputs of the location and time of each TEMPO observation, and the location (36.5∘ N, 100∘ W) and altitude (35 786 km) of the TEMPO sensor. The terrain reflectivity and terrain pressure are sampled from the WRF-Chem nature run (NR; see Sect. 3) for each TEMPO pixel. All the parameters have an hourly frequency consistent with the TEMPO temporal observation pattern. Consequently, the NO2 profile with high spatiotemporal resolution captures the diurnal variation in NO2 and its urban–rural contrast. This contrast is essential to accurate interpretation of the measured spectrum (Russell et al., 2011; Laughner et al., 2016).

To generate synthetic TEMPO data, the modeled 3-D concentration fields from the NR are sampled in as similar a manner to the planned TEMPO measurements as the transport model permits: using the computed BAMF vertically, hourly frequency, 2 × 4.5 km nadir resolution and variations following the Earth's curvature horizontally. Figure 2 shows an example of the spatial distribution of TEMPO data over Denver, CO.

We describe the observation error as a relative value (σrel) and a random draw from a Gaussian distribution to avoid using a fixed value. The magnitude of the relative mean uncertainty of the NO2 column is different between clean and polluted areas (Boersma et al., 2004). We follow their categorization of clean versus polluted regions and summarize the mean and standard deviation of a Gaussian distribution for each scenario in Table 4. For polluted regions, we give a mean uncertainty of 7.5 %, which is lower than the 35 % minimum in the OMI NO2 retrievals. First, most of these errors are systematic, affecting comparison of different cities, but have smaller variation across a single, small-area scene of observations. Second, a relatively lower observation error improves the efficiency of data assimilation and helps to examine the sensitivity to other parameters. Finally, as TEMPO is expected to be operational no sooner than 2018, it is reasonable to expect that the retrieval error that is dominated by the air mass factor (AMF) in regions with large columns will be reduced as a result of future improvements in AMF simulation (Laughner et al., 2016). The synthetic observations assimilated are obtained by sampling the NR using the TEMPO observation simulator and adding observation error as yobs=N(ytrσ2), where ytr are the TEMPO NO2 observations sampled from the true emissions, and σ is the observation error standard deviation computed as σ=ytr×σrel.

The success of ensemble-based assimilation relies on how well the ensemble system represents the uncertainty. One way to test the success of an OSSE is to compare the RMSE computed with respect to the true observations with the ensemble spread directly. Figure 3 shows the evolution of the RMSE and spread for mesonet observations of zonal wind for ENS.1 and ENS.3. Overall, for each experiment the variation and magnitude of prior ensemble spread are similar to those of the prior RMSE, indicating that the ensemble develops a good amount of spread for the success of OSSE.

We find that the errors in the observation space of mesonet winds are reduced by 50 % on average from the prior to the posterior estimates. The prior wind RMSE exhibits the peaks in the afternoon and this results in the largest error reduction. The posterior wind RMSE shows a temporal average of 0.39 and 0.47 m s-1 in ENS.1 and ENS.3, respectively. Because ENS.1 is initialized with a meteorology ensemble with its mean close to the true ensemble, the wind RMSE on the first day is low and gradually grows to about 1 m s-1. In contrast, the prior wind RMSE in ENS.3 is as high as 2 m s-1 on the first day as a result of using an initial meteorology ensemble that is very different from the true ensemble. The wind RMSE evolution in the two experiments becomes very similar after the afternoon of the third day of assimilation, 4 July 2014. We conclude that the ensemble wind assimilation system performance is independent of the initialization approach after the first day.

We assimilate hourly TEMPO NO2 column observations and take their difference with the modeled column to correct the predicted NO2. Figure 4 shows the TEMPO NO2 column RMSE evolution for all experiments. With perfect knowledge of meteorology, REF shows significant reduction in TEMPO NO2 RMSE in the first three update cycles and succeeds in recovering the true emissions (Fig. 5). The prior TEMPO NO2 RMSE in the last 3 days varies below 3 × 1014 molecules cm-2 as a result of perfect NO2 transport and improved emissions. This ideal case with the assumption of perfect meteorology sets the upper limit of error reduction in NO2 concentrations by assimilating the TEMPO NO2 observations. Compared with REF, ENS.1 shows a prior TEMPO NO2 RMSE of 5–10 × 1014 molecules cm-2 due to the errors in NO2 transport and emissions. By assimilating NO2 observations, the TEMPO NO2 RMSE is reduced by more than 50 % from the prior to the posterior emissions, indicating the potential of TEMPO NO2 observations to improve the modeled atmospheric NO2 composition for the chemical reanalysis product. Without updating the NO2 concentrations in ENS.2, there is no reduction in the TEMPO NO2 RMSE as expected. We find that the TEMPO NO2 RMSE varies above 1 × 1015 molecules cm-2, being the largest among all experiments because the emission estimations show very poor results (shown in Sect. 4.3). The TEMPO NO2 RMSE development in ENS.3 is very similar to ENS.1 except for the first day when ENS.3 shows higher errors in the wind field, which contribute to the NO2 transport errors. We find that the NO2 forecast using a single meteorology field in REA is very similar to the ensemble NO2 forecast in ENS.1. This is because there is very little difference between the 1 h meteorology forecast and the ensemble forecast. In addition, the emission estimation results are also very similar. This is different from the previous study on CO2 forecasts, which showed that for a 6 h forecast, the CO2 transport driven by a single meteorological field has weaker vertical mixing and a stronger CO2 vertical gradient when compared to the mean of the ensemble CO2 forecasts initialized by the ensemble meteorological field (Liu et al., 2011).

We compare the TEMPO NO2 column spread in REF and ENS.1 in Fig. 6. For both experiments, the prior NO2 column spread varies with a magnitude that is similar to the prior RMSE (Fig. 4), which is the range desired for the NO2 ensemble spread. The NO2 forecast uncertainty represented by the NO2 ensemble spread results from the uncertainties in NO2 transport and emissions since the uncertainties in chemical production and removal processes are not included in this study. The uncertainties in NO2 transport are determined by the prior wind ensemble spread, which is widest in the afternoon and stays as low as ∼ 0.5 m s-1 at other times for zonal wind (Fig. 3). The prior NOx emission uncertainties are 60 % after inflation (Fig. 5). Under these circumstances, the mean prior TEMPO NO2 column spread is 4.55 × 1014 molecules cm-2 in REF, which does not include NO2 transport uncertainties, and is 7.03  × 1014 molecules cm-2 in ENS.1, which takes uncertainties in transport and emissions into account. The difference indicates that NO2 transport contributes to 35 % of the total NO2 forecast uncertainties in our assimilation setup. The TEMPO NO2 column spread in REF is very stable because it is determined by the constant emission spread of 60 %. ENS.1 shows fluctuations in the evolution of TEMPO NO2 column spread, which corresponds to the wind spread variation, with increasing spread in the afternoon.

We show the time evolution of the averaged urban emissions for all experiments in Fig. 5. For all experiments, the posterior emission ensemble spread is reduced compared to the prior spread, suggesting the effectiveness of assimilated NO2 columns in constraining the emission uncertainties. In making these comparisons, we ignore the emission correction of the first assimilation cycle since the first update produces a significant overcorrection to emissions because of the accumulated underestimation of the NO2 concentrations. By neglecting the first update, the prior emission ensemble mean of the second cycle is still 70 % of the true emission ensemble mean. During the nighttime when TEMPO observations are not available, we calculate the ratio of the posterior to true ensemble mean in the last cycle of daytime and use this together with the true nighttime emissions to derive the ensemble mean for the nighttime emissions. The prior and posterior emission ensembles of each nighttime hour are the same.

Not surprisingly, under the condition of perfect knowledge in meteorological fields, assimilating TEMPO NO2 observations successfully improves the emissions within the first few updates. The estimated emissions agree well with the true emissions throughout the assimilation period. This demonstrates the capability of a geostationary NO2 column observation system to constrain city-scale emissions and the reliability of the ensemble-based assimilation method to project the observed information to emissions.

We find that the errors in estimated emissions correlate with the wind errors. In ENS.1, the posterior emission is corrected to the true emission at the second cycle and stays close to the true emission throughout the first day. The good performance on the first day benefits from an initial meteorology ensemble with its mean close to the true ensemble. For the following 3 days, the emission estimates succeed in recovering the true emissions during the morning and show deviations from the true emissions in the afternoon as a result of the increased error in boundary layer winds. Figure 7 shows the dependence of errors in the inverted emissions to the prior wind RMSE. The emission errors show high sensitivity to the wind errors, with a slope of the regression line of 32.5 mol × km-2h-1 / (m × s-1). With a RMSE of model-predicted wind vectors of 1 m s-1, the errors in the estimated emissions are 30 mol × km-2 h-1 on average. For the daytime cycles, the prior emission ensemble spread after inflation is approximately 60 % and is reduced by more than half after assimilation (Fig. 5). Even though the posterior ensemble mean does not match with the true ensemble mean in the afternoon, the true ensemble mean falls within the range of the posterior ensemble spread with a few exceptions.

We find that the simultaneous update of emission and concentration performs better than the emission-update-only scheme with an hourly assimilation window. ENS.2 is a parallel assimilation run with ENS.1 but updates emissions only. As shown in Fig. 5, the estimated emissions have very large differences from the true emissions and the posterior ensemble spread does not cover the true emissions. For example, at 10:00 MST on 3 July, the posterior ensemble mean (red) is very close to the true emissions. As a result of this, we have a very good prior ensemble estimate (black) at 11:00. However, the posterior emission at 11:00 is largely underestimated compared with the true emissions. This is because the posterior emissions from 07:00 to 09:00 are overestimated, which results in overestimated NO2 concentrations at 10:00 and 11:00. As a result, even though the prior emissions from 10:00 to 11:00 are good, the model still overestimates NO2 at 11:00 due to the NO2 overestimation at 10:00. Without updating the concentrations, the observed differences in NO2 columns are dominated by the NO2 concentration errors of an hour ago and should not be attributed to the emissions.

We also find that the emission estimation should start after the meteorology assimilation becomes stable. As a comparison to ENS.1, ENS.3 is initialized with a meteorology ensemble that is very different from the true emissions. On the first day, the prior wind RMSE varies from 1 to 2 m s-1 (Fig. 3) and leads to enhanced NO2 transport errors. As a result, the emission estimations are not successful for the first day. After the afternoon of the second day (3 July), the wind RMSE evolution is similar between ENS.1 and ENS.3 and as a result, the emission estimations perform in a similar way. We recommend allowing meteorology assimilations to stabilize from the initial transport errors before assimilating chemical observations to constrain the emissions.

With an hourly re-initialization of meteorology, the NO2 transport error statistics are not important to emission estimation if the current practice of using a single meteorological field to transport NO2 is adopted. The emission estimation performance in REA is very similar with that in ENS.1 (Fig. 5). This is because the difference in the 1 h NO2 forecast driven by an ensemble meteorological field and a single ensemble mean field is very small. Though the wind uncertainties represented by the meteorological ensemble reach 1.5 m s-1 in the afternoon, our results show that the information of wind uncertainties is not important for estimating NOx emissions.

Finally, we examine the emission estimation performance in ENS.1 at the scale of the model grid (3 km). As shown in Fig. 8, the true emission shows high spatial variation from the city center to the suburbs as well as distinct point emission sources. In the example of the emission estimate at 09:00, the posterior emission recovers the true emission very well with the posterior RMSE of 21.6 mol/(km2 × h). In contrast, the emission estimate at 16:00 shows a RMSE of 46.5 mol/(km2 × h) due to relatively high wind errors. The posterior emission underestimates the emissions significantly all over the city except for the regional overestimation in the east. The emission hot spot of ∼ 250 mol/(km2 × h) in the city center is not fully represented in the posterior estimate. In conclusion, when wind errors are low, the difference between posterior emission and the true emission can be reduced to ±25 mol/(km2 × h) at most grid points. With high wind errors, this difference varies significantly from point to point and grows as large as 100 mol/(km2 × h).