Inverse Modeling of Nitrogen Oxides Emissions from the 2010 Russian Wildfires by Using Satellite Measurements of Nitrogen Dioxide

Nitrogen oxides (NOx) play a major role in the atmospheric oxidation processes leading to ozone and secondary organic aerosol formation in the lower atmosphere. Wildfires are one of the important sources of NOx emissions; however, knowledge of NOx emissions from fires is currently insufficient and available estimates provided by emission inventories have mostly not been validated against atmospheric measurements. Recent studies indicated that useful observational constraints to biomass burning (BB) NOx emissions are provided by satellites measurements of nitrogen dioxide (NO2), but available BB NOx emission estimates inferred from such measurements involve quantitative assumptions regarding the atmospheric NOx lifetime. In this study, we investigated NOx emissions from the extreme wildfires that occurred in the European part of Russia in summer 2010. To this end, we analyzed tropospheric NO2 retrievals from measurements performed by the OMI satellite instrument in the framework of an original inverse modeling method. A quantitative relationship between BB NOx emissions and tropospheric NO2 columns was simulated using the mesoscale CHIMERE chemistry transport model. Our analysis indicated that such a relationship depends strongly on BB emissions of volatile organic compounds and that a dependence of the effective NOx lifetime on the NOx fluxes can be essentially nonlinear. Our estimates of the total NOx emissions in the study region are found to be at least 40% larger compared to the respective data from the GFASv1.0 and GFED4.1s global fire emission inventories.


Introduction
Nitrogen oxides (NO x = NO + NO 2 ) are important atmospheric constituents affecting climate processes and air quality specifically by serving as precursors of tropospheric ozone [1,2] and influencing secondary aerosol formation [3,4].One of the significant sources of NO x on a global scale is associated with open biomass burning (BB): it is estimated that BB provides around 15% of total NO x emissions globally [5].On a regional scale, BB NO x emissions can play a predominant role in the oxidation processes leading to ozone formation inside smoke plumes from wildfires [6] over other NO x sources and provide a major contribution to NO 2 column amounts over fire spots [7].
Despite the important role played by BB NO x emissions in atmospheric processes, the current knowledge of the amounts of NO x emitted into the atmosphere from wildfires is insufficient.Available BB NO x emission estimates provided by fire emission inventories (e.g., [8,9]) based on indirect measurements of the amounts of biomass burned have mostly not been validated against atmospheric measurements and are likely to be rather uncertain as indicated by a diversity of the NO x emission factor values involved in such inventories and reported in literature for similar types of vegetation cover [10].Validation of BB NO x emission estimates is more difficult compared to validation of BB emissions of some other species (such as, e.g., CO) particularly due to high reactivity and a relatively short atmospheric lifetime of NO x , leading to a strong variability of NO x concentrations both in space and time.
Nonetheless, several studies [7, [11][12][13][14] have recently examined the relationship between the satellite-retrieved fire radiative power (FRP) and the tropospheric NO 2 columns over fire spots and reported reasonable estimates of the fire emission rate (FER) [7,11] or the emission coefficient (EC) [12][13][14], both of which allow one to calculate NO x emissions, given the observed values of FRP.The measurement-based estimates of FER or EC for different regions and different types of biophysical model applications (BioMA) are useful, as they provide insight into the capability of available parameterizations to capture spatial and temporal variability of NO x emissions.However, such estimates are presently rather uncertain, particularly because they involve explicit quantitative assumptions regarding the NO x lifetime and NO 2 /NO ratio.For example, it has been argued [13] that as the NO x lifetime is likely to vary across individual fire plumes between 2 and 6 h, the estimates of EC can be uncertain at least by a factor of 3.
In this study, we also use FRP and NO 2 columns derived from satellite measurements, but unlike the previous studies, we do not make any explicit assumptions on the NO x lifetime and NO 2 /NO ratio.Instead, we follow the inverse modeling approach that has earlier been successfully used (e.g., [15][16][17][18]) to estimate anthropogenic NO x emissions.Within this approach, the relationship between NO 2 columns and NO x emissions can be simulated by a chemistry transport model, and the NO x emissions (or related emission parameters) as well as the NO x lifetime can be estimated by fitting simulated NO 2 columns to satellite data.The goals of our study were (1) to examine feasibility of using an inverse modeling approach to estimate BB NO x emissions in a region affected by numerous and intense wildfires; and (2) to assess the impact of chemical nonlinearities on the relationship between NO x emissions from wildfires and corresponding NO 2 columns over such a region.We focused on the disastrous mega-fire event that took place in the European part of Russia in 2010.Emissions of some pollutants (such as CO and aerosol) from the Russian 2010 fires were already investigated using inverse methods (e.g., [19][20][21]), but, to the best of our knowledge, there have yet been no similar studies focusing on NO x emissions from those fires.

Satellite Data
We used tropospheric NO 2 column amounts retrieved from measurements of visible and ultraviolet back scattered radiation by the Ozone Monitoring Instrument (OMI) [22] onboard the NASA EOS Aura satellite and provided by KNMI as the DOMINO version 2 data product [23,24].OMI provides global coverage daily at the 13 × 24 km 2 nominal spatial resolution; the measurements are taken in the early afternoon, as the Aura satellite operates in a sun-synchronous polar orbit with an equator crossing at 13:45 LST.The DOMINO version 2 data product was evaluated against ground-based (MAX-DOAS) measurements [25], and only a minor negative bias (~10%) was found in the satellite data.NO 2 data retrieved from the OMI measurements (although with slightly different algorithms) were found to be useful in earlier studies of BB NO x emissions [7,11,12,14].
Following recommendations of the data providers, potentially biased data retrieved for the scenes with the cloud fraction and surface albedo exceeding 30% and 0.3%, respectively, were disregarded.The details of the retrieval algorithm can be found elsewhere [23].Note that the tropospheric NO 2 column retrieval procedure does not explicitly account for optical effects of BB aerosol.However, such effects were taken into account and corrected for in the same way as similar effects associated with clouds.Scenes strongly contaminated by cloud or aerosol were discarded, and so the bias is likely to remain limited (<20%) [26].The orbital NO 2 data available for the study period that spans from 15 July to 16 August 2010 were projected onto a 0.5 by 0.5 degree rectangular grid covering the study region (48 • N-66 • N; 20 • E-56 • E).Any data falling to the same grid on the same day were averaged.
As a primary source of information on NO x emissions from fires, we used the Fire Radiative Power (FRP) data [27,28] retrieved from satellite measurements of infrared radiation with the MODIS instruments operating onboard the Aqua and Terra satellites.Both the Aqua and Terra satellites are in sun-synchronous polar orbits with corresponding equator overpass times of 13:30 and 10:30 LST (at daytime) and 01:30 and 22:30 LST (at nighttime).We used the standard MODIS Level 2 "thermal anomalies & fire" (MOD14 and MYD14, Collection 5) data product available free from the NASA Land Processes Distributed Active Archive Center [29].The data were provided for each satellite overpass at the nominal 1 × 1 km 2 resolution.The same data have been widely used (e.g., [7,9,21]) to study fire emissions, and details about the retrieval algorithm and potential uncertainties can be found elsewhere [27].
Finally, our analysis involved satellite retrievals [30] of aerosol optical depth (AOD) at a 550 nm wavelength.The measurements were also performed by the MODIS instruments onboard Aqua and Terra satellites.We used the Level 3 MYD08_D3/MOD08_D3 data product obtained from the NASA Giovanni-Interactive Visualization and Analysis system [31] in the framework of an earlier study [21].The data had the spatial resolution of 1 by 1 degree and the temporal resolution of one day.

Simulation Data
Along with NO 2 data derived from satellite measurements, we used NO 2 columns simulated with the CHIMERE chemistry transport model (CTM) [32].The CHIMERE CTM is a typical Eulerian three-dimensional model enabling simulations of air pollution on various scales, from urban to continental ones.It takes into account major physical and chemical processes (including over 300 chemical and photochemical reactions) affecting the evolution of ~80 gaseous species in the lower atmosphere.It also enables simulations of aerosol species but simulated aerosol concentrations were not used in this study.In-detail descriptions of the model structure and of parameterizations of physical and chemical processes is available elsewhere [32].The model documentation and the source code can be downloaded from the CHIMERE website [33].CHIMERE was successfully used in a number of studies, including those dedicated to investigations of atmospheric effects of wildfires (e.g., [19,21,34,35]).
The CHIMERE configuration was the same as in a previous study [21] of the atmospheric impacts of the 2010 Russian wildfires, which was focused on simulation of BB aerosol.Specifically, the simulations were performed with a horizontal resolution of 0.5 • × 0.5 • with the model grid covering most of European Russia and a portion of Eastern Europe (48 • N-66 • N; 20 • E-56 • E).In vertical, the model grid had 12 levels, with the top of the upper level fixed at 200 hPa.
Fire emissions were calculated and introduced into CHIMERE by using the emission model that had been successfully used and described in detail earlier [19,21,36].Briefly, it assumes that the BB emission rate, E s , of a species, s, in a given grid cell of the horizontal domain in an hour, t, is proportional to the daily mean FRP values, φ d , that were inferred from daily maximum FRP values derived from the MODIS measurements (see Section 2.1.1)for a given grid cell: where α is a conversion factor from FRP to dry BB rate, which is referred to below also as the FRP-to-BBR conversion factor and for which a "reference" value, α r , of 0.368 kg•s −1 •MW −1 is adopted, taking into account the experimental data [37], β s l are the emission factors for a species s and a land cover type l, ρ l is the fraction of the land cover type l, h el is the diurnal variation of fire emissions, and c is an ad hoc correction factor which was calculated (see [19,21]) using the measured AOD values and was intended to compensate for a possible attenuation of FRP measured from satellites by very heavy smoke and also to account (at least partly) for emissions from peat fires.The emission factor values, β s l , for the three aggregated vegetative land cover types (forest, grassland, and agricultural land) were taken to be the same as in our previous study (see [21] and Table 2 therein).The emission diurnal cycle was also adopted from the previous study (see [21] and Figure 1 therein), where it had been derived for the study region from the FRP measurements using a method developed earlier [36].The emissions were distributed in the vertical direction by using a well-known parameterization [38] of the maximum injection height of BB emission as a function of FRP and the boundary layer height.The emission profiles were calculated for each grid cell and each hour by assuming that BB emissions corresponding to individual fire pixels are uniformly distributed from the ground up to the altitude corresponding to the maximum injection height.
Note that our fire emission model given by Equation (1) disregards possible variations of the FRP-to-BBR conversion factor both in space and time.It also does not explicitly take into account emissions from peat fires which are not visible from space.These simplifications are mainly due to the lack of observational information about such variations.Available estimates of α for different vegetation land cover types [9] are based on emission inventory data and, for this reason, were not quite suitable for our study based on the inverse modeling approach.
A noteworthy feature of our simulations is that hourly values of the photolysis rates were calculated "offline" for each grid cell and hour using the TUV model [39] and the satellite AOD data described in Section 2.1.1 (see also [19] for details of our calculations).CHIMERE runs were driven with meteorological data obtained from the WRF-ARW (v.3.6) model [40].Further details on meteorological data, anthropogenic and biogenic emission data, and boundary and initial conditions used in the CHIMERE runs performed in this study can be found elsewhere [21].
The hourly BB NO 2 concentration data obtained from the CHIMERE runs were matched in time and space to the satellite NO 2 data and integrated vertically by applying the averaging kernels [41].
The averaging kernels provide information on contribution of different atmospheric layers to the tropospheric NO 2 column amounts retrieved from the OMI measurements and were available as a part of the DOMINO data product.The hourly BB NO 2 concentrations available for the same day and grid cell were averaged.
The model was run for the period from 12 July to 16 August 2010 both with and without fire emissions.Only the difference of nitrogen oxides concentrations from the two "twin" runs was considered in this study in order to minimize an impact of probable biases in biogenic and anthropogenic emissions on our estimates: such a difference was considered as a contribution of BB emissions to the nitrogen oxides concentrations.The first three days of the model runs were withheld from the analysis for the model's spin-up.The three-day spin-up was found to be sufficient in the case considered for evaluation of the BB fraction of tropospheric NO 2 columns, since there had been no significant fire emissions in the study region before the initial date of the simulation.

Method
Estimation of NO x emissions was based on a general approach established in previous studies [19,21,36].The idea is to optimize one or more parameters of the fire emission model by fitting modeled concentrations of a species considered to respective observations.Following one of the previous studies [21], we optimized the FRP-to-BBR conversion factor (α) by assuming (in accordance to Equation ( 1)) that the same value of that factor is applicable to any types of vegetation land cover.Although, in reality, it is not necessarily true, large uncertainties in the measurement and simulation data prevent us from obtaining estimates of α separately for individual biome types.Variability of the true values of α is expected to be taken into account in the confidence intervals for our estimates.
In this study, the optimal value of α, α opt , was inferred by fitting the NO 2 columns simulated with the CHIMERE model to those derived from the OMI observations: where C o are the observed tropospheric NO 2 columns, C b are the background parts of the tropospheric NO 2 columns (that is, the tropospheric NO 2 column amounts which would be present in the atmosphere if there were no fires and which were estimated as explained below), C mf are the simulated tropospheric column amounts of NO 2 originating from fires and i is the index of a day.The NO 2 column amounts (C o , C b , C mf ) involved in Equation ( 2) are the averages of the corresponding spatially-distributed data for a given day over the study region.Note that the spatial averaging was performed in order to minimize the impact of possible random uncertainties in the spatial variations of the NO 2 columns (due to, e.g., errors in the spatial distributions of fire emissions evaluated using Equation ( 1)) on our emission estimates.
To estimate the background NO 2 columns in a given grid cell (i) and in a given day (d), we considered the tropospheric NO 2 columns derived from the OMI measurements for the same grid cell but for another day chosen from the period from 15 July to 19 July 2010, when, according to our simulations, a contribution of fires to the mean NO 2 columns over the study region was negligible.If such "background" data were available for more than one day, a nearest, to d, day was selected.On the other hand, if there were no observational data for any of the days in the indicated period, then the given grid cell i was excluded from further analysis.
Importantly, estimation of the background NO 2 columns in such a way does not rely on the accuracy of the simulations of NO 2 columns in the background conditions.This allows us to minimize the effect of possible biases (due to, e.g., uncertainties in anthropogenic and biogenic NO x emissions, as well as in the boundary conditions for NO x and related species) in the background simulations with CHIMERE for the study region [42,43] on our estimates.Note that C mf involved in Equation ( 2) was obtained as the difference between the results of two "twin" model runs with and without fire emissions (as mentioned in Section 2.1.2),and so C mf also could not be directly influenced by possible inaccuracies of the simulations for the background conditions.Furthermore, the analysis of our results (see Section 3.3 below) does not show any evidence that the dependence of C mf on BB NO x emissions is significantly affected by the background conditions in an indirect way (e.g., through chemical interactions) either.
Equation (2) was resolved iteratively.In each iteration, C mf , was assumed to depend on BB NO x emissions (and, thus, on α) linearly, that is: where α (n) and α (n−1) are values of the conversion factor in two consecutive iterations, n is the iteration index and the symbol "|" denotes conditioning.After substituting α (n) (instead of α opt ) and C mf given by Equations (3) into (2), the latter can be resolved analytically: In this study, the first iteration (based on the initial model run) was performed with the reference value of the conversion factor, α r (see Section 2.1.2).Three iterations were found to be sufficient in order to ensure that α (n) is converged to the optimal estimate of α with a relative numerical uncertainty of less than 5%.
Confidence intervals for α opt were evaluated by means of a Monte Carlo experiment based on the bootstrapping method [44].Specifically, the simulations performed with the optimal value of α were used to represent the "true" values of the BB fraction of the tropospheric NO 2 columns.The corresponding "observed" values were generated by sampling random errors from the residuals of the modeled (optimal) data for the NO 2 columns (see the right-hand part of Equation ( 2)) and adding them to such "true" values.The re-sampling procedure and estimation of α opt (assuming a linear dependence of C mf on α) were repeated 1000 times.The confidence intervals were evaluated (and are reported below) in terms of the 95th percentile.In this way, we took into account any model and measurement errors contributing to the cost function involved in the right-hand part of Equation (1).Such errors may be due to various non-systematic uncertainties in the retrieval procedure used to derive tropospheric NO 2 columns from the OMI measurements [23,26,45], as well due to transport errors in our model.A part of the uncertainties taken into account in the confidence intervals for α opt may be associated with our fire emission model (see Section 2.1.2),specifically with the simplifying assumptions concerning the FRP-to-BBR conversion factor as well as with possible inaccuracies of the injection height, with variability of the emission factors and with inaccuracies in the input FRP data.Indeed, it seems reasonable to expect that the errors associated with the emission model varied from day to day during the study period, reflecting temporal and spatial variations in the burning conditions and in the types and density of fuel.
It should be noted, however, that the confidence intervals reported below cannot fully account for systematic errors (biases) both in the OMI retrieval and in our simulations.Such biases may, in particular, be due to a probable underestimation of the NO 2 columns retrieved for the strongly polluted scenes.The biases may also be due to possible inconsistencies between the vertical distribution of NO 2 in the real atmosphere and the vertical profiles used in the retrieval procedure [45] and predicted by CHIMERE in this study.Evaluation of such systematic errors and their effects on the corresponding NO x emission estimates is a challenging task that goes beyond the scope of this study.
Since the tropospheric NO 2 columns derived from satellite measurements provide information only on NO x emissions, there is an issue concerning specification of BB emissions of other species (such as CO and volatile organic compounds, VOCs).As the main option, we used the same values of the conversion factor to calculate the BB emissions of all model species.This estimation case is labeled below as "VOCbyNO x ".However, as it was pointed out earlier [21,36], estimates of α derived from measurements of different species may be different, partly due to uncertainties in the assumed emission factors.Therefore, as another option, we calculated the BB emissions of CO and VOCs by using the value of α optimized in a previous study [21] against ground-based measurements of CO concentrations in the Moscow region: this CO-measurement-based value of α had been found to be a factor of 1.88 larger than its reference value α r .The second estimation case is labeled below as "VOCbyCO".
Note that the estimation method described above is similar but not identical to those employed in the preceding studies [21,36] where satellite measurements and the CHIMERE model were used to constrain emissions of CO and aerosol from wildfires in Russia.The differences (that will not be discussed here in detail) are mainly due to the fact that CO and aerosol are much less reactive species compared to NO x .Some specific assumptions (e.g., those concerning the origin of possible systematic uncertainties in simulated data) involved in the preceding studies were no longer valid in the case considered in this study and should have been avoided.For example, it was assumed that the bias in the simulated CO columns in the background conditions was mainly due to errors in the boundary conditions: accordingly, it was estimated by averaging the differences between the CO columns from the simulations and measurements over a number of grid cells and days representing similar environment conditions.In contrast, errors in the corresponding NO 2 columns may predominantly come from uncertainties in the biogenic and anthropogenic emissions specified in the model; furthermore, such errors are likely to strongly vary both in time and space because of a short lifetime of NO x .Consequently, estimation of BB NO x emissions using exactly the same methods as those employed in the previous studies turned out to be infeasible, and such methods had to be modified accordingly.The major difference is that here we estimate the background NO 2 columns directly from the measurement data and thus avoid the problem of estimating the bias in the corresponding simulated data.
To study a potential impact of chemical nonlinearities on BB NO x emission estimates based on satellite measurements, we performed several additional model runs using BB emissions calculated with different values of the conversion factor.Specifically, the reference value of the conversion factor was scaled with a factor ranging from 0. 5 to 2, and the resulting values were used in Equations ( 3) and (4) as the "zero-order" estimate, α (0) , to obtain the "first-order" estimate (constrained by satellite measurements according to Equation ( 2)) of the conversion factor, α (1) .Furthermore, we evaluated the effective lifetime of NO x , τ nox , corresponding to each value of α (0) as follows: where e ij are the BB NO x emission rates (g•hour −1 ) in a grid cell j (in the horizontal domain) and in a day i, ν ij are values (simulated by the CHIMERE model) of the tropospheric column amounts of NO x originating from wildfires (g), N c and N d are the total numbers of grid cells and days in the study region and period, and θ ij is the selection operator-which is equal to unity if the measurement data for a given grid cell and day is available and to zero otherwise.Equation ( 5) assumes that the evolution of the total (integral) amount of NO x from BB burning over the study region can be roughly approximated by a simple balance equation describing the loss of NO x as a first order decay process, with the rate expressed as τ nox −1 .The definition given by Equation ( 5) is based on the known concept [46] of the mean lifetime of an atmospheric substance and follows from a consideration of a simple balance equation for NO x originating from fires (NO , describing the loss of NO f x as a first order decay process in each model grid cell in the three dimensional domain: where the square brackets denote the mass concentration of NO f x , F in and F out are the fluxes of NO f x in and out of the given grid cell, respectively, E is the local BB NO x emission (or injection) rate, and L is the rate of losses of NO f x due to chemical and deposition processes.Note that the inverse of L gives an estimate of the "instant" lifetime of NO f x with respect to chemical and deposition processes in a given grid cell.After (i) averaging both the left and right parts of Equation ( 6) over the study region (both in the horizontal and vertical directions) and the study period; (ii) taking into account that concentration of NO f x approaches zero both at the beginning and at the end of the study period; (iii) disregarding the integral flux of NO f x from the study region (over which the persistent blocking anticyclone was developed in summer 2010 [47]); and (iv) multiplying both parts of the equation with the average amount of NO f x , we arrive to the following approximate relationship: where the angle brackets denote the average quantities.We further note that the term on the left-hand side of Equation ( 7) has the meaning of the mean NO f x lifetime evaluated as the inverse of the weighted average of L (with local NO f x concentrations being the weights), while the term on the right-hand part of Equation ( 7) is analogous to the term on the right-hand part of Equation ( 5).The main difference between Equation (7) and Equation ( 5) is that the latter includes only those values of the NO f x concentrations and BB NO x emissions that correspond in space and time to the available OMI observations.Therefore, the effective lifetime, τ nox , defined according to Equation ( 5) can be regarded as an approximation for the NO f x lifetime given by Equation (7).Note that we considered only those values of NO f x that have counterparts in the satellite data, because the primary purpose of evaluation of τ nox in this study was to investigate the effects of chemical nonlinearities on the BB NO x emission estimates that can be derived from satellite measurement using either our method or simpler techniques involving a priori assumptions regarding the NO x lifetime [12][13][14].Note also that the relationship between α (1) and α (0) depends not only on the NO x lifetime but also on the NO 2 /NO ratio: this ratio, in turn, depends on ozone concentration and can be affected by changes in the NO x emissions.In addition, unlike τ NOx calculated using Equation ( 5), estimation of α (1) partly takes into account BB NO x emissions in grid cells (days) for which the measurement data are not available.Therefore, the dependence of τ nox on α (0) cannot fully characterize that of the NO 2 columns retrieved from OMI measurements on the BB NO x emission rate in the study region and period.Nonetheless, we believe that the estimates of τ nox provided below can be helpful in characterizing the processes determining the relationship between the NO 2 columns and NO x emissions.Furthermore, such estimates can eventually contribute to reducing uncertainties associated with FER or EC estimates [7, [11][12][13][14] based on the analysis of the empirical relationships between FRP and tropospheric NO 2 columns.However, we do not recommend using our estimates of τ nox outside of this specific context.  1 and 2 were calculated with the conversion factor equal to its reference value α r specified above (see Section 2.1.2).Note also that the spatial distributions of CO and aerosol on the same days were considered in a preceding study [21].

Estimation of the FRP-to-BBR Conversion Factor
As is evident from Figure 1, the simulations tend to overestimate the BB part of NO 2 columns (that is the difference of C o and C b ), although the model captures, to a significant extent, the temporal variability of NO 2 column amounts from wildfires (specifically, the correlation coefficient exceeds a value of 0.75).The fact that, for some days, C b is larger than C o indicates that there may be considerable uncertainties in our estimates of background NO 2 values as well as in the original satellite NO 2 data.We assume that such uncertainties are mostly random in nature (varying from day to day) and thus are taken into account in the confidence intervals of our emission estimates reported below.
Atmosphere 2016, 7, 132 8 of 20 fully characterize that of the NO2 columns retrieved from OMI measurements on the BB NOx emission rate in the study region and period.Nonetheless, we believe that the estimates of τnox provided below can be helpful in characterizing the processes determining the relationship between the NO2 columns and NOx emissions.Furthermore, such estimates can eventually contribute to reducing uncertainties associated with FER or EC estimates [7, [11][12][13][14] based on the analysis of the empirical relationships between FRP and tropospheric NO2 columns.However, we do not recommend using our estimates of τnox outside of this specific context.

Estimation of the FRP-to-BBR Conversion Factor
Estimation of the conversion factor (as explained in the previous section) is based on the analysis of daily time series of spatially averaged NO2 columns derived from the OMI measurements (Co) and simulated with the CHIMERE model (Cmf) and involves evaluation of the background fraction (Cb) of the tropospheric NO2 columns.The corresponding time series are presented in Figure 1, along with the time series of the difference of Co and Cb.Examples of underlying daily values of tropospheric NO2 columns (specifically, on 29 July and 8 August) spatially distributed inside of the study region are shown in Figure 2. Note that values of Cmf shown in Figures 1 and 2 were calculated with the conversion factor equal to its reference value αr specified above (see Section 2.1.2).Note also that the spatial distributions of CO and aerosol on the same days were considered in a preceding study [21].
As is evident from Figure 1, the simulations tend to overestimate the BB part of NO2 columns (that is the difference of Co and Cb), although the model captures, to a significant extent, the temporal variability of NO2 column amounts from wildfires (specifically, the correlation coefficient exceeds a value of 0.75).The fact that, for some days, Cb is larger than Co indicates that there may be considerable uncertainties in our estimates of background NO2 values as well as in the original satellite NO2 data.We assume that such uncertainties are mostly random in nature (varying from day to day) and thus are taken into account in the confidence intervals of our emission estimates reported below.Examples of spatial distributions of NO2 columns shown in Figure 2 indicate that the NO2 retrievals for many scenes in the study region and period were missing (apparently, due to interference of BB aerosol that is "shielding" the radiation coming to a satellite from the boundary layer).Nonetheless, many moderately polluted scenes showing considerable NO2 amounts which, according to our simulations, originated from wildfires can still be seen in the OMI retrievals.
Figure 3 presents the conversion factor estimates, α (n) , that were obtained according to Equations ( 2)-(4) by using the simulations in which BB emissions were calculated with the assumed conversion factor values, α (n−1) .For convenience, values of both α (n) and α (n−1) are normalized to the reference value of the conversion factor, αr.Most of the estimates shown in Figure 3 illustrate results of the first iteration (n = 1), except for the optimal estimates (circumvented by black circles in Figure 3) of α (αopt) that were obtained as a result of the third iteration (n = 3).The estimates were obtained separately for the two cases ("VOCbyNOx" and "VOCbyCO") that involve the different assumptions regarding the BB emissions of VOCs and CO.If the relationship between the simulated NO2 columns and the BB NOx emissions were linear, then any value of α (n−1) would yield the same value of α (n) , or, in other words, α (n) would be independent of α (n−1) .Our results show that α (n) is indeed very weakly (positively) dependent on α (n−1) , but only for the case "VOCbyNOx".A more pronounced (decreasing) dependence of α (n) on α (n−1) is found for the case "VOCbyCO".Overall, our results shown in Figure 3 indicate that the effects of chemical nonlinearities on the relationship between the BB emissions and tropospheric NO2 columns in the situation considered cannot be disregarded, at least without certain constraints on VOCs emissions, although these effects are not very strong.In particular, the increase of α (0) from 0.5 to 2 (that is, by a factor 4) in the "VOCbyCO" case resulted in the decrease of α (1) from Examples of spatial distributions of NO 2 columns shown in Figure 2 indicate that the NO 2 retrievals for many scenes in the study region and period were missing (apparently, due to interference of BB aerosol that is "shielding" the radiation coming to a satellite from the boundary layer).Nonetheless, many moderately polluted scenes showing considerable NO 2 amounts which, according to our simulations, originated from wildfires can still be seen in the OMI retrievals.
Figure 3 presents the conversion factor estimates, α (n) , that were obtained according to Equations ( 2)-(4) by using the simulations in which BB emissions were calculated with the assumed conversion factor values, α (n−1) .For convenience, values of both α (n) and α (n−1) are normalized to the reference value of the conversion factor, α r .Most of the estimates shown in Figure 3 illustrate results of the first iteration (n = 1), except for the optimal estimates (circumvented by black circles in Figure 3) of α (α opt ) that were obtained as a result of the third iteration (n = 3).The estimates were obtained separately for the two cases ("VOCbyNO x " and "VOCbyCO") that involve the different assumptions regarding the BB emissions of VOCs and CO.If the relationship between the simulated NO 2 columns and the BB NO x emissions were linear, then any value of α (n−1) would yield the same value of α (n) , or, in other words, α (n) would be independent of α (n−1) .Our results show that α (n) is indeed very weakly (positively) dependent on α (n−1) , but only for the case "VOCbyNO x ".A more pronounced (decreasing) dependence of α (n) on α (n−1) is found for the case "VOCbyCO".Overall, our results shown in Figure 3 indicate that the effects of chemical nonlinearities on the relationship between the BB emissions and tropospheric NO 2 columns in the situation considered cannot be disregarded, at least without certain constraints on VOCs emissions, although these effects are not very strong.In particular, the increase of α (0) from 0.5 to 2 (that is, by a factor 4) in the "VOCbyCO" case resulted in the decrease of α (1)  from 0.96 to 0.67 (that is, only by about 30 percent), which is an effect of the corresponding increase (by a factor of ~1.3) of the ratio of the mean BB NO 2 column amounts and NO x emission rates in the respective simulations.
It is especially noteworthy that the sensitivity of the optimal estimates of α to changes in BB VOC emissions turned out to be relatively small: specifically, while BB VOCs emissions for the "VOCbyCO" case were almost a factor of 3 larger than for the "VOCbyNO x " case (when α = α opt ), the optimal estimate of the conversion factor is found to be only 17 percent larger for the former case (0.298 ± 0.053 kg•s −1 •MW −1 ) than that for the latter one (0.254 ± 0.045 kg•s −1 •MW −1 ).Unfortunately, there are presently no data that would allow us to characterize the uncertainty of the regionally averaged emission factors for VOCs, although such uncertainty is likely much smaller than the standard deviation (close to 100% [48]) of individual emission factor measurements.Note that systematic uncertainties in our estimates of α due to biases in the emission factors for VOCs are probably only partly accounted for in the confidence intervals for these estimates, to an extent as such uncertainties are associated with errors in the simulated daily variations of the tropospheric NO 2 columns.
Atmosphere 2016, 7, 132 10 of 20 0.96 to 0.67 (that is, only by about 30 percent), which is an effect of the corresponding increase (by a factor of ~1.3) of the ratio of the mean BB NO2 column amounts and NOx emission rates in the respective simulations.
It is especially noteworthy that the sensitivity of the optimal estimates of α to changes in BB VOC emissions turned out to be relatively small: specifically, while BB VOCs emissions for the "VOCbyCO" case were almost a factor of 3 larger than for the "VOCbyNOx" case (when α = αopt), the optimal estimate of the conversion factor is found to be only 17 percent larger for the former case (0.298 ± 0.053 kg•s −1 •MW −1 ) than that for the latter one (0.254 ± 0.045 kg•s −1 •MW −1 ).Unfortunately, there are presently no data that would allow us to characterize the uncertainty of the regionally averaged emission factors for VOCs, although such uncertainty is likely much smaller than the standard deviation (close to 100% [48]) of individual emission factor measurements.Note that systematic uncertainties in our estimates of α due to biases in the emission factors for VOCs are probably only partly accounted for in the confidence intervals for these estimates, to an extent as such uncertainties are associated with errors in the simulated daily variations of the tropospheric NO2 columns.The dependence is shown for the two estimation cases, "VOCbyNOx" and "VOCbyCO", see Section 2.2.The estimates circumvented by black circles are the optimal estimates (αopt) obtained as a result of the third iteration (that is, with n = 3) of the iterative procedure described in Section 2.2, whereas the other estimates are a result of the initial iteration (n = 1).
Another potential source for a bias in our emission estimates is due to uncertainties in estimates of the background estimates of the NO2 columns.To test the sensitivity of our results to this factor, we repeated our estimation procedure for the VOCbyNOx case, but with the background NO2 columns estimated using available observational data for other days (12-14 July 2010 instead of 15-19 July 2010 as in the base case).The optimal estimate of α for the test case was found to be only 10 percent larger than for the base case.This result indicates that our BB NOx emission estimates are sufficiently robust with regard to random uncertainties in the background NO2 column amounts.Furthermore, we investigated whether or not the background NO2 columns changed significantly over the study period (e.g., due to changes in meteorological conditions or in biogenic emission rates).To this end, we selected data points (grid cells and days) where the simulated NO2 column amounts originated from fires were infinitesimal (less than 10 −2 % relative to the background NO2 columns estimated for the same grid cells/days using the OMI data for the period 15-19 July 2010).The selected data were averaged separately over the periods 15-19 July 2010 and 20 July-16 August 2010.As a Figure 3. Dependence of the FRP-to-BBR conversion factor values optimized under the assumption of linearity of the relationship between the NO 2 columns and the BB NO x emission rate on an assumed value of the same conversion factor.The conversion factor values are normalized to their reference value.The dependence is shown for the two estimation cases, "VOCbyNO x " and "VOCbyCO", see Section 2.2.The estimates circumvented by black circles are the optimal estimates (α opt ) obtained as a result of the third iteration (that is, with n = 3) of the iterative procedure described in Section 2.2, whereas the other estimates are a result of the initial iteration (n = 1).
Another potential source for a bias in our emission estimates is due to uncertainties in estimates of the background estimates of the NO 2 columns.To test the sensitivity of our results to this factor, we repeated our estimation procedure for the VOCbyNO x case, but with the background NO 2 columns estimated using available observational data for other days (12-14 July 2010 instead of 15-19 July 2010 as in the base case).The optimal estimate of α for the test case was found to be only 10 percent larger than for the base case.This result indicates that our BB NO x emission estimates are sufficiently robust with regard to random uncertainties in the background NO 2 column amounts.Furthermore, we investigated whether or not the background NO 2 columns changed significantly over the study period (e.g., due to changes in meteorological conditions or in biogenic emission rates).To this end, we selected data points (grid cells and days) where the simulated NO 2 column amounts originated from fires were infinitesimal (less than 10 −2 % relative to the background NO 2 columns estimated for the same grid cells/days using the OMI data for the period 15-19 July 2010).The selected data were averaged separately over the periods 15-19 July 2010 and 20 July-16 August 2010.As a result, the mean value over the second period was found to be very insignificantly (~6%) lower than that for the first period.This result confirms that uncertainties in our estimates of α due to uncertainties associated with evaluation of the background NO 2 columns are unlikely to exceed the statistical uncertainties represented by the confidence intervals for the values of α opt .
Figure 4 illustrates the performance of our NO 2 simulation using optimized NO x emissions for the VOCbyNO x case.Note that the simulation data for the VOCbyCO case are almost indistinguishable from those in the VOCbyNO x case and are not presented here.The daily time series shown in Figure 4 are the same as those in Figure 1, except that the BB NO x emissions used in the simulation presented in Figure 4 were calculated with the optimal estimate of α (α opt ) instead of its reference value (α r ) as in Figure 1.Compared to the model results obtained with the reference value of α, the performance of the "optimal" simulation is noticeably better.Specifically, the root mean square error (RMSE) has reduced by more than 20% and a considerable difference (~40%) between the mean values of the NO 2 columns from the model and measurements has practically been eliminated.Furthermore, the absolute values of the differences between the daily values of the NO 2 columns from the measurements and simulations have been reduced in the 19 of 28 days considered (after excluding the initial 5 days used for estimation of the background NO 2 columns).A simple statistical test based on the binomial distribution and involving the statistical hypothesis that our inversion results simply in adding random errors to the simulated NO 2 columns confirms that the improvement of the performance of our NO 2 simulations is statistically significant with the probability of type 1 error being less than 0.05.It is noteworthy that the optimization of the NO x BB emissions did not affect a value of the correlation coefficient (r).This observation implies that the correlation coefficient in the given case can be considered as an independent (of α) measure of accuracy of the spatial-temporal field of the BB NO x emissions used in our simulations.
Atmosphere 2016, 7, 132 11 of 20 result, the mean value over the second period was found to be very insignificantly (~6%) lower than that for the first period.This result confirms that uncertainties in our estimates of α due to uncertainties associated with evaluation of the background NO2 columns are unlikely to exceed the statistical uncertainties represented by the confidence intervals for the values of αopt.
Figure 4 illustrates the performance of our NO2 simulation using optimized NOx emissions for the VOCbyNOx case.Note that the simulation data for the VOCbyCO case are almost indistinguishable from those in the VOCbyNOx case and are not presented here.The daily time series shown in Figure 4 are the same as those in Figure 1, except that the BB NOx emissions used in the simulation presented in Figure 4 were calculated with the optimal estimate of α (αopt) instead of its reference value (αr) as in Figure 1.Compared to the model results obtained with the reference value of α, the performance of the "optimal" simulation is noticeably better.Specifically, the root mean square error (RMSE) has reduced by more than 20% and a considerable difference (~40%) between the mean values of the NO2 columns from the model and measurements has practically been eliminated.Furthermore, the absolute values of the differences between the daily values of the NO2 columns from the measurements and simulations have been reduced in the 19 of 28 days considered (after excluding the initial 5 days used for estimation of the background NO2 columns).A simple statistical test based on the binomial distribution and involving the statistical hypothesis that our inversion results simply in adding random errors to the simulated NO2 columns confirms that the improvement of the performance of our NO2 simulations is statistically significant with the probability of type 1 error being less than 0.05.It is noteworthy that the optimization of the NOx BB emissions did not affect a value of the correlation coefficient (r).This observation implies that the correlation coefficient in the given case can be considered as an independent (of α) measure of accuracy of the spatial-temporal field of the BB NOx emissions used in our simulations.1, except that the simulated time series, Cmf, was obtained from the model run using the optimal value of the FRP-to-BBR conversion factor for the VOCbyNOx case.
The spatial distributions of the average (over the study period) NO2 column amounts obtained using the OMI measurements and given by the CHIMERE model are compared in Figure 5a,b.For the comparison purpose, the simulated BB NO2 column amounts (Cmf) calculated with the optimal estimate of the FRP-to-BBR conversion factor for the VOCbyNOx case were added to the background values of the NO2 columns (Cb).Visual comparison of Figure 5a,b reveals that such "composed" data demonstrate a rather reasonable, although evidently imperfect, agreement with the measurement data.In particular, the both two-dimensional fields of NO2 columns exhibit the large-scale negative  1, except that the simulated time series, C mf , was obtained from the model run using the optimal value of the FRP-to-BBR conversion factor for the VOCbyNO x case.
The spatial distributions of the average (over the study period) NO 2 column amounts obtained using the OMI measurements and given by the CHIMERE model are compared in Figure 5a,b.For the comparison purpose, the simulated BB NO 2 column amounts (C mf ) calculated with the optimal estimate of the FRP-to-BBR conversion factor for the VOCbyNO x case were added to the background values of the NO 2 columns (C b ).Visual comparison of Figure 5a,b reveals that such "composed" data demonstrate a rather reasonable, although evidently imperfect, agreement with the measurement data.
In particular, the both two-dimensional fields of NO 2 columns exhibit the large-scale negative gradients in the north-east direction, as well as the "hot spots" around Moscow.There are also the enhancements in the NO 2 column amounts south of Moscow.Quantitatively, a degree of agreement between the NO 2 columns in the corresponding grid cells can be characterized by the correlation coefficient that is found to be of 0.73.This value indicates that the composed data (C mf + C b ) account for about a half of the total variance of the data.The rest of the variance includes, in particular, small scale variability in the both fields, which may partly be due to random uncertainties in C o and C b .A part of the discrepancies between the composed data and the measurements may also be due to errors in the BB emission data as well as due to the limited spatial coverage of the satellite measurements in the situation considered.For example, one of the prominent discrepancies is that spots with high NO 2 columns east of Moscow at approximately 45 • E in Figure 5b,c (which, according to our additional analysis, are mostly due to strong emissions from fires on 26 July) are missing in Figure 5a.This discrepancy may be due to, e.g., mismatches between the MODIS and OMI measurement in space and time: that is, the smoke plumes from the fire spots which were "seen" by the MODIS instruments could be outside the "vision field" of the OMI instrument (at least partly).Nonetheless, the reasonable overall agreement between the data shown in Figure 5a,b provides one more argument in favor of reliability of the results of our analysis.Note that, in accordance to our results shown in Figure 4, a contribution of fires to the tropospheric NO 2 columns is found to be relatively small (see Figure 5c).gradients in the north-east direction, as well as the "hot spots" around Moscow.There are also the enhancements in the NO2 column amounts south of Moscow.Quantitatively, a degree of agreement between the NO2 columns in the corresponding grid cells can be characterized by the correlation coefficient that is found to be of 0.73.This value indicates that the composed data (Cmf + Cb) account for about a half of the total variance of the data.The rest of the variance includes, in particular, small scale variability in the both fields, which may partly be due to random uncertainties in Co and Cb.A part of the discrepancies between the composed data and the measurements may also be due to errors in the BB emission data as well as due to the limited spatial coverage of the satellite measurements in the situation considered.For example, one of the prominent discrepancies is that spots with high NO2 columns east of Moscow at approximately 45°E in Figure 5b,c (which, according to our additional analysis, are mostly due to strong emissions from fires on 26 July) are missing in Figure 5a.This discrepancy may be due to, e.g., mismatches between the MODIS and OMI measurement in space and time: that is, the smoke plumes from the fire spots which were "seen" by the MODIS instruments could be outside the "vision field" of the OMI instrument (at least partly).Nonetheless, the reasonable overall agreement between the data shown in Figure 5a,b provides one more argument in favor of reliability of the results of our analysis.Note that, in accordance to our results shown in Figure 4, a contribution of fires to the tropospheric NO2 columns is found to be relatively small (see Figure 5c).

NO x Lifetime Estimates
The NO x lifetime estimates (τ nox ) obtained in accordance to Equation ( 5) are presented in Figure 6 as a function of α for the two estimation cases ("VOCbyNO x " and "VOCbyCO").Similar to the dependencies of α (n) on α (n−1) that are shown in Figure 3, the dependencies of τ nox on α for the two cases are qualitatively different.Specifically, while the case "VOCbyNO x " features almost constant NO x lifetimes irrespectively of the assumed values of the conversion factor, the values of τ nox obtained for the "VOCbyCO" case are increasing by a factor of 2.1 with the increase of α by a factor of 4. The NO x lifetime values corresponding to the optimal estimates of the conversion factor are 4.2 and 3.1 h for the "VOCbyNO x " and "VOCbyCO" cases.These values are within a rather broad range of lifetimes (2-6 h) assumed in earlier studies of BB NO x emissions [11][12][13][14].
Importantly, the relative difference between the lifetimes calculated for the "VOCbyNO x " and "VOCbyCO" cases is much larger compared to the relative difference between values of α opt (see Figure 3) for the same cases.As mentioned above (see Section 3.1), our estimates of α depend on the ratio of the mean BB NO 2 column amounts and NO x emissions.Since this ratio depends not only on the NO x lifetime but also on the NO 2 /NO ratio, a comparison of the results shown in Figures 3 and 6 indicates that the difference of the lifetimes is counterbalanced by the difference of the NO 2 /NO ratio.

NOx Lifetime Estimates
The NOx lifetime estimates (τnox) obtained in accordance to Equation ( 5) are presented in Figure 6 as a function of α for the two estimation cases ("VOCbyNOx" and "VOCbyCO").Similar to the dependencies of α (n) on α (n−1) that are shown in Figure 3, the dependencies of τnox on α for the two cases are qualitatively different.Specifically, while the case "VOCbyNOx" features almost constant NOx lifetimes irrespectively of the assumed values of the conversion factor, the values of τnox obtained for the "VOCbyCO" case are increasing by a factor of 2.1 with the increase of α by a factor of 4. The NOx lifetime values corresponding to the optimal estimates of the conversion factor are 4.2 and 3.1 h for the "VOCbyNOx" and "VOCbyCO" cases.These values are within a rather broad range of lifetimes (2-6 h) assumed in earlier studies of BB NOx emissions [11][12][13][14].
Importantly, the relative difference between the lifetimes calculated for the "VOCbyNOx" and "VOCbyCO" cases is much larger compared to the relative difference between values of αopt (see Figure 3) for the same cases.As mentioned above (see Section 3.1), our estimates of α depend on the ratio of the mean BB NO2 column amounts and NOx emissions.Since this ratio depends not only on the NOx lifetime but also on the NO2/NO ratio, a comparison of the results shown in Figures 3 and 6 indicates that the difference of the lifetimes is counterbalanced by the difference of the NO2/NO ratio.Exhaustive theoretical interpretation of the dependencies shown in Figure 6 goes beyond the scope of this study.Here, we discuss the chemical mechanisms underlying these dependencies only very briefly.In particular, we note that NOx is mainly removed from the atmosphere in a reaction of NO2 with OH [1].Both OH and NO2 concentrations are typically growing functions of ozone (O3) concentration [1].Our simulation data for O3 and OH concentrations (not presented here) indicate that "hot spots" featuring strong BB emissions typically coincide in space and time with depleted concentrations of these species, as well as with reduced values of NO2/NO ratio.It can be speculated that the behavior of the O3 formation rate is the main factor determining a nearly linear dependence of NO2 concentration on the BB NOx emission rate over the hot spots.Specifically, in the "high NOx limit" (in which OH concentration is relatively small), the O3 formation rate is known to be proportional to the ratio of VOC to NOx concentrations [1] and thus can be expected to be independent of α in the "VOCbyNOx" case.In contrast, the VOC emission rate is independent of α in Figure 6.The effective NO x lifetime (τ nox ) estimated a function of the FRP-to-BBR conversion factor (α) normalized to its reference value (α r ).Black circles depict the NO x lifetime values corresponding to the optimal estimates of α for the two estimation cases ("VOCbyNO x " and "VOCbyCO") considered in this study.
Exhaustive theoretical interpretation of the dependencies shown in Figure 6 goes beyond the scope of this study.Here, we discuss the chemical mechanisms underlying these dependencies only very briefly.In particular, we note that NO x is mainly removed from the atmosphere in a reaction of NO 2 with OH [1].Both OH and NO 2 concentrations are typically growing functions of ozone (O 3 ) concentration [1].Our simulation data for O 3 and OH concentrations (not presented here) indicate that "hot spots" featuring strong BB emissions typically coincide in space and time with depleted concentrations of these species, as well as with reduced values of NO 2 /NO ratio.It can be speculated that the behavior of the O 3 formation rate is the main factor determining a nearly linear dependence of NO 2 concentration on the BB NO x emission rate over the hot spots.Specifically, in the "high NO x limit" (in which OH concentration is relatively small), the O 3 formation rate is known to be proportional to the ratio of VOC to NO x concentrations [1] and thus can be expected to be independent of α in the "VOCbyNO x " case.In contrast, the VOC emission rate is independent of α in the "VOCbyCO" case.Thus the O 3 formation rate is likely to decrease with an increase of α, leading to the observed increase in the NO x lifetime.
Such an interpretation of the results presented in Figure 6 is consistent with the dependencies presented in Figure 3. Indeed, given that the NO x lifetime is almost independent of α in the "VOCbyNO x ", the results shown in Figure 3 for the same case imply that the NO 2 /NO ratio and thus O 3 concentration are also kept nearly constant.On the other hand, the fact that the relative range of the changes of α (n) in the "VOCbyCO" case in Figure 3 is much smaller than that of the changes of τ nox in Figure 6 indicates that the NO 2 /NO ratio decreases with an increase of α in that case: this observation, in turn, implies that O 3 concentration accordingly decreases.

NO x Emission Estimates
We used our optimal estimate of the FRP-to-BBR conversion factor (0.254 kg•s −1 •MW −1 ) for the VOCbyNO x case to calculate NO x emission rates from wildfires in the study region and period.Figure 7 shows the time series of the daily BB NO x emission rates that were obtained by integrating either over all grid cells and hours of a given day or only over selected grid cells/hours that were provided with the OMI NO 2 data.According to our calculations, the "full" emissions tended to increase until 6 August and then started to decrease, consistently with results of other studies [9,19,21,49] that reported on the strong air pollution in the study region in the beginning of August.Two major peaks of the BB NO x emission rate occurred on 4 August and 6 August.A difference between the two time series indicates to what extent the information provided by the OMI retrievals on BB NO x emissions is representative of the whole study period.Evidently, the BB NO x emission rates corresponding to the scenes provided with the OMI NO 2 retrievals represent only a part (around 30%, on the average) of the integral emission rates in the study region and period.Therefore, there is a question whether or not our optimal estimate of the FRP-to-BBR conversion factor is representative (at least, on average) of all fires in the study region.
Atmosphere 2016, 7, 132 14 of 20 the "VOCbyCO" case.Thus the O3 formation rate is likely to decrease with an increase of α, leading to the observed increase in the NOx lifetime.Such an interpretation of the results presented in Figure 6 is consistent with the dependencies presented in Figure 3. Indeed, given that the NOx lifetime is almost independent of α in the "VOCbyNOx", the results shown in Figure 3 for the same case imply that the NO2/NO ratio and thus O3 concentration are also kept nearly constant.On the other hand, the fact that the relative range of the changes of α (n) in the "VOCbyCO" case in Figure 3 is much smaller than that of the changes of τnox in Figure 6 indicates that the NO2/NO ratio decreases with an increase of α in that case: this observation, in turn, implies that O3 concentration accordingly decreases.

NOx Emission Estimates
We used our optimal estimate of the FRP-to-BBR conversion factor (0.254 kg•s −1 •MW −1 ) for the VOCbyNOx case to calculate NOx emission rates from wildfires in the study region and period.Figure 7 shows the time series of the daily BB NOx emission rates that were obtained by integrating either over all grid cells and hours of a given day or only over selected grid cells/hours that were provided with the OMI NO2 data.According to our calculations, the "full" emissions tended to increase until 6 August and then started to decrease, consistently with results of other studies [9,19,21,49] that reported on the strong air pollution in the study region in the beginning of August.Two major peaks of the BB NOx emission rate occurred on 4 August and 6 August.A difference between the two time series indicates to what extent the information provided by the OMI retrievals on BB NOx emissions is representative of the whole study period.Evidently, the BB NOx emission rates corresponding to the scenes provided with the OMI NO2 retrievals represent only a part (around 30%, on the average) of the integral emission rates in the study region and period.Therefore, there is a question whether or not our optimal estimate of the FRP-to-BBR conversion factor is representative (at least, on average) of all fires in the study region.8a,b) correspond to the two respective time series presented in Figure 7. Expectedly, the distribution obtained only with the selected data typically features smaller BB NOx emission rates compared to the one obtained using all the available emission data.Nonetheless, it is important to note that both the coverage and spatial structure of the emission rates shown in the different distributions are rather similar.In particular, both distributions Figure 8 presents the spatial distributions of the BB NO x emission rates averaged over the study period.The two different distributions (shown in Figure 8a,b) correspond to the two respective time series presented in Figure 7. Expectedly, the distribution obtained only with the selected data typically features smaller BB NO x emission rates compared to the one obtained using all the available emission data.Nonetheless, it is important to note that both the coverage and spatial structure of the emission rates shown in the different distributions are rather similar.In particular, both distributions show that there were strong NO x emissions from fires in the regions south-east and east of Moscow as well as around Russia's border with Kazakhstan (near the bottom right-hand corner of the model domain).Furthermore, only 9% of the fire spots (grid cells with non-zero fire emissions) shown in Figure 8a are missing in Figure 8b.Therefore, a comparison of the spatial distributions shown in Figure 8a,b provide evidence that our optimal conversion factor estimate that was used to scale BB NO x emissions rates across the study region is, to a considerable extent, representative of the whole region and period considered.Note that, according to a special test involving splitting the study period into two approximately equal parts, the difference between the optimal values of the conversion factor for those periods was less than the statistical uncertainty of our estimate for the whole period.Although the result of this test provides further evidence in favor of applicability of our optimal conversion factor estimates across the study region and period, the question regarding the representativeness of the conversion factor estimates derived from observations of the limited number of fire scenes still remains and requires further investigations that go beyond of the scope of this study.
Atmosphere 2016, 7, 132 15 of 20 show that there were strong NOx emissions from fires in the regions south-east and east of Moscow as well as around Russia's border with Kazakhstan (near the bottom right-hand corner of the model domain).Furthermore, only 9% of the fire spots (grid cells with non-zero fire emissions) shown in Figure 8a are missing in Figure 8b.Therefore, a comparison of the spatial distributions shown in Figure 8a,b provide evidence that our optimal conversion factor estimate that was used to scale BB NOx emissions rates across the study region is, to a considerable extent, representative of the whole region and period considered.Note that, according to a special test involving splitting the study period into two approximately equal parts, the difference between the optimal values of the conversion factor for those periods was less than the statistical uncertainty of our estimate for the whole period.Although the result of this test provides further evidence in favor of applicability of our optimal conversion factor estimates across the study region and period, the question regarding the representativeness of the conversion factor estimates derived from observations of the limited number of fire scenes still remains and requires further investigations that go beyond of the scope of this study.Figure 9 compares our estimates of the total BB NOx emissions in the study region and period with corresponding estimates obtained using the data of fire emission inventories, such as GFED4.1s[8] and GFASv1.0[9].The GFED inventory is based on satellite measurements of burned area and other parameters from a biosphere model, while the GFAS inventory infers BB emissions from the FRP satellite measurements by using a method similar to one employed in this study.However, unlike our method, where the conversion factor is optimized against atmospheric composition measurements, the GFAS inventory uses conversion factor values calibrated with the GFED data.Thus the GFED4.1sand GFASv1.0inventories are not fully independent, although the spatial structure and temporal variability of regional emission fields provided by these inventories may be significantly different.Our results suggest that both GFED4.1s and GFASv1.0considerably underestimate BB NOx emissions (by 33% and 30%, respectively, relative to our estimate for the VOCbyNOx case) and that the difference between our emission estimate and the respective inventory data cannot be explained by statistical uncertainties in our estimates.This finding is qualitatively consistent with the results of other studies (see, e.g., [19][20][21]36]) where those inventories were found to underestimate emissions of other species (such as CO and aerosol) from wildfires in Russia.It should be kept in mind, however, that the confidence intervals shown in Figure 9 may not fully account for possible biases in our estimates due to several factors mentioned above, including uncertainties in the VOC BB emissions and in background NO2 column amounts, probable negative biases in the satellite NO2 retrievals for the strongly polluted scenes, possible inconsistencies between the NO2 vertical profiles used in the retrieval and predicted by our model, as well as possibly Figure 9 compares our estimates of the total BB NO x emissions in the study region and period with corresponding estimates obtained using the data of fire emission inventories, such as GFED4.1s[8] and GFASv1.0[9].The GFED inventory is based on satellite measurements of burned area and other parameters from a biosphere model, while the GFAS inventory infers BB emissions from the FRP satellite measurements by using a method similar to one employed in this study.However, unlike our method, where the conversion factor is optimized against atmospheric composition measurements, the GFAS inventory uses conversion factor values calibrated with the GFED data.Thus the GFED4.1sand GFASv1.0inventories are not fully independent, although the spatial structure and temporal variability of regional emission fields provided by these inventories may be significantly different.Our results suggest that both GFED4.1s and GFASv1.0considerably underestimate BB NO x emissions (by 33% and 30%, respectively, relative to our estimate for the VOCbyNO x case) and that the difference between our emission estimate and the respective inventory data cannot be explained by statistical uncertainties in our estimates.This finding is qualitatively consistent with the results of other studies (see, e.g., [19][20][21]36]) where those inventories were found to underestimate emissions of other species (such as CO and aerosol) from wildfires in Russia.It should be kept in mind, however, that the confidence intervals shown in Figure 9 may not fully account for possible biases in our estimates due to several factors mentioned above, including uncertainties in the VOC BB emissions and in background NO 2 column amounts, probable negative biases in the satellite NO 2 retrievals for the strongly polluted scenes, possible inconsistencies between the NO 2 vertical profiles used in the retrieval and predicted by our model, as well as possibly insufficient spatial and temporal representativeness of the observational constraints provided by the available NO 2 satellite measurements to BB NO x emissions.Quantitative understanding of these factors and their impacts on BB NO x emission estimates inferred from satellite NO 2 measurements calls for further dedicated studies.
insufficient spatial and temporal representativeness of the observational constraints provided by the available NO2 satellite measurements to BB NOx emissions.Quantitative understanding of these factors and their impacts on BB NOx emission estimates inferred from satellite NO2 measurements calls for further dedicated studies.

Conclusions
In this paper, we examined the feasibility of estimating NOx emissions from wildfires within an inverse modeling approach by using satellite measurements of NO2 columns.For this purpose, we considered the situation of the mega-fire event that occurred in the European part of Russia in July-August 2010.We used the tropospheric NO2 columns available from satellite measurements performed with the OMI instrument along with the NO2 column amounts simulated with the CHIMERE chemistry transport model (CTM) in which emissions of NOx and other species from biomass burning (BB) were taken into account.The BB emissions were calculated using the Fire Radiative Power (FRP) data that were available from the MODIS satellite instrument.The measured and simulated NO2 columns were combined in the framework of a simple inverse modeling method aimed at estimating the conversion factor (α) from FRP to BB rate.BB emissions of individual model species were then calculated using estimates of α and typical emission factors reported in literature.
The focus in our study was given to analysis of the effect of chemical nonlinearities on the relationship between BB NOx emissions and respective NO2 column amounts.While in our study this relationship was simulated with CTM, several previous studies (mentioned in the Introduction) in which BB NOx emissions had been investigated using NO2 OMI measurements, involved explicit quantitative assumptions regarding the dependence of NO2 columns on BB NOx emissions.To test the robustness of such assumptions, we performed several model runs where a typical "reference" value of the conversion factor (and thus the mean BB NOx emission rate) was scaled with a factor ranging from 0.5 to 2.0.The simulations were done for the two cases involving different assumptions regarding emissions of volatile organic compounds (VOCs) and CO.Specifically, in one of the cases ("VOCbyNOx"), VOCs and CO emission rates were scaled in the same way as the NOx emissions, while in another case ("VOCbyCO"), the VOCs and CO emission rates were calculated with the α value inferred in a previous study from ground-based measurements of CO and were kept constant irrespectively of changes in the NOx emission rates.The corresponding linearized relationships

Conclusions
In this paper, we examined the feasibility of estimating NO x emissions from wildfires within an inverse modeling approach by using satellite measurements of NO 2 columns.For this purpose, we considered the situation of the mega-fire event that occurred in the European part of Russia in July-August 2010.We used the tropospheric NO 2 columns available from satellite measurements performed with the OMI instrument along with the NO 2 column amounts simulated with the CHIMERE chemistry transport model (CTM) in which emissions of NO x and other species from biomass burning (BB) were taken into account.The BB emissions were calculated using the Fire Radiative Power (FRP) data that were available from the MODIS satellite instrument.The measured and simulated NO 2 columns were combined in the framework of a simple inverse modeling method aimed at estimating the conversion factor (α) from FRP to BB rate.BB emissions of individual model species were then calculated using estimates of α and typical emission factors reported in literature.
The focus in our study was given to analysis of the effect of chemical nonlinearities on the relationship between BB NO x emissions and respective NO 2 column amounts.While in our study this relationship was simulated with CTM, several previous studies (mentioned in the Introduction) in which BB NO x emissions had been investigated using NO 2 OMI measurements, involved explicit quantitative assumptions regarding the dependence of NO 2 columns on BB NO x emissions.To test the robustness of such assumptions, we performed several model runs where a typical "reference" value of the conversion factor (and thus the mean BB NO x emission rate) was scaled with a factor ranging from 0.5 to 2.0.The simulations were done for the two cases involving different assumptions regarding emissions of volatile organic compounds (VOCs) and CO.Specifically, in one of the cases ("VOCbyNO x "), VOCs and CO emission rates were scaled in the same way as the NO x emissions, while in another case ("VOCbyCO"), the VOCs and CO emission rates were calculated with the α value inferred in a previous study from ground-based measurements of CO and were kept constant irrespectively of changes in the NO x emission rates.The corresponding linearized relationships (predicted by the model) between the NO 2 columns and BB NO x emission rate were used to obtain optimal estimates of α.Furthermore, using results of the same model runs, we evaluated the effective NO x lifetime.
It is found that the available measurement data and simulations yield a reasonable estimate of the conversion factor with a statistical uncertainty (evaluated in terms of the 95th percentile) of about ±20%.The optimal value of the conversion factor for the VOCbyNO x case is estimated to be ~0.25 kg s −1 •MW −1 .This value is about 30% smaller than the respective "reference" estimate (of 0.368 kg•s −1 ) obtained earlier in a laboratory experiment.The optimal estimate for the VOCbyCO case is found to be about 15% larger compared to the estimate for the VOCbyNO x case.Note that the differences between the reference and our estimates of the conversion factor may, in principle, compensate for biases in the NO x emission factors specified in our simulations, since our emission model involves a multiplicative combination of both factors.
Our results indicate that chemical nonlinearities may have considerably different effects on the relationship between BB NO x emissions and NO 2 columns, depending on an assumed ratio of the NO x and VOC emission rates.Specifically, in the VOCbyNO x case, where that ratio was kept constant, both the NO 2 columns-NO x emissions relationship and the effective NO x lifetime were found to be almost independent of variations of an assumed value of the conversion factor α. The effective NO x lifetime for this case was estimated to be ~4.2 h which is within a broad range of NO x lifetimes (2-6 h) assumed in previous studies [11][12][13][14].In contrast, in the VOCbyCO case, both the BB NO 2 columns/BB NO x emission rate ratio and the effective NO x lifetime were found to substantially increase with an increase of the NO x emission rate (scaled uniformly with α).In particular, the effective NO x lifetime was found to increase from ~2.0 to 4.2 h as the conversion factor used in our simulations increased from 0.184 to 0.736 kg•s −1 •MW −1 .These results imply that in a common case where the BB VOC emission rates are not constrained by respective measurements, the NO x lifetime (as well as the relationship between the NO 2 columns and BB NO x emission rates) remains, to some extent, uncertain and the effects of chemical nonlinearities on BB NO x emission estimates cannot be "a priori" disregarded.
The optimized values of the conversion factors were used to estimate the total NO x amount emitted from wildfires in the study region in the period from 15 July to 16 August.Our estimates are found to be at least a factor of 1.4 larger compared to the corresponding values predicted by the GFED4.1sand GFASv1.0fire emission inventories.The differences between our estimates and the inventory data considerably exceed the statistical confidence intervals of our estimates.This result suggests that both of the inventories are likely to underestimate NO x emissions from the Russian 2010 wildfires.However, it should be noted that the statistical confidence intervals for our emission estimates do not necessarily account for all kinds of systematic uncertainties in measurement and simulation data used in our analysis.Such uncertainties may include those in the BB VOC emissions, in background NO 2 column amounts, probable negative biases in satellite NO 2 retrievals for the strongly polluted scenes, as well as biases due to limited spatial and temporal coverage of available NO 2 satellite measurements.Evaluation of these uncertainties goes beyond the scope of this study and should be addressed in future studies.Nonetheless, even in view of the probable uncertainties, we believe that our independent BB NO x emission estimates constrained by satellite measurements are a useful contribution to a practically important research direction dealing with the evaluation of BB emissions, especially taking into account that available data provided by fire emission inventories may also be subject to various poorly known uncertainties.
Estimation of the conversion factor (as explained in the previous section) is based on the analysis of daily time series of spatially averaged NO 2 columns derived from the OMI measurements (C o ) and simulated with the CHIMERE model (C mf ) and involves evaluation of the background fraction (C b ) of the tropospheric NO 2 columns.The corresponding time series are presented in Figure 1, along with the time series of the difference of C o and C b .Examples of underlying daily values of tropospheric NO 2 columns (specifically, on 29 July and 8 August) spatially distributed inside of the study region are shown in Figure 2. Note that values of C mf shown in Figures

Figure 1 .Figure 1 .
Figure 1.Time series of the daily NO2 column amounts averaged over the study region.Co: the tropospheric NO2 columns retrieved from OMI measurements; Cb: a background part of tropospheric NO2 columns; Cmf: the simulated tropospheric column amounts of NO2 from wildfires.The vertical Figure 1.Time series of the daily NO 2 column amounts averaged over the study region.C o : the tropospheric NO 2 columns retrieved from OMI measurements; C b : a background part of tropospheric NO 2 columns; C mf : the simulated tropospheric column amounts of NO 2 from wildfires.The vertical dash-dot lines mark the data for 29 July and 8 August.The RMSE and the correlation coefficient indicated in the figure legend for C b and C mf were calculated relative to C o and C o − C b , respectively.

Figure 2 .
Figure 2. (a,b) Spatial distributions of the tropospheric NO2 columns (10 15 molec.•cm−2 ) derived from the OMI measurements on 29 July and 8 August 2010;(c,d) the tropospheric NO2 column amounts originated from wildfires, according to the simulations using the reference value of the FRP-to-BBR conversion factor.Note that the simulation data were processed with the averaging kernels from the OMI retrievals and are, accordingly, shown only where the measurement data were available.

Figure 2 .
Figure 2. (a,b) Spatial distributions of the tropospheric NO 2 columns (10 15 molec.•cm−2 ) derived from the OMI measurements on 29 July and 8 August 2010;(c,d) the tropospheric NO 2 column amounts originated from wildfires, according to the simulations using the reference value of the FRP-to-BBR conversion factor.Note that the simulation data were processed with the averaging kernels from the OMI retrievals and are, accordingly, shown only where the measurement data were available.

Figure 3 .
Figure 3. Dependence of the FRP-to-BBR conversion factor values optimized under the assumption of linearity of the relationship between the NO2 columns and the BB NOx emission rate on an assumed value of the same conversion factor.The conversion factor values are normalized to their reference value.The dependence is shown for the two estimation cases, "VOCbyNOx" and "VOCbyCO", see Section 2.2.The estimates circumvented by black circles are the optimal estimates (αopt) obtained as a result of the third iteration (that is, with n = 3) of the iterative procedure described in Section 2.2, whereas the other estimates are a result of the initial iteration (n = 1).

Figure 4 .
Figure 4.The same as in Figure1, except that the simulated time series, Cmf, was obtained from the model run using the optimal value of the FRP-to-BBR conversion factor for the VOCbyNOx case.

Figure 4 .
Figure 4.The same as in Figure1, except that the simulated time series, C mf , was obtained from the model run using the optimal value of the FRP-to-BBR conversion factor for the VOCbyNO x case.

Figure 5 .
Figure 5.The spatial distributions of the average (over the study period) NO2 column amounts obtained using the OMI measurements (a); The modeled data that were composed by summing up the simulated tropospheric column amounts of NO2 from fires and the background values of the tropospheric NO2 columns (b); and The simulated tropospheric column amounts of NO2 from fires (c) are also shown separately.

Figure 5 .
Figure 5.The spatial distributions of the average (over the study period) NO 2 column amounts obtained using the OMI measurements (a); The modeled data that were composed by summing up the simulated tropospheric column amounts of NO 2 from fires and the background values of the tropospheric NO 2 columns (b); and The simulated tropospheric column amounts of NO 2 from fires (c) are also shown separately.

Figure 6 .
Figure 6.The effective NOx lifetime (τnox) estimated a function of the FRP-to-BBR conversion factor (α) normalized to its reference value (αr).Black circles depict the NOx lifetime values corresponding to the optimal estimates of α for the two estimation cases ("VOCbyNOx" and "VOCbyCO") considered in this study.

Figure 7 .
Figure 7. Time series of the daily mean BB NOx emission rates that were obtained by integrating either over all model grid cells (see the green curve) or only over selected grid cells that are provided with the OMI NO2 data for a given day (see the brown curve).

Figure 8
Figure8presents the spatial distributions of the BB NOx emission rates averaged over the study period.The two different distributions (shown in Figure8a,b) correspond to the two respective time series presented in Figure7.Expectedly, the distribution obtained only with the selected data typically features smaller BB NOx emission rates compared to the one obtained using all the available emission data.Nonetheless, it is important to note that both the coverage and spatial structure of the emission rates shown in the different distributions are rather similar.In particular, both distributions

Figure 7 .
Figure 7. Time series of the daily mean BB NO x emission rates that were obtained by integrating either over all model grid cells (see the green curve) or only over selected grid cells that are provided with the OMI NO 2 data for a given day (see the brown curve).

Figure 8 .
Figure 8. Spatial distributions of the BB NOx emission rates averaged over the study period.The two different distributions are obtained by averaging either over all model grid cells and hours in the study period (a); or only those grid cells/hours which are provided with the OMI NO2 retrievals (b) and correspond to the green and brown curves in Figure 7, respectively.

Figure 8 .
Figure 8. Spatial distributions of the BB NO x emission rates averaged over the study period.The two different distributions are obtained by averaging either over all model grid cells and hours in the study period (a); or only those grid cells/hours which are provided with the OMI NO 2 retrievals (b) and correspond to the green and brown curves in Figure 7, respectively.

Figure 9 .
Figure 9. Optimal estimates of the total NOx emissions in the study region and period in comparison with corresponding estimates based on the data of the GFED4.1sand GFASv1.0emission inventories.The optimal estimates are shown separately for the two estimation cases, "VOCbyNOx" (i) and "VOCbyCO" (ii).The confidence intervals represent statistical uncertainty evaluated in terms of the 95th percentile.

Figure 9 .
Figure 9. Optimal estimates of the total NO x emissions in the study region and period in comparison with corresponding estimates based on the data of the GFED4.1sand GFASv1.0emission inventories.The optimal estimates are shown separately for the two estimation cases, "VOCbyNO x " (i) and "VOCbyCO" (ii).The confidence intervals represent statistical uncertainty evaluated in terms of the 95th percentile.