Quantification of CO emissions from the city of Madrid using MOPITT satellite retrievals and WRF simulations

The growth of mega-cities leads to air quality problems directly affecting the citizens. Satellite measurements are becoming of higher quality and quantity, which leads to more accurate satellite retrievals of enhanced air pollutant concentrations over large cities. In this paper, we compare and discuss both an existing and a new method for estimating urban-scale trends in CO emissions using multiyear retrievals from the MOPITT satellite instrument. The first method is mainly based on satellite data, and has the advantage of fewer assumptions, but also comes with uncertainties and limitations as shown in this paper. To improve the reliability of urban-to-regional scale emission trend estimation, we simulate MOPITT retrievals using the Weather Research and Forecast model with chemistry core (WRFChem). The difference between model and retrieval is used to optimize CO emissions in WRF-Chem, focusing on the city of Madrid, Spain. This method has the advantage over the existing method in that it allows both a trend analysis of CO concentrations and a quantification of CO emissions. Our analysis confirms that MOPITT is capable of detecting CO enhancements over Madrid, although significant differences remain between the yearly averaged model output and satellite measurements (R2 = 0.75) over the city. After optimization, we find Madrid CO emissions to be lower by 48 % for 2002 and by 17 % for 2006 compared with the EdgarV4.2 emission inventory. The MOPITT-derived emission adjustments lead to better agreement with the European emission inventory TNO-MAC-III for both years. This suggests that the downward trend in CO emissions over Madrid is overestimated in EdgarV4.2 and more realistically represented in TNO-MACC-III. However, our satellite and model based emission estimates have large uncertainties, around 20 % for 2002 and 50 % for 2006.


Introduction
During the last decades, global urbanisation has led to an increase in the number of large cities. Several hundred cities currently have more than a million inhabitants. These highly populated cities with dense traffic networks are important sources of many kinds of air pollutants that directly affect the large fraction of the population living there (e.g., Pascal et al. (2013); Kan 20 et al. (2012); Romero-Lankao et al. (2013)). Therefore, global urbanisation increases the need for air quality monitoring and prediction in large cities. Large cities are also important sources of several greenhouse gases (GHGs). A recent development of emission strength. Further, the Relative Difference (RD) quantifies the relative change in the proxy of emission strength between the two time periods.
In our study, the same spatial averaging and wind rotation techniques were used. For the wind data, 3-hourly wind fields were used from the ERA Interim reanalysis project of the European Centre for Medium-Range Weather Forecasts (Berrisford et al., 2009). These fields were averaged at 1°x1°resolution and 60 hybrid sigma-pressure levels from the surface to the top of 25 the atmosphere using the pre-processor that is used for generating wind fields for the global transport model TM5 (Krol et al., 2005). For each day, the wind direction was taken for the grid box in which the city centre of the respective city is located and the time step closest to the local overpass time of MOPITT. An average wind direction was constructed over the lowest 15 hybrid pressure layers of the TM5 model, roughly representing the average wind direction in the planetary boundary layer (PBL) up to about 750 hPa. For every MOPITT overpass, the associated modelled wind direction was recorded. This procedure 30 is close but not identical to P13, who used 0.75°x0.75°data from ECMWF averaged from the surface to 700 hPa.
The urban concentration enhancement was finally estimated according to P13. First, for the total column CO, wind rotations and averages were made for the two periods. The emission proxy in molecules/cm 2 was then calculated as the difference between the average of the five maximum downwind total columns (CO totdownwind i; molec/cm 2 ) minus the average of the 5 Atmos. Chem. Phys. Discuss., https://doi.org/10.5194/acp-2017-418 Manuscript under review for journal Atmos. Chem. Phys. Discussion started: 3 July 2017 c Author(s) 2017. CC BY 3.0 License. five minimum upwind CO total columns (CO totupwind i; molec/cm 2 ) in a 20 km broad band from 100 km upwind to 100 km downwind of the city in the respective period, V d − V u, according to Eq. 3 (from P13): The standard deviations of the 5 highest downwind and of the 5 lowest upwind concentrations were calculated. The sum of these two standard deviations is used as the uncertainty in V d − V u. From V d − V u, the relative difference (RD) between 10 period 1 and period 2 was calculated to estimate the trend in the concentration enhancement. The RD is defined as the change between the two periods with respect to period 1 and is expressed as a percentage.

Emission estimation: WRF optimization
To quantify emissions, additional information is required to determine the relation between emissions and concentrations, involving transport. To take this into account, we combined the satellite data with model data from the Weather Research 15 and Forecast (WRF) model. We minimized the difference between the model and the satellite gridded data by changing the emissions in WRF to find the most probable emissions. The method will be described in more detail in this section.

WRF model
Model simulations of CO over Madrid were performed using the WRF model (http://www.wrf-model.org/) version 3.2.1, with the Advanced Research WRF core (ARW). WRF is a numerical non-hydrostatic model developed at the National Centers for 20 Environmental Prediction (NCEP). It has several choices of physical parameterizations, which allows application of the model to a large range of spatial scales (Grell et al., 2005). For this study we used an updated version of the Yonsei University (YSU) boundary layer scheme (Hu et al., 2013), the Unified Noah land surface model for surface physics (Ek et al., 2003;Tewari et al., 2004), and the Dudhia scheme (Dudhia, 1989) [2000][2001][2002][2003][2004][2005][2006][2007][2008] average MOPITT CO concentration per month is taken over a half-degree zone adjacent to each boundary or the nearest land pixels of MOPITT. The data were interpolated to provide the vertical profile for all vertical layers of WRF. These four, monthly varying, profiles have been implemented into WRF as lateral boundary conditions for CO. This is considered sufficiently detailed, since the background concentrations will be scaled in our optimization technique and no significant background pattern is expected to come with the data, which is also confirmed in section 3.5. The initial 10 concentrations of CO within the domains were set to zero and are expected to adapt quickly to the boundary conditions by lateral transport. Initial and boundary conditions for meteorological parameters were based on data from the NCEP at a 1°x1°s patial and 6-hourly temporal resolution.  In Fig.A1, lower panel, the comparison with these data is shown; the concentrations match also very reasonably for as well the 15 peaks as the yearly patterns, the concentrations do most of the time overlap within 0.1 mg/m 3

Simulation period
To reduce the random noise and to increase the signal from relatively small sources, it is required to average MOPITT data over longer time periods as earlier studies already mentioned (e.g., Clerbaux et al. (2008); Girach and Nair (2014); Deeter et al.
(2014)). Averaging times ranged in these studies from 1 month for the second study to 7 years for the first study; it should 20 be noted, however, that these studies used coarser spatial resolutions. In our study we chose to average 1 year of data, which resulted in quite good comparison with WRF (R 2 =0.75) and a clearly visible enhancement of CO mixing ratio over the city of Madrid. A description of the more detailed test we did that resulted in the use of a period of a year can be found in Appendix B. Since tracer transport in WRF is linear, the CO contribution from Madrid scales linearly with its emission. Because of this, the optimal, i.e., best fit, emission was linked to the inventory emission by a scaling factor (f emis ) of the simulated urban plume: the difference between CO in the emission and background simulation. To make this method easily applicable to other regions and to limit the required WRF computation time, we implemented only direct anthropogenic CO emissions and assumed a uniform distribution of other sources of CO (e.g., direct natural sources and indirect sources of CO such as the atmospheric 5 oxidation of natural and anthropogenic volatile organic carbon compounds and methane from the city or the surrounding forests). To account for these missing sources in the domain, a background correction factor (f back ) was introduced that has no spatial pattern but is simply a multiplication factor of the concentrations in the background simulation.
After a WRF simulation, the WRF data were sampled according to the MOPITT retrievals, the AK matrix and MOPITT a priori profile were applied, and the mixing ratios were gridded on a 2x2 km 2 grid and averaged over the entire column with 10 the oversampling technique of Fioletov et al. (2011), as described in section 2.2 and used in P13. Taking the column value in molec/cm 2 as was done in P13 seemed to be less appropriate here, since the effect of orography would also be influencing the match between the model and satellite. Instead, the whole column average CO mixing ratio was taken to still maximize the available information.
To estimate CO emissions, we used a simple optimization scheme based on Brent's method (Brent, 1973;Press et al., 1992). 15 We minimized the difference between MOPITT and WRF average column mixing ratios by varying f backg and f emis iteratively using Brent's method. Brent's method is a root finding algorithm, which we used to find the minimum of the quadratic cost function J (ppb 2 ), defined in Eq. 4: In this function, n is the number of grid cells within the 200x200 km 2 optimization domain. X mod[i] is the total column 20 average mixing ratio (ppb) in the i th grid cell of the model and X sat[i] the mixing ratio (ppb) in the corresponding MOPITT grid cell. To analyse the robustness of the method, we repeated the optimisation using different data filters to test the sensitivity to retrieval uncertainty, and investigated the effect of optimising the absolute difference instead of the quadratic difference in Eq. 4. Four different filtering criteria were used: 1) Filtering of MOPITT data that were more than three or 2) four standard deviations from the yearly 200x200 km 2 mean MOPITT CO concentration, and filtering of data that were more than 3) three 25 or 4) four standard deviations from the mean difference between WRF and MOPITT. The default procedure was to minimize quadratic differences and filter out differences of more than three times the standard deviation between WRF and MOPITT.
3 Results and discussion

Emission trend estimation and uncertainty based on satellite data only
The first method we used to estimate emission trends from large cities is the one applied before by P13. To estimate the 30 uncertainty in these values, we used both version 5, as in P13, and version 6 of the MOPITT multispectral data in these calculations. 9 Atmos. Chem. Phys. Discuss., https://doi.org/10.5194/acp-2017-418 Manuscript under review for journal Atmos. Chem. Phys. Discussion started: 3 July 2017 c Author(s) 2017. CC BY 3.0 License.
The changes between the 2000-2003 and 2004-2008 periods, used to assess the trend in the emissions, are between +0.2 × 10 17 and −2.4 × 10 17 molecules/cm 2 . This results in negative trends (RDs, see section 2.2) in the order of −48% to −4% for most cities (Fig. 2) and a positive RD of 15% for Delhi and +5% for Madrid. As we attempted to use exactly the same method as P13, with only a slight difference in the use of wind data, our results suggest that the uncertainties of the emission proxies in 10 P13 (0.01-0.1 × 10 17 molecules/cm 2 ) were underestimated. A more realistic uncertainty for the emission proxy should rather be in the order of the mean discrepancy we found, i.e., 0.5 × 10 17 molecules/cm 2 .
Comparisons of the MOPITT V6 data with P13, expected to give small differences due to the different retrieval algorithm of V6 compared to V5, also show rather large differences (Table A1), with an average discrepancy of 0.4 × 10 17 molecules/cm 2 .
When the results of our approach are compared between using V5 and V6 of the data, we find discrepancies between 0.009 × 15 10 17 and 1.04 × 10 17 molecules/cm 2 with an average discrepancy of 0.3 × 10 17 molec/cm 2 . The differences between V5 and V6 with our approach are thus smaller than the individual ones compared to P13, but still not negligible.
For Madrid, using V6, we find a negative trend of −33% (Table A1). The magnitudes of the RDs, see Fig. 2, found in our study are clearly different from those found in P13 and in the case of Sao Paulo the RD even shows an opposite sign (+40% vs. −27% in P13). Using V6, only one of our RDs was within the error range of P13 given for the RD. For V5, only two of the 20 RD estimations were inside the error range given in P13. The RD estimations, however, do agree with an absolute uncertainty of~20% for most cities, so the method still has some value to make a rough estimation of trends in a very simple and fast way.
An explanation for the large discrepancies in RDs, while the V d − V u values are relatively close, is that the absolute changes between the two periods are close to our revised uncertainty estimate, and the RDs are thus almost in the uncertainty range of the method.

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Our results demonstrate that the method described in P13 gives a useful first guess of trends in emission, but also that the robustness of the method is only limited: the emission trends are small in comparison with the uncertainty in the upwind−downwind estimates and they are thus not well resolved by the method. V6 differs from V5 mainly by a correction for the geolocation bias, an updated a priori and different meteorological fields (Deeter, 2013a). In an attempt to better understand the factors limiting the robustness of the approach, we identified a number of limitations inherent to the method, partly based on the differences 30 between MOPITT V5 and V6, which will be discussed in the next section (3.2).

Limitations of the satellite-only approach
When using only satellite data to estimate emission trends, it is important to consider how satellite data are obtained: the maximum a posteriori retrieval is based on a set of measured radiances, a radiative transfer model, and a model-derived a priori profile. The averaging kernel represents the weighing of the measured signal and the a priori information in the retrieved CO profile (see section 2.1). In this section, we will analyse the possible influence of temporal variations in these terms on the 2013, 2014), are not tested here. The influence is however, expected to be negligible, since the total column product is used to estimate emission trends which has a drift of 0.001±0.003% per year for the V5 and 0.003 ±0.002% per year for the V6 multispectral product and the drift is existent in both the upwind and the downwind CO column.

Sampling differences and averaging period
The a priori information that is used in the MOPITT retrievals is the same each year, but accounts for seasonal variation. Close 10 to cities this seasonal variation reflects both the change in emissions over the year, with higher emissions in winter and low emissions in summer and the seasonal cycle of the OH sink, which varies with season and peaks in summer (e.g. Girach and Nair (2014); Lal et al. (2000); Novelli et al. (1998)), leading also to low CO mixing ratios in summer. Because of this, seasonal variations in measurement coverage may bias annual averages. For example, a year with below average cloud cover during summer -so less data filtered out -would lead to a lower annual average CO estimation compared to an average year, even if 15 the CO mixing ratios were exactly the same in those years. However, uneven sampling would not affect the RD calculation as long as the background and the city signal are influenced equally. To investigate the sensitivity of the RD calculation to uneven sampling, we analysed the a priori data for the years 2000-2008. The a priori is a good measure for this, since it is extracted from the retrieval data and therefore sampled in the same way as the retrievals.
When we averaged a priori data, annual mean a priori CO varied by 1×10 1 6-1×10 1 7 molec/cm 2 between years, which is of 20 the same order of magnitude as the long term trends in CO that are estimated with the satellite-only method (Fig. 3, left). The Some recent studies on CO trends over larger regions overcame the uneven sampling problem by de-seasonalizing the data before studying trends (Strode et al., 2016;Girach and Nair, 2014). In our method using the WRF model (see below), the problem of uneven sampling is largely solved as we sample our model according to the availability of satellite data.

Role of the a priori
The a priori information of MOPITT version 6 is based on monthly climatologies, temporally and spatially interpolated to generate a priori values for a specific location and day (Deeter et al., 2014) on a 1°x1°(latitude x longitude) spatial resolution.
This results in a priori fields which are already quite detailed: the a priori data of the eight cities of P13 and Madrid reveal already the location of some of the large cities. The MOPITT V5 and V6 data make use of different a priori information. For all 5 of the cities there are slightly different concentration patterns in the a priori products between these two versions. This raises the question to what extent the differences in emissions trends derived from the two MOPITT versions in Fig. 2 are explained by different a priori. To investigate this in more detail, we compared the emission estimation of the satellite-only approach for the standard and a uniform a priori over the whole domain. From this test, however, we could only find a minor contribution of the a priori to the RD. For Madrid we find, for example, 2% change in RD estimation when a uniform a priori was used,

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for Baghdad we find a 3% change, for New Delhi a 6% change and for Moscow a 2% change. The differences are, however, somewhat larger, i.e. in the order of 5%, when we replace the version 6 a priori with the version 5 a priori data. This last step, however, required the use of the data that was available in both V6 and V5 of the data, leading to a decrease in the amount of data where the estimations were based on. To be sure to look at the effect of the a priori only, we used the WRF model data for the years 2002 and 2006 to calculate the RD with a uniform a priori (the average MOPITT a priori) and the standard MOPITT 15 a priori. From this test, we found a decrease in the RD of only 1.2% when the uniform a priori was used. The change in a priori thus causes around 5% change in RD estimation between version 5 and 6.

Averaging kernel stability
Since the city CO emissions take place in the lowest layers of the atmosphere, the amplitude of the retrieved city signal depends strongly on the sensitivity of the MOPITT retrieval to these altitudes; any temporal change in this sensitivity will influence the The AK trends may not be large but the city CO signal compared to background is not large either. As the CO concentration gradient around sources is largest in the layers near the surface, and lower higher up, the trend in the AK causes an artificial negative trend in the concentration enhancement over cities, biasing the emission trends derived from the satellite-only method. that the stability of the AK is influencing the emission trend estimation using the satellite-only method, which introduces an uncertainty when using satellite data from MOPITT and potentially also other instruments. It should be noted, however, that the averaging kernel is quite specific for each retrieval and replacing it by a corrected AK, as done here, is justified as a sensitivity test but is not considered a solution to the problem, as indicated by the data description paper published in Deeter (2002).

the rotation point selection 10
In the satellite-only approach, a wind rotation technique is applied to calculate upwind − downwind differences. This technique selects a single point in the centre of the city as rotation point. However, we found that the estimated upwind − downwind differences are sensitive to the location of this rotation point, which is problematic since it is hard to tell what the exact centre of a city is. Moving this rotation point for example from the centre defined by Wikipedia to the centre point defined by Google Maps (GM), which differs 0.7-3.9 km for our selected cities -both locations could be equally well defined as centre -gives 15 downwind−upwind differences varying by 0.03 × 10 17 -0.3 × 10 17 molec/cm 2 , corresponding to RDs varying by 8%-25% (Fig.5). As a solution for this problem, we using the weighted emission centre of the city instead of the general centre would be a fairer way to use this method. We tested this for the city of Madrid for the weighted centre point in the TNO-MACC emission inventory and weighted centre point of the EdgarV4.2 emission inventory. We found a positive RD of +3% for the Edgar centre and a negative RD of −4% for the MACC centre, which was located 8 km more southwards. These last estimations are 20 probably better estimations of the real trend, since it uses the centre of the emissions instead of the centre of the buildings, but it also shows that this problem is difficult to solve, since the exact centre of emissions is also not known.
The satellite-only method is thus highly sensitive to the selected location of the rotation point, which introduces a large uncertainty in the estimated emission trends. This outcome is particularly relevant for the use of MOPITT data, because of a location bias in MOPITT version 5, which has been corrected in version 6. This can be an important reason for the differences 25 in emission trends found between V5 and V6. The geolocation bias correction that was used in P13 and our study was slightly different from the correction done for V6 of the data by the MOPITT team (Deeter, 2012). As we saw in this paragraph only a small shift in the location already can change the RD estimation substantially.

Emission estimation based on WRF optimization method
To overcome the limitations of the satellite-only approach and to be able to quantify emissions, we developed a different method in the same way by uneven seasonal sampling. Therefore, its influence on the derived trend is expected to cancel out. The model optimization approach does not need wind rotation, avoiding the uncertainties introduced by this procedure. Likewise, any variation or trend in the AK influences the model in the same way as it does with the measurements. In addition, the model accounts for influences of varying meteorological conditions on the dispersion of the city plume. Besides these advantages of using WRF, there is one notable drawback, which is the computational cost of a simulation covering several years. As explained in the methods section, we do simulations of 1 year; the accompanying R 2 between the gridded oversampled WRF and MOPITT is then 0.75.   It must be noted, however, that our method is quite sensitive to specific settings used in the inversion. To further investigate the robustness of the WRF optimization method a series of sensitivity experiments have been performed, varying the data filtering method (section 2.3.6) and the a priori emissions (using EdgarV4.2, TNO-MACC-II and TNO-MACC-III). The results of these tests are summarized in Fig. 8 (Fig. 9, upper panel). This is quite close to the estimates  (Fig. 9, lower panel), based on the new average value, this is an uncertainty of 56%. The large sensitivity to 10 the a priori emission pattern can be explained by the use of a single scaling factor to optimize the city emissions. Therefore, uncertainties in the emission inventory pattern, for example due to missing sources, are difficult to correct for, using our current

Trend estimation with the WRF optimization method
To infer the trend in CO emissions from Madrid using the WRF optimization method, emissions were optimized for two In all cases, the emission estimation and trend seem to be lower and less negative than emission and trend reported by EdgarV4.2 over Madrid and more similar to the TNO-MACC-III inventory.

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As described in the previous paragraphs, the optimization method combining MOPITT retrievals and WRF model output has advantages over the satellite-only approach, but comes with its own limitations and uncertainties.
An important source of uncertainty is the background optimization. As can be seen in the images in the right most columns of Fig. 6 and 7, considerable differences between MOPITT and WRF remain in the background column mean mixing ratios after optimization. Optimizing the background with a single scaling factor for the whole domain is clearly insufficient to account for the complex pattern of differences between the model and the satellite.
Part of the pattern is probably still related to noise in the MOPITT data, since we did not filter for very low or high values in MOPITT, although they can have an important effect on several cells with the oversampling technique. We performed an 5 additional optimization in which we reduced the spatial resolution by averaging the retrievals and model data to a 20x20 km 2 grid (instead of 2x2 km 2 ) in the domain around Madrid. Using this approach, we find reduced optimal emissions, with differences up to 20% (Table 1, optimization method: 20x20).
Another possible explanation for the remaining differences between the modelled and observed patterns might be other sources of CO, which are not (yet) included in the WRF model, such as the atmospheric oxidation of volatile organic carbon Emission patterns differ between the TNO-MACC and the Edgar inventories (sensitivity 2). The cost function minimum was 35 slightly lower for the simulation with the TNO-MACC-III inventory compared to the simulation that uses Edgar emissions.
The TNO-MACC-III simulation, however, also produces a minimum that is clearly less confined and therefore less robust. the satellite-only method was only able to determine a trend in the emissions. We identified and discussed limitations of the satellite-only technique: it is influenced by sampling differences between years, it is slightly dependent on the a priori information used in the MOPITT retrievals (RD changes~3%-5%), it is influenced by a trend in the averaging kernel (RD 25 changes 5%) and it is strongly dependent on the exact location of the wind-rotation (RD changes up to 25% for locations up to 5 kilometres apart). Our results suggest that the uncertainties of the emission proxies in P13 (0.01-0.1 × 10 17 molecules/cm 2 ) are too optimistic. A more realistic uncertainty for the emission proxy should rather be in the order of the mean discrepancy that we found between our results for V5 of the MOPITT data and P13, i.e., 0.5 × 10 17 molecules/cm 2 . The absolute changes between the two periods in emission proxy are close to our revised uncertainty estimate. This leads to RDs that are very often 30 in the uncertainty range of the method.
Some effort can be made to overcome the largest part of these problems, by e.g., deseasonalizing the data, accounting for the change in AK and using the emission inventory centre for wind rotation of the data. This will probably increase the reliability and robustness of the satellite-only trend estimation. We chose, however, to investigate another method, which also enabled us to quantify the emissions. With this method, we do not suffer from the limitations of the satellite-only approach, as in our approach the model data is sampled according to the satellite data and no wind rotation is required because the model accounts for influences of varying meteorological conditions on the dispersion of the city plume. For the WRF-optimization method, it is needed to average one year of data to sufficiently reduce the noise in the MOPITT retrievals to observe a clear signal from These uncertainties are comparable to our estimated uncertainty in the satellite-only method, but we also note that this new 10 method is able to quantify emissions and that the uncertainties are based on one-year average MOPITT and model data, instead of the 4 and 5 year averages which were used in the satellite-only method. Our relatively simple method can thus be used to make an (approximate) estimation of city emissions. Our study confirms that estimating city CO emissions using MOPITT and WRF is feasible, however, further development of the method is needed to improve precision and robustness. season. WRF was sampled for each individual MOPITT retrieval applying the AK, as described earlier, and a spatial comparison was made between the WRF and MOPITT-derived images of 200x200km 2 over Madrid. For each period the oversampling method was applied to grid the data on this 2x2km 2 grid. The scatterplots of these gridded data are shown in Fig. A6. Each subplot consists of the 10,000 points of this grid (note that for the shorter periods, there are overlapping points, originating from neighbouring grid cells that rely on the same data). Generally, the spatial variation in the WRF column averaged CO 5 mixing ratios is much smaller compared to the MOPITT data, because of the limited precision of the individual data and the smaller variability in the CO signal in WRF. After averaging 10 days and 1 month of data the variability in MOPITT is still much higher than the variability in WRF, R2 values are respectively 0.43 and 0.33. This is probably partly due to the high measurement noise in MOPITT and partly caused by the stability of the model. Using four summer months (JJAS) or one year 710 leads to better results, with R2 values of 0.55 and 0.75 respectively. The period of a year gave clearly the best, and useful, results and was therefore selected for emission estimation. A CO mixing ratio enhancement over the city was also best visible for the yearly period (not shown). Earlier studies already mentioned the need of averaging MOPITT data over longer periods to reduce the random noise and to increase the signal from sources (e.g., Clerbaux et al. (2008); Girach and Nair (2014); Deeter et al. (2014)). Averaging times ranged from 1 month for the second study to 7 years for the first study. It should be noted that 715 these studies used coarser spatial resolutions.