Interactive comment on “ Quantification of CO 2 and CH 4 emissions over Sacramento , California based on divergence theorem using aircraft measurements

Response to Reviewer #2: Thank you very much for your efforts on behalf of our paper titled “Quantification of CO2 and CH4 emissions over Sacramento, California based on divergence theorem using aircraft measurements” submitted by Ju-Mee Ryoo, Laura T. Iraci, Tomoaki Tanaka, Josette E. Marrero, Emma L. Yates, Inez Fung, Anna M. Michalak, Jovan Tadic, Warren Gore, T. Paul Bui, Jonathan M. Dean-Day, Cecilia S. Chang. We found Reviewer #2’s comments very useful, and they contribute to improving the


Introduction
The ability to obtain accurate emission estimates of greenhouse gases (GHG) has been highlighted as an important issue for many decades, not only for regulating local air quality but also for assessing national-scale air 65 quality and climate concerns. In particular, urban emissions need to be well-understood because approximately 70 % of anthropogenic greenhouse gas emissions originate from urban areas (International Energy Agency, 2008;Gurney et al., 2009Gurney et al., , 2015. This often causes urban domes with higher GHG mixing ratios than surrounding areas (Oke, 1982;Idso et al., 1998Idso et al., , 2002Koerner and Klopatek, 2002;Grimmond et al., 2004;Pataki et al., 2007;Andrews, 2008;Kennedy et al., 2009;Strong et al., 2011). Therefore, estimating greenhouse gas emissions at a regional scale 70 requires an improved understanding of urban GHG emissions (Rosenzweig et al., 2010;Wofsy et al., 2010a, b).
The commonly used bottom-up inventories derive estimates of direct and indirect emissions of greenhouse gases based on an understanding of emission factors from the constituent sectors (Andres et al., 1999;Marland et al., 1985;Boden et al., 2010;California Air Resources Board, 2015;US EPA, 2016). These estimates rely on monthly or quarterly statistical averages of emission activities and often time-invariant emission factors, which mask 75 behavioral patterns. Recent bottom-up inventory data have improved from coarse estimates by using proxy data to produce fine spatial resolution estimates using specific activity data and emission factors corresponding to each emission source. In contrast, top-down methods (or inverse modeling), in which observed mixing ratios are partitioned into their sources, have also been used for constraining or cross-checking bottom-up emissions (Huo et al., 2009;Zhang et al., 2009;Cohen and Wang, 2014;Fischer et al., 2016;Miller and Michalak, 2017).
As part of the Indianapolis Flux Experiment (INFLUX) project, airborne and tower measurements have been collected throughout Indianapolis to generate an extensive database. Over the western U.S., a legacy network over Salt Lake City has collected measurements of CO2 using surface tower systems for more than a decade (Pataki et al., 90 2005(Pataki et al., 90 , 2007Strong et al., 2011). Results from this extensive dataset have included seasonal variability over years and source apportionment into anthropogenic and biogenic sources. Since current emission inventories do not consider individual characteristics of each city, they have limitations due to their geographical differences in topography, climatology, different source attributions (such as types of industry and agriculture), as well as differences in the measurement and analysis methods.
The flight patterns can be classified into three different categories: 1) single-height transect flight, 2) single screen ("curtain") flight with multiple transects, and 3) enclosed shapes (box, cylinder) (see Fig. S1 in Supplementary Material). Commonly, there are assumptions made in these airborne sampling approaches. First, the 105 single-height transect approach assumes a well-mixed boundary layer. Karion et al. (2013) measured CO2 and CH4 along a single-height transect with an assumption of uniform distribution of trace gases with altitude within the PBL and with time. Turnbull et al. (2011) performed a flux estimate by incorporating detailed meteorological information and transecting an emission plume with an aircraft. These studies also assumed that emissions originate from point sources such as pipes and smokestacks, and travel downwind so that all pollution is reflected on the downwind 110 "curtain" with constant wind speed. Second, the single-screen multi-transect method does not assume a uniformly mixed boundary layer condition but is dependent upon constant wind speed. Without a well-mixed boundary layer assumption, Cambaliza et al. (2014) measured CH4 along multiple height transects downwind of the city of Indianapolis (See Fig. S1a in Supplementary Material). However, they assumed that winds at the time of measurement were the same as at the time of emission (i.e., winds after the methane release were time-invariant).

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Third, the enclosed 3-D shape flights do not presuppose any of the assumptions described above. Gordon et al. (2015) measured various GHG with a stacked box flight pattern, to capture the vertical variation in mixing ratio both upwind and downwind. Tadić et al. (2017) and Conley et al. (2017) accomplished emission estimates by flying a cylinder pattern around an emission source to measure GHG both upwind and downwind for analysis based on the divergence theorem. More recently, Baray et al. (2017) used both a screen flight and box flight approach around oil 120 sands facilities and showed that each flight pattern could be preferred, depending on the types of emissions and spatial characteristics.
The method of extrapolation to unsampled areas can also be a large source of uncertainty. For example, Gordon et al. (2015) demonstrated the significant impact of extrapolation methods over the unsampled, near-surface region on the final emission estimate, unlike Cambaliza et al. (2014) who assumed that the city plume is rarely 125 observed in a transect between the surface and the lowest altitude flight measurement. Assumptions can break down when wind direction and speed vary with time and three dimensional space (see Fig. S1); incorrect use of wind data can result in increased uncertainty and reduction of accuracy. Flux estimates also require an estimate of the planetary boundary layer height (PBLH), an important physical parameter. State-of-the-art atmospheric models and reanalysis products often estimate the PBLH, but substantial differences exist in both models and reanalysis data 130 ). In addition, entrainment from the free troposphere into the planetary boundary layer (PBL) and fluxes from the surface have been ignored in most previous studies. Thus, more careful consideration and understanding of these factors are required for determining emission estimates using any of the three mass balance flight patterns.
The primary goals of this study are: i) to assess the impact of different interpolation and extrapolation methods 135 on the emission estimate, ii) to test the sensitivity of emission estimates to a variety of factors such as wind 5 treatment, background mixing ratios, and different flux estimation methods, and finally iii) to examine the importance of vertical mass transfer on the flux estimates. To address these goals, we present here CO2 and CH4 data collected during two research flights over Sacramento (See Fig. 1a, Fig. S2 in Supplementary Material) for urban (25-40 km) 140 and local scales (< 3 km), and determine emission fluxes using various treatments of wind conditions, background mixing ratios, and vertical mass transfer. The data and methodology are presented in section 2. Calculated CO2 and CH4 fluxes for all flights are shown in section 3. The sensitivities of flux estimates to different treatment of the wind, background, and vertical mass transfer are also investigated. The conclusions of this study are presented in section 4.

Data collection
In situ measurements of CO2 and CH4 were performed as part of the Alpha Jet Atmospheric eXperiment (AJAX) project. As can be seen in Fig Chen et al. (2010) were applied to calculate the dry mixing ratios of CO2 used during this study. The overall uncertainty was determined to be 0.16 ppm for CO2 and 2.2 ppb for CH4 160 Tadić et al., 2014). The Meteorological Measurement System (MMS) measures high-resolution pressure, temperature, and 3-D (u, v, and w) winds (Hamill et al., 2016). The CO2 and CH4 mixing ratios and horizontal wind speed are plotted in Fig. 2.

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Because the lowest flight level was typically between 250 and 380 m above the surface and there were no ground-based measurements along the flight tracks, there is always a gap in measurement data between the surface and the lowest flight altitude. Many studies adopt a well-mixed layer assumption below the lowest flight altitude (Karion et al., 2013), but the unmeasured values can lead to a significant bias and large uncertainties in estimating GHG mixing ratios and fluxes, depending on interpolation and extrapolation schemes, especially at lower altitudes 6 where there are no aircraft data available (Gordon et al., 2015). Thus, here we investigated four methods to extrapolate mixing ratio values to the surface, which are termed 1) constant, 2) exponential, 3) gaussian, and 4) kriged (see Fig. 3). The constant method assumes an elevated plume with a constant mixing ratio. The constant mixing ratio here is derived from the lowest flight measurement: X(t, z) = X(t, zL) for z0 < z < zL, where zL is the lowest flight level. The exponential-fit method assumes an exponential increase of X(t, z) from zL to z0. The 175 gaussian fit method is similar to the exponential fit method, except that the surface-sourced plume dispersion follows a gaussian distribution function. The detailed calculation method is based on Gordon et al. (2015). The kriged fit was applied down to the surface level, extended from the sampled area above.
Figures 3a and 3b show observed and estimated CO2 mixing ratios at several locations over Sacramento on November 18, 2013. These results demonstrate that a large source of uncertainty and difference comes from not only 180 the interpolation between flight levels but also the extrapolation of the data between the lowest flight level and the surface. For example, uncertainty in estimated GHG mixing ratios below the lowest flight level (indicated by the yellow diamond) can be large (up to ~ 20 %). In the worst cases, CO2 mixing ratios span more than 80 ppm at the surface among the methods (Fig. 3b); CH4 ranges > 0.15 ppm. Note that the differences between interpolation schemes where data exists (above ~ 250-380 m) are smaller than the differences between various methods below the 185 lowest flight data. Without ground-based data, a proper choice of extrapolation schemes requires knowledge or presumption of the mixing ratio behavior in this region. Gordon et al. (2015) proposed that the case of elevated sources beneath the lowest flight level is best suited to constant extrapolation of mixing ratio to the surface (blue curve), while a ground-source should be represented with an exponential-fit extrapolation (red).
The various fits rely on different assumptions; the ordinary kriging method (magenta trace in Figs. 3b and 3f) 190 also requires some assumptions (e.g., constant mean, constant variance, second-order stationarity and isotropy, and validity of the theoretical model), but the method leverages spatial and statistical properties of the observations to derive estimates, and seems to be less arbitrary than alternative interpolation/extrapolation methods. We note the similarity between the kriged values and the constant extrapolation method for both CO2 and CH4 (not shown). The gaussian and the exponential extrapolations produce large values below the measurement level, increasing the 195 uncertainty. However, the values above the lowest measurement level are very similar among the different fit methods. This indicates how sensitive the final flux estimate can be depending on the given interpolation and extrapolation method and how much care should be taken when selecting the extrapolation methods when no data is available.

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Because the aircraft flew in a cylindrical pattern around the city, the flight paths were transformed into a polar coordinate system. The path was projected to the surface first and fit into an ellipse using the least squares method to minimize the difference between the measured data and the fitted data. Then, we computed each point using the major and minor axis of the ellipse and parameter t. Each point on the ellipse was represented by a single parameter (t, eccentric anomaly), according to the equations: where a and b are the radius of the major and minor axes of the ellipse, φ is the angle between the X-axis and the major axis of the ellipse, and the parameter t is obtained from Eqn. (1), varying from 0 to 2π. Then, the data was 210 gridded into a two-dimensional plane [t, height].
In order to assess the strengths of a kriging approach to quantifying emissions, two interpolation methods were assessed: interpolation using kriging and interpolation using an exponential weighting function (see Fig. S3). The exponential weighting function at a given point (P) was defined as the weighted average of all the other points where the weights decrease exponentially with distance to P. Both approaches captured the general plume pattern 215 (regions with high and low concentrations of CO2), but the kriging approach did better at capturing individual plume features such as the range and magnitude, while interpolation with the exponential weighting function could not resolve such details. Another benefit of kriging is that it can estimate values at unsampled locations using a weighted average of neighboring samples, thus reproducing the characteristics of the observed values.
Interpolation was performed by the ordinary kriging method (Chilés and Delfiner, 2012), modified from the 220 IDL v8.1 kriging tool to fit an elliptical pattern. We chose ordinary kriging because there is no obvious trend in the data we use. Before kriging, we modeled the variograms for all relevant variables. A variogram (or semivariogram) is a function describing the degree to which the data are correlated as a function of the separation distance between observations. The empirical semivariogram of the data was fit using an exponential variogram model, based upon visual inspection of the experimental variograms. Three parameters were used to fit the theoretical variogram, 225 namely the sill (the expected value of the semivariance between two observations as the lag distance goes to infinity), the range (the distance at which the variogram reaches approximately 95% of the sill), and nugget (representative of measurement error and amount of microscale variability in the data). Variogram modeling was first performed to derive parameters required to obtain ordinary kriged estimates. Various other types of kriging exist in the literature on quantifying greenhouse fluxes (Tadić et al., 2017), but examining their differences is 230 beyond the scope of this study.
We kriged the CO2, CH4, wind, temperature, and pressure observations to obtain both the estimate and the  In Section 3.1 we will first describe the "base case" calculation of fluxes, and in Section 3.2 we report the sensitivity of the fluxes to variations in several aspects of the method.

Base case experiment
Our base case experiment used the entire gridded, enclosed elliptical data curtain using kriging as both the interpolation and extrapolation method. We averaged the measured wind in vertical layers 100 m thick so that air 255 (mass) coming into the cylinder equaled air leaving the cylinder (which we refer to as "mass-balanced wind"). We assigned the background to be the minimum concentration found in each 100 m layer. PBLH was determined as the altitude of the maximum gradient from a vertical profile of potential temperature (Wang et al., 2008)   We determined kriged data for each field from the measured CO2, CH4, wind, temperature, and pressure, and 270 then subtracted background values from the trace gas data at each grid point. To convert the volume mixing ratio [ppmv] to a mass concentration [g m -3 ], the number of CO2 or CH4 molecules were computed based on the ideal gas law using the kriged temperature and pressure. Then, the net mass flow [g m -2 s -1 ] was integrated in the horizontal and vertical directions from the surface up to the top of the cylinder.

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The vertical stretching pattern of CO2 mixing ratios in Fig. 5(d) appears to be due to the large scale difference between the horizontal length (> 120 km) and the vertical length (< 1 km). When we applied our method to the local scale (horizontal scale < 3 km, see Fig. 7), or took a small horizontal portion of the large oval (see Fig. S3 in Supplementary Material), the vertical stretching pattern disappeared.
As shown in the top row of Table 1, we determined urban-scale flux values of 25.6 ± 2.6 Mt CO2 yr -1 and 87.1 295 ± 8.7 Gg CH4 yr -1 for this base case experiment. Note that we do not consider the uptake of CO2 by vegetation, but the biological impact on CO2 flux will be important especially during summer.

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As shown in Fig. 3b, there is a large source of uncertainty and difference due to extrapolation of the data between the lowest flight level and the surface. For example, CO2 mixing ratios span more than ~80 ppm near the surface among the methods (~20%); CH4 ranges > 0.15 ppm (~8%). This implies that a proper choice of extrapolation scheme requires knowledge or presumption of the mixing ratio behavior in this region when there is no ground-based data. Gordon et al. (2015) proposed that the case of elevated sources beneath the lowest flight level is 305 best suited to constant extrapolation of mixing ratio to the surface (cyan curve), while a ground-source should be represented with an exponential-fit extrapolation (red). Note that the differences of the mixing ratio between interpolation schemes where data exists (above ~ 250-380 m) are smaller than the differences of the mixing ratio between various methods below the lowest flight data for both CO2 and CH4.
10 310 While it is important to make the best possible choice among different GHG mixing ratio extrapolations, similar uncertainty in how best to treat the wind below the lowest flight level makes calculations propagating the effect of each extrapolation scheme challenging, and exploration of the isolated impact of the extrapolation of GHG mixing ratios is of limited value. In general terms, and making reasonable assumptions for the estimation of wind, boundary layer height, and background, we expect the sensitivity of calculated flux to the interpolation method is 315 small above the lowest flight level, but the sensitivity of calculated flux to the extrapolation method below the lowest flight level will be more than 20% depending on the usage of wind, leading to difference in the final flux estimate.

Sensitivity of calculated flux to wind treatment
Wind variability and measurement assumptions can lead to errors in the CO2 and CH4 flux estimates (Mays et 320 al., 2009;Cambaliza et al., 2014Cambaliza et al., , 2015Nathan et al., 2015;Karion et al., 2013Karion et al., , 2015, and the way in which winds are estimated and quantified especially matters. To test the sensitivity of fluxes to the treatment of wind, we applied the measured high-resolution (1 Hz) in-situ wind data to the flux calculation in two different ways. We averaged horizontal wind on each vertical level (100 m for the base case, 500 m (not shown), or the whole cylinder as one layer), so that air (mass) coming into the cylinder equaled air leaving the cylinder. We also evaluated the calculated 325 fluxes when the measured wind was used without any averaging (hereafter we refer to it as "raw wind"). In this case, inflow and outflow are not required to be balanced.
For November 18, 2013, the wind was southwesterly at the low altitudes, but it changed its direction to southeasterly as height increased. Figure 6 demonstrates the clear difference in flux estimates when the 2-D raw wind or the mass-balanced wind is used. The right column in Fig. 6 shows that we captured high fluxes when we 330 used the mass-balanced wind (middle and bottom rows), while we were less likely to obtain a strong emission signal when using the raw wind data (top), which might be attributed to an imbalance of inflow and outflow to the cylinder.
The total flux was ~7 times different between wind cases: 3.7 Mt CO2 yr -1 and 13.0 Gg CH4 yr -1 calculated with raw wind, and 25.6 Mt CO2 yr -1 and 87.1 Gg CH4 yr -1 using mass-balanced wind with 100 m vertical average, leading to 86% and 85% difference compared to the base case (see Table 1).

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The importance of wind data on the flux calculation is also seen in local-scale emission calculations, but not as dramatically as in those for the urban scale (see Table 2). For the small cylinder over the landfill site on July 29, 2015, Figure 7 shows the observed and kriged CH4 mixing ratio and the flux estimation using the raw wind and mass-balanced wind over the landfill site. As before, the kriged CH4 is a good representation of the local characteristics of the CH4 field. Reassuringly, the elevated CH4 concentration was reconstructed over 121.19º W, 340 38.52º N, which was close to the nearby landfill (See also Fig. 4, Fig. S6 in Supplementary Material). Considering light wind conditions (< 4 m s -1 ) and high temperature during July, the high flux estimates are attributed to the local emissions. For local-scale, the difference in the flux estimate using the raw wind and mass-balanced wind is relatively small. For example, even when using raw-wind over the landfill, the difference of the calculated flux from base case is ~25 % for CH4, which is about 1/3 smaller than the difference of calculated flux from the base case for 345 11 urban-scale (~ 85%) for CH4. For CO2, when using raw-wind the difference of calculated flux from base case gets larger, but it is still smaller than the difference for urban-scale (See Table 1).
Another interesting finding here is the importance of the vertical averaging effect of wind, which is also shown in Figs. 6 and 7. Even when using the mass-balanced wind, the whole-column-averaged wind can underestimate or overestimate the final flux estimate depending on the situation. Certainly, care needs to be paid when treating wind  Table 1 and Table 2).

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Background values are one of the most important factors in obtaining flux estimates, and theoretically, the background values should be cancelled out for the enclosed-shape mass-balance flight. Here we used several distinct methods to determine background values and calculate emission fluxes for each gas to assess if our method could remove some of the uncertainty due to assigning the background. As in the base case, we used the minimum concentration over the layer height (e.g., 100 m or whole column averaging). In comparison, we also calculated 365 fluxes using the average concentration in each layer as the background. Third, we also tested two different, vertically invariant, constant values.
Tables 1 and 2 show the calculated CO2 and CH4 emission fluxes using two different wind methods and two different background treatments. The rows labeled "min" were generated using the minimum kriged mixing ratio in each altitude band as the background for all data at that level. The rows identified by "avg" used the average mixing 370 ratio in each altitude band as the background on that level.
The bottom two rows of Tables 1 and 2 show the sensitivity of calculated flux to the choice of the background treatment was significant when we used raw wind; the estimate using average concentration for the background closely matched the base case, but using the minimum concentration for the background resulted in significantly different calculated fluxes, as we mentioned earlier. This was true both with the vertical mass transfer (Table 1) and 375 without (not shown). In contrast, when we use the mass-balanced wind, the emission estimates for both CO2 and CH4 are nearly identical for either choice of background treatment. Interestingly, when an average mixing ratio at a given vertical level is used for the background concentration, emission estimates with raw wind are similar to emission estimates with mass-balanced wind. To satisfy mass conservation, we also computed the entrainment flux from the top (z=h) and the surface flux from the bottom of the cylinder (z=0). The data from Table 1 is also shown 380 in Fig. 8 as the non-hatched bars.

Sensitivity of calculated flux to vertical mass transfer
Many previous studies assume that vertical mass transfer can be neglected (Cambaliza et al., 2014;Conley et al., 2017). To quantify the validity of this assumption, we compare in Fig. 8

Sensitivity of calculated flux to the PBLH estimate
We also considered the sensitivity of the calculated flux to the PBLH. The potential temperature profile, which indicates atmospheric static stability and which significantly affects pollutant diffusion, is one of the most common operational methods to determine PBLH. No significant sensitivity was found using several different PBLH detection algorithms, such as the parcel method (the interaction between dry adiabatic lapse rate and temperature), 395 rapid decrease in water vapor , or Richardson number method (Wang et al. 2008). A simple example is shown in Supplementary Material Fig. S5. When we determined the PBLH based on the largest gradient of the vertical profile of the potential temperature, the uncertainty due to PBLH estimate for the urban scale is about ~10 %, and that for the local-scale is about 1-5 %, thus the change of PBLH does not affect the total flux estimate, especially for the local-scale. As seen in Fig. S5, the vertical range of the largest gradient of potential temperature is 400 very small for the local-scale, compared to the urban-scale. This leads us to another important message: the uncertainty can increase when we consider urban-scale flux estimates.

Sensitivity of calculated flux to the closed shape
Our city-wide estimate of about 25.6  2.6 Mt CO2 yr -1 (e.g., using the base case of mass-balanced wind with 405 minimum background concentration) is higher than the result by Turnbull et al. (2011), who reported 13.4 Mt CO2 yr -1 (3.5 MtC yr -1 ) over Sacramento in February 2009 (See Table 3 (Maasakkers et al., 2016), is in good agreement with our whole-cylinder observations. Slight adjustments to the grid boxes we choose from Maasakkers et al. (2016) give a range of 58.8-120.5 Gg yr -1 . Direct comparison between different flux estimates is challenging due to various 425 factors, such as i) differences in the areas covered, ii) differences between bottom-up inventory and top-down estimates, iii) the variance of measurement methods (tower, aircraft, and model), iv) underestimation of the emissions from known sources, v) seasonal and interannual variability, and vi) lack of understanding of unidentified sources. Consideration of these factors will be one of the most important areas for improvement for establishing better emission estimate databases in the future. Here we consider the uncertainty of the kriged CO2 and CH4 mixing ratios as sources of uncertainty in the overall flux estimates. We also consider uncertainty from the wind measurement (Mays et al., 2009;Karion et al., 2015;Tadić et al., 2017), estimation of the PBLH, and vertical fluxes. We did not consider the uncertainty of the 440 grid resolution, measurement error, and the selection of the variogram model (such as gaussian-cosine, linear, exponential, and exponential-bessel variogram), because these all have been shown to be small (< 4%, e.g., Nathan et al. (2015)). We also did not consider the uncertainty of the background in isolation, because this is somewhat coupled to the choice of wind treatment in this study, and the uncertainty is small when we chose the mass-balanced wind. However, in general, the uncertainty of the background can contribute significantly to the overall flux 445 uncertainty, especially for the curtain-shaped mass-balanced flight. The uncertainty can be also impacted by meteorological conditions and distance from the emission sources, which are not considered in this study.
The uncertainty in the kriged results was assessed using the variance (and the standard deviation) of the kriged estimate. By assuming that the errors of each factor are gaussian in nature, each measurement (e.g., CO2 and wind) is independent; we estimate the total uncertainties in the calculated flux by adding the fractional uncertainties of the 450 individual kriged CO2 (or CH4) and winds in quadrature (Nathan et al., 2015). We also added the fractional uncertainty of the PBLH estimates and vertical fluxes in quadrature to the uncertainty of the flux. For urban scales, the fractional uncertainty of fluxes due to kriged interpolation was 4%, PBLH estimation was 10%, and vertical fluxes <1%. For local scales, the fractional uncertainty of fluxes due to kriged interpolation was (35%, 17%), PBLH estimation (1%, <5%), and vertical fluxes (<1%, <1%) over the landfill and rice field, respectively. By including all 455 14 these factors, the overall uncertainty of the emission flux estimate over the urban scales is about 11% for both CO2 and CH4. The overall uncertainties over the local scales for both CO2 and CH4 were about 35% at the landfill site and 18% at the rice field location.
Although we used much more accurate in-situ wind measurements than most past studies for flux calculation, the wind was still the most important variable for the uncertainty of flux estimates, consistent with previous studies.

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This partially stems from the uncertainty in the wind at interpolated locations or the sparsity of the measurements.

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We have estimated CO2 and CH4 fluxes over Sacramento, California, on two days using an airborne in-situ dataset from the Alpha Jet Atmospheric eXperiment (AJAX) project and have tested the sensitivity of emission estimates to a variety of factors. We deployed cylindrical flight patterns of two sizes that differ from common curtain flights to estimate the total flux at urban and local scales. We also applied a kriging interpolation method to the data, capturing the characteristics of the data at both observed and unsampled locations. Then, we tested the 470 sensitivity of flux estimates to the wind treatments (either raw wind or mass-balanced wind) and background concentrations and found these two factors were the dominant factors in determining the total flux uncertainty.
When we used the mass-balanced wind for flux calculation, the sensitivity of the emission estimate to the choice of background was minimal (Table 1). Raw wind produced similar flux estimates when the background mixing ratio was set to the average value on each vertical layer. In contrast, choosing the background as the minimum value 475 observed on each level led to calculated fluxes that were substantially different.
Additionally, we took into account not only the inflow and the outflow through the cylinder around the city, but also the vertical mass transport (e.g., entrainment and surface flux) and tested the sensitivity of the total flux estimate to the vertical mass transfer for both urban and local scales. The winds observed on November 18, 2013 came from the southeast, showing high concentrations of CO2 downwind of industrial facilities. CH4 over a rice 480 field showed lower emission rates than those over the landfill, and this may be due to the relatively high wind, no particular point source, and reduced CH4 emissions as a result of low humidity. Considering the wind speed was much lower in July (especially over the landfill), this indicates that most of the emission was produced from local sources for the July 29, 2015 case.
The advantage of the closed shape (i.e., elliptical in this study) approach over a curtain flight is to make a more 485 precise "total" emissions estimate possible by taking into account all unknown sources of emissions. Regarding the balanced incoming and outgoing fluxes within a closed volume, we suggest that emission estimates using massbalanced wind computed over a closed shape can be beneficial for several reasons. First, the flux estimates calculated using mass-balanced wind show reduced sensitivity to the choice of background. Figure 6 and Tables 1 and 2 show that the background value is one of the major sources of variability in both CO2 and CH4 emission 490 estimates when using raw wind, but not when using mass-balanced wind. Vertical averaging of wind also affects the flux estimate, but the choice of raw wind or mass-balanced wind is more important than the thickness of the vertical averaging for mass-balanced wind on both urban and local scales. Second, when we analyze only a small portion of the large loop (e.g., downtown hot spot region) to mimic the curtain flight style, the final flux estimates are highly sensitive to the background choice no matter how the measured wind data are treated. Thus, we propose that the flux 495 estimates for the closed elliptical loops have a reduced sensitivity to the choice of background values in comparison to the curtain geometry.
The spatial variation of CO2 and CH4 observed in the cylindrical flight pattern measured over Sacramento reveals that there were several local sources throughout the entire city, not only concentrated on the downwind side.
Our sensitivity study reveals that the unbalanced wind varying with time and space may be a source of There are still several issues to be addressed in future studies. First, sector-specific emissions and their 510 uncertainties for CO2 and CH4 need to be further identified (Miller and Michalak, 2017). Second, the variability of emission estimates with season needs to be examined. We expect that the biological impact on CO2 flux by the CO2 uptake by vegetation will be important especially during summer. Finally, understanding the sources of uncertainties in emission estimates, and how different they can be under various meteorological conditions (such as temperature, atmospheric stability) need to be investigated further. In this sense, the changing climate over California makes it 515 harder to predict future emission patterns. The use of aircraft measurements presented here provides a tremendous opportunity to measure the entire urban plume.
This effort is not limited to one particular city. There has been increasing interest in performing inter-city comparisons to validate datasets in a more efficient and adequate manner, to create a uniform database that is useful for emission controls (Urban greenhouse gas measurements workshop, 2016). Given that data are available over 520 several cities which have different conditions, we can test how to obtain emission estimates from several cities.
Differences in the socio-economic, geologic, and industrial characteristics of cities lead to a need to compare emission estimates between them, as together they can contribute significantly to the total GHG emission at national and global scales. Thorough comparison among datasets and a customized sharing system between different research groups will lead to reducing the uncertainty of emission estimates.