Background Heterogeneity and Other Uncertainties in 1 Estimating Urban Methane Flux : Results from the 2 Indianapolis Flux ( INFLUX ) Experiment 3 4

Abstract. As natural gas extraction and use continues to increase, the need to quantify emissions of methane (CH4), a powerful greenhouse gas, has grown. Large discrepancies in Indianapolis CH4 emissions have been observed when comparing inventory, aircraft mass-balance, and tower inverse modeling estimates. Four years of continuous CH4 mole fraction observations from a network of nine tower-based cavity ring-down spectrometers measuring atmospheric CH4 mole fractions at 39 to 136 m above ground as part of the Indianapolis Flux Experiment (INFLUX) are utilized to investigate four possible reasons for the abovementioned inconsistencies: (1) differences in definition of the city domain, (2) a highly temporally variable and spatially non-uniform CH4 background, (3) temporal variability in CH4 emissions, and (4) the presence of unknown CH4 sources. Reducing the Indianapolis urban domain size to be consistent with the inventory domain size decreases the CH4 emission estimation of the inverse modeling methodology by about 35 % and thereby lessens the discrepancy by bringing total city flux within an error range of one of the inventories. Nevertheless, the inverse modeling estimate still remains about 40 % higher than the inventory value. Hourly urban background CH4 mole fractions are shown to be heterogeneous and temporally variable. Statistically significant, long-term biases in background mole fractions of 2–5 ppb are found from single point observations from most wind directions. Random errors in single point background mole fractions observed for a few hours are 20–30 ppb, but decrease substantially when data are averaged over multiple days. Boundary layer budget estimates suggest that Indianapolis CH4 emissions did not change significantly when comparing 2014 to 2016. However, it appears that CH4 emissions may follow a diurnal cycle with daytime emissions (12–16 LST) approximately twice as large as nighttime emissions (20–5 LST). The strongest CH4 source in Indianapolis is the South Side Landfill. Other point sources, perhaps leaks from the natural gas distribution system, are localized and transient, and do not appear to be a consistently large source of CH4 emissions in Indianapolis. Long-term averaging, spatially-extensive upwind mole fraction observations, mesoscale atmospheric modeling of the regional emissions environment, and careful treatment of the times of day and areal representation of emission estimates is recommended for precise and accurate quantification of urban CH4 emissions.


, errors in atmospheric transport modeling (Hendrick et al., 2016;Deng et al., 2017;76 Sarmiento et al., 2017;), and complexity in atmospheric background conditions (Cambaliza et al., 77 2014;Heimburger et al., 2017). In this work, detailed analysis of urban CH4 mole fractions is 78 performed in the city of Indianapolis to better understand the aforementioned uncertainties of 79 urban CH4 emissions. comprised of in situ aircraft measurements (Heimburger et al., 2017;Cambaliza et al., 2014), in 85 situ observations from communications towers using cavity ring-down spectroscopy (Richardson 86 et al., 2017;Miles et al., 2017), and automated flask sampling systems for quantification of a wide 87 variety of trace gases (Turnbull et al., 2015). Meteorological sensors include a Doppler lidar 88 providing continuous boundary layer depth and wind profiles, and tower-based eddy covariance 89 measurements of the fluxes of momentum, sensible and latent heat (Sarmiento et al., 2017). The 90 network is well suited for emissions estimates using top-down methods such as tower-based 91 inverse modeling (Lauvaux et al., 2016) and aircraft mass balance estimates (Cambaliza et al.,92 reported on the WMO X2004A scale. Flask to in-situ comparisons and round-robin style testing 144 indicated compatibility across the tower network of 0.6 ppb CH4 (Richardson et al., 2017). is available at http://www.nws.noaa.gov/asos/pdfs/aum-toc.pdf. The accuracy of the wind speed 152 is ±1 m/s or 5% (whichever is greater) and the accuracy of the wind direction is 5 degrees when 153 the wind speed is ≥ 2.6 m/s. The anemometer is located about 10 meters AGL. The wind data 154 reported in ISD are given for a single point in time recorded within the last 10 minutes of an hour 155 and are closest to the value at the top of the hour. 156 The planetary boundary layer height (BLH) was determined from a Doppler lidar deployed 157 in Lawrence, IN, about 15 km to the northeast of downtown. The lidar is a Halo Streamline unit,158 which was upgraded to have extended range capabilities in January 2016. The lidar continuously 159 performs a sequence of conical, vertical-slice, and staring scans to measure profiles of the mean 160 wind, turbulence, and relative aerosol backscatter. All of these measurements are combined using 161 a fuzzy-logic technique to automatically determine the BLH continuously every 20-min (Bonin et 162 al., 2018). The BLH is primarily determined from the turbulence measurements, but the wind and 163 aerosol profiles are also used to refine the BLH estimate. The BLHs are assigned quality-control 164 flags that can be used to identify times when the BLH is unreliable, such as when the air is 165 exceptionally clean, the BLH is below a minimum detectable height, or clouds and fog that 166 Atmos. Chem. Phys. Discuss., https://doi.org/10.5194/acp-2019-48 Manuscript under review for journal Atmos. Chem. Phys.

CH4 Sources 171
Only a few known CH4 point sources exist within Indianapolis (Cambaliza et al., 2015, Lamb et 172 al., 2016. The Southside Landfill (SSLF), located near the center of the city, is the largest point 173 source in the city with emissions of about 28-45 mol/s, accounting for 22% to 63% of total Marion 174 County CH4 emissions (Cambaliza et al., 2015;Maasakkers et al., 2016;Lamb et al., 2016). Other 175 city point sources are comparatively small; the wastewater treatment facility located near SSLF 176 contributes approximately 4-10% to city CH4 totals or about 3-7 mol/s, and the transmission-177 distribution transfer station at Panhandle Eastern Pipeline (also known as a city gate and further in 178 this study abbreviated as PEP) is estimated to be about 0.5-1% or 1 mol/s. The remaining CH4 179 sources, mainly from NG and livestock, are considered to be diffuse sources and are not well 180 known. Potential sources of emissions related to NG activities include gas regulation meters, 181 emissions from transmission and storage, and Compressed Natural Gas (CNG) fleets. These 182 diffuse NG sources account for 21-69% or 20-64 mol/s of the city emissions (Cambaliza et al., 183 flux estimate (Cambaliza et al., 2014;Lamb et al., 2016). The CH4 mole fraction enhancement is 190 defined as, 191 "#$%#&"'"#( = *+,#,-#* − /0 (1) where *+,#,-#* is the CH4 mole fraction measured downwind of the source and /0 is the CH4 192 background mole fraction, which can be measured upwind of the source, but this is not necessary. 193 Background, as defined in this body of literature, is a mole fraction measurement that does not 194 contain the influence of the source of interest, but which is measured simultaneously. Because 195 choosing the background involves a degree of subjectivity (Cambaliza et al., 2014;Heimburger et 196 al., 2017) we consider how this choice may influence emission estimates and introduce error, both 197 random and systematic, using data from the INFLUX tower network. where an arc of 45° represents a direction (e.g. winds from N are between 337.5° and 22.5°). 202 Criterion 1 is based on the concept that the lowest CH4 mole fraction measured at any given 203 time is not affected by the city sources and therefore is a viable approximation of the background 204 methane mole fractions outside of the city (Miles et al., 2017;Lauvaux et al., 2016). Given this 205 assumption, the tower with the lowest median of the CH4 enhancement distribution (calculated by 206 assuming the lowest measurement among all towers at a given hour as a background) for each of 207 the wind directions over the November, 2014 through December, 2016 time period is chosen as a 208 background site (Miles et al., 2017). Criterion 2 requires that the tower is outside of Marion 209 County (outside of the city boundaries) and is not downwind of any known regional CH4 source 210 (Fig. 3). For some wind directions, there are multiple towers that could qualify as a background; 211 we pick towers in such a manner that they are different for each criterion given a wind direction 212 in order to calculate the error associated with the use of different but acceptable backgrounds. The 213 towers used for both criteria and for each of the eight wind directions are displayed in Table 1. 214 Quantifying differences between these two backgrounds allows for an opportunity to better 215 understand the degree of uncertainty that exists in the Indianapolis background atmosphere. 216 217

Frequency and bivariate polar plots 218
Frequency and bivariate polar plots are used in this work to gain more knowledge regarding CH4 219 background variability based on criteria 1 and 2, and to identify sources located within the city. 220 To generate these polar plots, we use the openair package (from R programming language) created 221 specifically for air quality data analysis (Carslaw and Ropkins, 2012). Bivariate and frequency 222 polar plots indicate the variability of a pollutant concentration at a receptor (such as an 223 observational tower) as a function of wind speed and wind direction, preferably measured at the 224 location of the receptor or within several kilometers of the receptor. The frequency polar plot is 225 generated by partitioning the CH4 hourly data into the wind speed and direction bins of 1 m s -1 and 226 10° respectively. To generate bivariate polar plots, wind components and are calculated for 227 hourly CH4 concentration values, which are fitted to a surface using a Generalized Additive Model 228 (GAM) framework in the following way, 229 where is the CH4 mole fraction transformed by a square root to improve model diagnostics such 230 as a distribution of residuals, is mean of the response, is the isotropic smoothing function of 231 the wind components and , and is the residual. For more details on the model see Carslaw 232 and Beevers (2013).

Temporal Variability 235
Temporal variability may play an important role in the quantification of urban methane emissions.  We apply a simplified atmospheric boundary layer budget, not to estimate precisely the 243 actual city emissions, but rather to evaluate temporal variability of the emissions. We begin by 244 assuming CH4 emissions % (mass per unit time per unit area) are not chemically active and are 245 constant over a distance ∆ spanning a significant portion of the city. The next assumption is that 246 a CH4 plume measured upwind of the city is well mixed within a layer of depth -. We treat wind 247 speed as constant within the layer for every hour considered. Given the above-mentioned 248 assumptions we can write a continuity equation describing mass conservation of CH4 249 concentration within a box in the following fashion, 250 where / is the CH4 mole fraction upwind of the city (or background), and % is the CH4 251 concentration above the mixed layer (Hanna et al., 1982;Arya, 1999;Hiller et al., 2014). The CH4 concentrations are derived from CH4 mole fractions by approximating average 263 molar density of dry air (in mol m -3 ) within the boundary layer for every hour of the day, where 264 variability of pressure with altitude is calculated using barometric formula and it is assumed that 265 temperature decreases with altitude by 6.5 K per kilometer. The hourly surface data for pressure 266 and temperature is taken from KIND weather station. The difference between concentrations 267 ( − / ) is instantaneous and not lagged, where / represents air parcel entering the city and 268 represents the same air parcel exiting the city (for more details see Turnbull et al., 2015). The CH4 269 enhancements ( − / ) are estimated for daytime by averaging observations spanning 12-16 LST we need to know the approximate area of the city and the distance over which the plume is affected 278 by the city CH4 sources. The area of the city is about 1024 km 2 (the area of Marion County) and 279 the length that plume traverses when it is over the city ranges from 32 to 35 km depending on 280 which downwind tower is used. We assume that CH4 measurements at towers 8 and 13 are 281 representative of a vertically well-mixed city plume as the towers are located outside of the city 282 boundaries and allow for sufficient vertical mixing to occur. For S and SW wind directions tower 283 8 observations are used to represent downwind conditions with background observations coming 284 from towers 1 and 13, respectively (based on Criterion 1 shown in Table 1). For W wind direction, 285 tower 13 observations represent the downwind with background obtained from tower 1. The wind 286 direction is required to be sustained for at least 2 hours, otherwise the data point is eliminated. and emission results from the inverse modeling. However, even the decreased inverse modeling 315 estimate is about 40% higher than the inventory. 316 The subject of the domain is also relevant for airborne mass balance flights because a priori 317 the magnitude and variability of background plume is unknown and could be easily influenced by 318 upwind sources. The issue of background is discussed further in the next section. 319 320

Variability in Background Tower Mole Fraction 321
Comparisons between Criterion 1 and Criterion 2 CH4 mole fraction enhancements as a 322 function of wind direction are visualized using frequency and bivariate polar plots (Fig. 4). To 323 make the comparison as uniform as possible, only data from 12-16 LST are utilized (all hours are 324 inclusive), when the boundary layer is typically well-mixed (Bakwin et al., 1998) autocorrelation is found between 12-16 LST hours, i.e., the hourly afternoon data are correlated to 326 the next hour, but the correlation is not significant for samples separated by two hours or more. 327 Therefore, hours 13 and 15 LST are eliminated to satisfy the independence assumption for hourly 328 samples. Furthermore, we make an assumption that the data satisfy steady state conditions. If the 329 difference between consecutive hourly wind directions exceeds 30 degrees or the difference 330 between hours 16 and 12 LST exceeds 40 degrees, the day is eliminated. Days with average wind 331 speeds below 2 m/s are also eliminated due to slow transport (the transit time from tower 1 to 332 tower 8 is about 7 hours at a wind speed of 2 m/s). 333 Both backgrounds generally agree on the higher CH4 originating from the SW, SE, and E 334 wind directions (Figs. 4c-f); however, the values themselves differ especially when winds are from 335 NW, SW, and SE. As the background difference plots indicate, there is noticeable variability in 336 the magnitudes of the CH4 mole fraction background, where criterion 2, by design, typically has 337 higher background mole fractions. The background differences, at a given hour, suggest that the 338 CH4 field enveloping the city is heterogeneous with differences between towers ranging from 0 to 339 over 20 ppb (Fig. 4g). Because large gradients in CH4 background over the city could pose 340 challenges for flux estimations using top down methods such as inverse modeling and aircraft mass 341 balance, it is imperative to establish whether the background differences vary randomly or 342 systematically and how to choose a background to minimize these errors. background, the mentioned background variability becomes less impactful on results, but because 371 Indianapolis is a relatively small emitter of CH4, the uncertainties due to background are 372 comparatively large. Our random error assessment suggests that the highly variable CH4 emission 373 values of Indianapolis from the aircraft mass balance calculations (Fig. 1)  The images reveal that the most consistent and strongest source in the city is the SSLF. 407 This is most evident from the 40+ ppb CH4 enhancements detected at towers 7, 10 and 11 coming 408 from the location of the SSLF (by triangulation). Enhancements from the landfill appear to also 409 be detectable at towers 2, 4, 5, and 13. Based on these observations it can be concluded that there 410 is no other source in Marion County comparable in strength to the SSLF. A small fraction of the 411 SSLF plume is likely due to the co-located wastewater facility, but the inventory estimates suggest 412 that the wastewater treatment facility is responsible for no more than 7% of this plume (Cambaliza 413 et al., 2015;Massakkers et al., 2016). The PEP, located in the northwestern section of the city, 414 may be partially responsible for a plume of 5-10 ppb at towers 5 and 11. However, the plume is 415 less detectable using the criterion 2 background value that has higher background (using tower 8 416 as a background) from NW wind direction (not shown), adding uncertainty to the true magnitude 417 of the enhancement from this source. The same is true for towers 2 and 13, which have pronounced 418 plumes when winds are from the NW with the criterion 1 background, but when background 2 is 419 used these plumes vanish (not shown). Such inconsistency makes it difficult to attribute these 420 plumes to an urban source. 421 Another important point is the cluster of large enhancements surrounding tower 10 in 2014 422 -2015. Because no other tower sees these enhancements (at least at comparable magnitudes), we 423 believe that these plumes are the result of local NG leaks likely from residential sector of 424 Indianapolis. These plumes are not consistent temporally or spatially as they mostly disappear in 425 2016, potentially indicating that they are transient NG distribution leaks. It is reasonable to 426 hypothesize that NG related CH4 is being emitted by diffuse, small leaks all across the city. 427 However, towers downwind of the city do not see a large or distinct enhancement from the city, 428 especially when compared to the SSLF source. Thus, the diffuse NG source suspected to be twice 429 as large as the SSLF source (Lamb et al., 2016) does not appear to be supported by these data. 430 This finding contradicts conclusions made by Cambaliza et al., (2015), who attributed most of the 431 CH4 emitted by Indianapolis to NG related activities. We hypothesize that the relatively high 432 Indianapolis CH4 emissions (see Fig. 1) reported by Cambaliza et al., (2015) are the result of the 433 low sample size of airborne flux estimates, which is prone to large random errors (see section 3.2). 434 Our results indicate that the main CH4 source in the city is SSLF and that other sources potentially 435 associated with NG distribution are difficult to identify with clarity. This conclusion is in to the domain that is analyzed by inventory and airborne mass balance methodologies (Mays et 445 al., 2009, Cambaliza et al., 2014, Lamb et al., 2016, is 107 mol/s compared to 160 mol/s that is 446 estimated for the larger domain (Hestia inventory domain). This partially explains higher 447 emissions in inverse modeling estimates shown by Lamb et al., (2016); however, 107 mol/s is still 448 about 40-50% higher than what EPA and Lamb et al., (2016) find in their inventories (Fig. 1). 449 The midday Indianapolis atmospheric CH4 mole fraction background is shown to be 450 heterogeneous with 2-5 ppb, statistically significant biases for NW, W, SW, S and SE wind 451 directions. We focus on midday atmospheric conditions to avoid the complexities of vertical 452 stratification in the stable boundary layer. Background random error is a function of sample size 453 and decreases as a number of independent samples increase. Low sample volumes, such as a few 454 hours of data from a single location, are prone to random errors on the order of 10-20 ppb in the 455 CH4 enhancement, similar to the magnitude of the total enhancement from the city of Indianapolis. 456 Longer-term sampling and/or more extensive background sampling is necessary to reduce the 457 random errors. Several days of measurements (e.g. 25 total hours of measurement) would reduce 458 random errors to 3-5 ppb, noticeably smaller than the typical enhancement from Indianapolis samples, the airborne studies converge to an average value of CH4 flux that is close to inventory 462 estimates for Indianapolis (see Fig. 1). 463 Measurement and analysis strategies can minimize the impacts of these sources of error. and aid in interpretation of data collected with moderately complex background conditions. 473 With regard to temporal variability, no statistically detectable changes in the emission rate 474 were observed when comparing 2014 and 2016 CH4 emissions. However, a large difference 475 between day and night CH4 emissions was implied from a simple budget estimate. Night (20-5 476 LST) emissions may be 2 times lower than the emissions during the afternoon (12-16 LST) hours. 477 Because prior estimates of top-down citywide emissions are derived using afternoon-only 478 measurements, overall emissions of Indianapolis may be lower than these studies suggest. This 479 bias may be present in studies performed in other cities as well. Our study suggests that day/night 480 differences in CH4 emissions must be understood if regional emission estimates are to be 481 One final point addressed in this study is the location of major CH4 sources in Indianapolis. 484 Analysis of the INFLUX observation data suggests that inventories for Indianapolis are mostly 485 accurate and that there is likely no evidence of a large, diffuse NG source of CH4 as implied by 486 Lamb et al., (2016). The only major source in the city is SSLF and it is observed at multiple 487 towers. There is evidence for occasional NG leaks, but they appear localized and limited in their 488

strength. 489
Overall, assessment of the CH4 emissions at Indianapolis highlights a number of 490 uncertainties that need to be considered in any serious evaluation of urban CH4 emissions. These 491 uncertainties amplify for Indianapolis since its CH4 emissions are comparable in magnitude to the 492 regional background flow and as our results show it may be difficult at times to distinguish noise 493 in the background from the actual city emissions signal. The evaluation of larger CH4 sources may 494 be easier with respect to separating signal from background. However, all of the points raised in 495 this work will be nonetheless relevant and need to be addressed for our understanding of urban 496 CH4 emissions to significantly improve. References 523 524 Alvarez, R. A., Zavala-Araiza, D., Lyon, D. R., Allen, D. T., Barkley, Z. R., Brandt, A. R., Davis, 525 production in north-eastern Pennsylvania, Atmos. Chem. Phys., 17, 13941-13966, 535 10.5194/acp-17-13941-2017 Bakwin, P. S., Tans, P. P., Hurst, D. F., and Zhao, C.: Measurements of carbon dioxide on very 537 tall towers: results of the NOAA/CMDL program, Tellus, 50B, 401-415, 1998. Lauvaux, T., Mays,K.,Whetstone,J.,Huang,J.,Razlivanov,I.,Miles,N. L.,and 552 Richardson, S. J.: Assessment of uncertainties of an aircraft-based mass balance approach 553 for quantifying urban greenhouse gas emissions, Atmos. Chem. Phys., 14, 9029-9050, 554 10.5194/acp-14-9029-2014, 2014 Carslaw, D. C., and Ropkins, K.: openair -An R package for air quality data analysis, 556

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Error bars show 95% confidence intervals (for more details see above-mentioned articles).