Assessing Urban Methane Emissions using Column Observing Portable FTIR Spectrometers and a Novel Bayesian Inversion Framework

Cities represent a large and concentrated portion of global greenhouse gas emissions, including methane. Quantifying methane emissions from urban areas is difficult, and inventories made using bottom-up accounting methods often differ greatly from top-down estimates generated from atmospheric observations. Emissions from leaks in natural gas infrastructure are difficult to predict, and are therefore poorly constrained in bottom-up inventories. Natural gas infrastructure leaks and emissions 5 from end uses can be spread throughout the city, and this diffuse source can represent a significant fraction of a city’s total emissions. We investigated diffuse methane emissions of the city of Indianapolis, USA during a field campaign in May of 2016. A network of five portable solar-tracking Fourier transform infrared (FTIR) spectrometers was deployed throughout the city. These instruments measure the mole fraction of methane in a total column of air, giving them sensitivity to larger areas of the 10 city than in situ sensors at the surface. We present an innovative inversion method to link these total column concentrations to surface fluxes. This method combines a Lagrangian transport model with a Bayesian inversion framework to estimate surface emissions and their uncertainties, together with determining the concentrations of methane in the air flowing into the city. Variations exceeding 10 ppb were observed in the inflowing air on a typical day, somewhat larger than the enhancements due to urban emissions (<5 ppb down15 wind of the city). We found diffuse methane emissions of 73(±22) mol s−1, about 50% of the urban total and 68% higher than estimated from bottom-up methods, albeit somewhat smaller than estimates from studies using tower and aircraft observations. The measurement and model techniques developed here address many of the challenges present when quantifying urban greenhouse gas emissions, and will help in the design of future measurement schemes in other cities. 1 https://doi.org/10.5194/acp-2020-1262 Preprint. Discussion started: 4 January 2021 c © Author(s) 2021. CC BY 4.0 License.


S1 Slanted Total Column Footprints
In order to create total column STILT footprints, model particles were released at altitudes of 25,50,75,100,150,200,300,400,600,800,1000,1500,2000, and 2800 meters relative to the instrument location. The latitude and longitude of the particle release were adjusted based on the solar zenith and azimuth angles at the time of the release. 1000 particles were released from each level.

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The total column air number density is calculated as: where p 0 is air pressure at the surface, N A is the Avogadro constant, g 0 is column-averaged standard gravity, and M air is the average molar mass of air (0.29 kg/mol).
The weighting factor for the footprint from a particle release at altitude z is calculated as: where n(z) is the air number density at altitude z, and ∆z is the thickness of the layer.   is because the emission is spread across a larger ( 10 km x 10 km) grid cell. This highlights the importance of using fine high-resolution inventories and giving special consideration to point sources.

S2 24-hour Background Simulation
Simulations using STILT footprint analysis and the EPA national gridded methane inventory show that the total column back-15 ground concentration can be expected to vary more than one part-per-billion over the course of a day ( Figure S4) due to continental emissions upwind. It is important to note that these values do not include the majority of the background methane (> 1.8 ppm), which is not attributable to emissions immediately upwind. Figure S4. Enhancements in the regional background concentration seen by each sensor site. This was created using the EPA national gridded inventory and STILT footprint analysis using the NAM12km meteorological product.

S3 Wind Error Calculations
In order to assess the uncertainty in the wind speed and direction values in the NAM-12km model, independent aircraft mea-20 surements were analyzed. An example flight path from one of these flights is shown in Figure S5. The distributions of difference between measured and model wind speed are shown in S6.

S4 Transport Error Calculations
In order to determine the effect of transport error, we begin with several assumptions: 1. The two errors that affect transport are errors in horizontal wind speed (w s ) and wind direction (w d ) 25 Figure S7. Footprint with no added transport error. The mean trajectory is shown in black.
2. Both errors can be characterized as having a normal distribution with known variances (σ 2 ws and σ 2 wd ) and are autocorrelated with respect to time, with known time scales (T ws and T wd ).
3. Wind speed and directions are completely correlated with respect to distance. This is an acceptable assumption because the domain of interest is small (≈ 100 km by 100 km) compared to reported error correlation length scales of meteorological products. The mean wind speed, w s (t), and direction, w d (t), can be extracted from the mean particle positions at each time step (x(t), An example footprint, along with mean particle positions at each time step are shown in Figure S7.
We can draw a sample time series for the wind speed error distribution, ε ws . An example is in figure S8.
A sample from the wind direction error distribution (ε wd (t) can also be drawn ( Figure S9) Figure S8. Example wind speed error time series, εws(t), for a particle release going back 7 hours. Figure S9. Example wind direction error time series, ε wd (t), for a particle release going back 7 hours.
The cumulative ground distance (∆x and ∆y) that must be added to each particle at any point in time is the accumulation of the error movements since the release time (t = 0).
These cumulative displacements are shown in Figure S10 45 Figure S10. Cumulative displacement in both the latitudinal (∆y(t)) and longitudinal (∆x(t)) directions. Figure S11. Footprint with added transport error. The adjusted mean transport is shown in red, while the original mean transport is in gray. Figure S7 shows a footprint for a receptor at an altitude of 51 m, where 1000 particles were moved backwards in time for 7 hours. Figure S11 shows a footprint from the same STILT simulation, however each particle's ground position has been shifted every minute to reflect the cumulative wind errors ∆x(t) and ∆y(t).
When the footprint with no added error is multiplied by the prior emissions field, and the contributions from each grid cell added together, this represents the concentration (in ppb) expected at the receptor. When this is done with the footprint with 50 error, there will be a resulting error in the expected concentration.
If this process is repeated a large number of times, each time drawing new time series for ε ws (t) and ε wd (t), the resulting distribution of enhancements will represent the distortion of the true model result due to transport errors. The results of 400 simulations at each of the release altitudes are shown in Figure S12. Figure S12. Density of Enhancements for 400 error simulations at each particle release level.
The errors from each height can be combined using the same pressure weighting scaling factors, w(z), as the footprints: Standard Error at each altitude, and the cumulative error in the column from the ground are shown in Figure S13. The value of σ mod is 0.25 ppb.
Figure S13. Standard error by particle release height and cumulative standard error. The blue points represent the standard deviations of the distributions shown in Figure S12, while the red points represent the cumulative sum of these values after being weighted with scaling factors w(z).