Mobile laboratory measurements provide information on the distribution of

Reducing emissions of short-lived greenhouse gases through regulations has
been considered a potentially viable way to mitigate climate change without
intensively regulating

Comparison of

* Uncertainty range reflects author-reported uncertainty on emission numbers, not necessarily measurement uncertainty. Some authors specify a 95 % confidence interval, others use 1 or 2 standard deviations and others compute upper and lower bounds.

To this end, various independent

Every technique has various advantages and disadvantages related to
operational cost, sampling efficiency, processing time and uncertainty.
These techniques have been used in different ways, from direct point source
emission estimation to area source emission rate estimation, and they use
data that may span a few hours up to years. For example, Kort et al. (2014)
used data spanning over 6 years at 0.33

Approximations of scalar dispersion were investigated as early as the 1930s
and were developed to describe non-reactive pollutant dispersal from
elevated stacks (Sutton, 1932; Bosanquet and Pearson, 1936). As models
improved, the Gaussian plume model was developed assuming that a scalar
concentration has a normal distribution function (Batchelor, 1949; Hilst,
1957). Additional investigation of near-surface conditions where particles
can either deposit to or reflect off the surface led to the current
Gaussian plume analytical model (shown in Eq. 1) to predict scalar
concentrations (

The Gaussian plume model is used to calculate emissions by comparing the
model output to the observations. This can be done in a variety of ways. The
stationary dispersion techniques used by Brantley et al. (2014) and
Foster-Wittig et al. (2015) utilize the model at a single point and relate
changes in concentration to changes in wind direction and thus speed. These
procedures either follow, or are related to, the well-defined U.S. Environmental Protection Agency (EPA)
OTM 33A and are not discussed further (U.S. EPA, 2014). The mobile dispersion techniques
investigated in this study and others (Lan et al., 2015; Rella et al., 2015;
Yacovitch et al., 2015) compare observed concentrations at continuous
downwind

Robust uncertainty analyses of Gaussian emission retrievals are not reported
in most studies, which instead focus on the novel application of the
methods. Yacovitch et al. (2015) reported an asymmetric 95 % confidence
interval on their emission rates of 0.334–3.34

The Gaussian model is attractive as a method for inferring emission rates as it is fast and generalizable with the ability to account for changes in stability, wind speed and source elevation. However, the uncertainties for this method change depending upon how it is implemented and whether it is extended to situations outside the reasonable limits of the generalized form. Such situations would include using the average Gaussian plume model with instantaneous measurements without uncertainty or sensitivity analysis or applications over complex topography. A method for implementation of this technique that identifies best practices and is supported by observations and modeling is needed.

In our study, we combine traditional Gaussian methods, advanced large eddy
simulation (LES) modeling and a controlled release to assess in situ variability
of emission retrievals from

Field data were collected in Pennsylvania during three campaigns in
July 2015, November 2015 and June 2016 using the Princeton atmospheric chemistry
experiment (PACE). PACE is a Honda CR-V that has been modified to
accommodate a roof rack that holds sensors

In addition, at select sites, a tower was set up to measure high-frequency
meteorological data. This tower included a second pair of LI-COR 7500A and
7700 along with a METEK uSonic-3 Class A sonic anemometer to measure the
three-dimensional instantaneous wind vector. The tower was typically set
alongside the road at a height between 2 and 3 m. Initially, the tower was
constructed using a standard tripod, but was later adapted to the bed of a
pickup truck to allow faster deployment. The air flow around the pickup
truck was modeled (using Fluent,

Summary of acquired data and data level.

Unconventional natural gas well pads were selected for sampling using a
pseudo-random method to efficiently isolate sites that could be measured
from public roads with the prevailing wind direction. All datasets were
accessed from the Pennsylvania Spatial Data Access
(

As a source of validation, an experimental controlled release of

The IGM approach has been used extensively as described in Sect. 1.1.
Applied here, the method uses the sampled source location as input to first
identify downwind transects. The peak

As discussed in Sect. 1.1, the comparison between the observations and
modeled output along a downwind transect is used to calculate emission rate.
First, the local background (

Large eddy simulation (LES) is used to simulate the dispersion of

A pseudo-spectral method is used for horizontal spatial derivatives and a second-order finite difference method is used for a vertical spatial derivative with the needed treatments to overcome the Gibbs phenomenon following Li et al. (2016a). The second-order Adams–Bashforth method is used for time integration. The inflow velocity is a turbulent logarithmic profile generated from a separate simulation over homogeneous flat terrain mimicking upwind conditions. The inflow scalar is kept at a constant background concentration.

In total, five sites were simulated in neutral conditions. Most sites were set
up with 1 or 2 m horizontal and vertical grid resolution with a total
simulation domain size of 256 m in

Site layouts showing emitting structures in yellow and the road in
magenta for

Summary of LES site conditions and parameters.

* Controlled release site.

Site layouts are shown in Fig. 3. Sites were simulated for at least 30 min
to allow the simulated turbulence to reach a statistically stationary state,
where the average and standard deviations of the wind and scalars approach a
constant value as shown in Fig. S2. The equations solved in LES are
non-dimensionalized using the friction velocity (

Comparison of instantaneous

LES has been previously used to investigate plume dispersion and is used
here as a reference that represents the best estimate for the “truth” of how
a plume evolves in a turbulent near-neutral environment (Nieuwstadt and de
Valk, 1987; Weil, 1990; Wyngaard and Weil, 1991; Mason, 1992; Weil et al.,
2004). A useful extension of the LES analysis would be to examine the output
as a reference case to understand how sampling the model environment by
taking instantaneous measurements of the concentration fields affects
emission retrievals. The turbulent structures that LES can resolve are
illustrated in Fig. 4, which contrasts instantaneous plumes and averaged
plumes in both the horizontal stream-wise (

The 5–95 % percent difference

Using the LES output, which is saved with 1 Hz resolution to match our
instrument sampling frequency, sample transects were picked from the full
time series, varying the number of repeat transects and their time
intervals. Time intervals of 30 s, 1 min, 2 min and random (meaning the time
interval was not consistent or constrained) were imposed upon the sample
picks and the number of repeat transects ranged from 1 to 70. These
transects were then integrated and used as

Finalized sampling and emission rate calculation strategy employed
in this study showing actual measurements with increasing complexity and
decreasing sample size as well as models with increasing complexity and
decreasing uncertainty. The second column denotes user inputs needed for each
pathway, with different pathways needing more or less inputs and different
types of inputs. For instance, the stability-derived dispersion
coefficients are necessary for level 1 and 2, but not level 3. In this
schematic

Field measurements were designed to target neutral stability found in the
morning and evening with each sampling outing typically lasting 4 h;
this minimizes the errors related to assigning stability and coincides with
LES conditions. Most sites were sampled 1–3 times (denoted as standard
sampling), occasional sites were sampled with

Field campaigns were deployed in the Marcellus Shale spanning northeast and
southwest Pennsylvania. In total, 940 well pads were sampled with standard
sampling, 53 with replicate sampling and 16 sites with intensive sampling.
These replicate sampling sites were generally chosen at the beginning and
end of each 4 h sampling period to observe changes in variability over
the course of the sampling period that may be due to changes in atmospheric
conditions. For the population of standard sampling sites with multiple
passes, the average rsd of emissions from repeat passes was 67 % and the
average maximum percent difference (highest observational deviation from the
mean of repeat measurements) between emission estimates at a single site was
58 %. The average rsd of the population of 53 emissions estimates for the
replicate sampling sites was 77 % and the average maximum percent
difference was 150 %. The rsd of emissions from repeat passes ranged from
12 % to 260 %. These populations offer insight into how sampling
strategy may change estimates of these statistics and offer the chance to
compare real results to the LES results shown in Sect. 3.1. These results
are consistent with the LES results shown in Sect. 3.1 predicting small
numbers of transects will yield an artificially low rsd and more transects
are needed to produce an accurate measure of variability. Additionally, the
lower maximum percent difference for standard sampling is consistent with
the Sect. 3.1 LES results showing few transects will sample more similar
plume structures. While there is a large range in the rsd observed,

Comparisons between the IGM-calculated emission rates and LES output should
be done with care because the LES cannot be scaled to different distances
and wind angles easily. The base scenario for the Gaussian method at all
sites (described in Sect. 2.3) assumes there is only one source at the
1 m elevation well-head location because the well head is the only geolocated
structure in a public database and is the only structure common at every
site. Sites may have varying numbers of well heads, but they are generally
very close together (

To compare to the LES results, the observations were indexed to coordinates
on the 256 by 256 m horizontal LES grid. The resulting transects were
interpolated within the range of observations to account for grid cells with
multiple data points or missing data points. The LES time series spanning

As terminology in boundary layer meteorology can be ambiguous and is not
always used consistently, the specific meaning of “meandering” is discussed
here in the context of the near-field regime applicable to this work. Many
previous boundary layer works have used “meandering” to describe the general
movement of a plume that does not correspond to the time-averaged profile,
meaning it includes all scales of motion (see Venkatram and Wyngaard, 1988).
However, Gaussian models do not simulate large-scale meandering or shifting
wind directions unless these are included in the diffusion coefficients.
Thus, we clarify that large-scale meandering as used in this work
corresponds to the effect of larger (

A theoretical site with an additional plume meandering scale added
shown in a top-down view at 3 m of the

As a conceptual exploration of the effects of the centering of the
Gaussian model on individual plumes (as described in Sect. 2.3), a simulated meandering
plume with a 100 m period and 10

Results from three controlled release experiments for

To investigate whether the difference between the approaches would lead to a significant bias, the results for the controlled release experiments were compared for three approaches: the Gaussian plume centered on each observation that we have employed, the average of the individually simulated Gaussian profiles for multiple observations and a single Gaussian plume that matches the apparent average wind direction (Fig. S3). The results show that all three scenarios are virtually identical. Additionally, the centering of the Gaussian model on the observed plume is expected to be more suitable as suggested by the standard deviations that are 0–20 % lower than results that rely on a single average Gaussian plume. This is likely due to the occurrence of wind conditions that are not symmetrical about the centerline and road geometries that allow for plumes of closer and farther distances. This centering can be thought of as a correction for the apparent conditions not matching ideal conditions in which a single Gaussian plume in the mean wind direction is theoretically appropriate. Yacovitch et al. (2015) also employed Gaussian plume centering to observations on the assumption that the source location was better constrained than the wind direction. Foster-Wittig et al. (2015) explored a similar concept of applying corrections to their methodology, which is based on the EPA OTM 33A protocol (U.S. EPA, 2014), to account for conditions that did not match the assumptions of the EPA protocol. They also observed that the differences between their methods were small. Overall, we expect uncertainty from the methodology we have employed to be constrained by the analysis present here, including using Gaussian model and LES outputs that are not varied based on the observed peak location. It should be noted that this centering may not always be necessary or optimal based on the specific goal of a campaign that might include source localization or atmospheric dispersion quantification.

When centering the observations to the LES (which cannot be modulated to
match apparent changing wind direction in the way the Gaussian model can) the sum
of the horizontal (

Summary of mean emissions from three scenarios
for the controlled
release (

The controlled release experiment (Site 5) utilized three leak rates:

The Gaussian method approach with in situ measured wind agrees quite well with the
release, surprisingly better than the LES. This may be due to the effects of
stability the Gaussian model can account for, but they were not simulated in the LES
where neutral conditions were assumed; this will be further discussed in
Sect. 5.1. In this case, the conditions shifted from slightly unstable to
neutral during the second release, with the friction velocity (an important
scaling parameter for LES) decreasing from 0.21 to 0.10 m s

A comparison of the convergence of the mean plume rate inferred
from the IGM by averaging randomly selected transects for

The controlled release was also used as an observational constraint to
investigate the sampling strategy identified by the LES. This was done by
randomly selecting an increasing number of transects from each release and
comparing the inferred mean release rate using the IGM. The results in
Fig. 10 are in excellent agreement with the LES results pattern seen in
Fig. 5, where the average converges beyond 10 transects. Note that the box plots
correspond to the distribution of means obtained from randomly selecting the
indicated number of transects, not total uncertainties on the means for each
number of transects. This reiterates the importance of the sampling protocol
and also shows the range of results possible if only a limited amount of
transects are used. Additionally, Fig. 10 shows that the IGM rarely
overestimates (

Comparison of three scenarios for Site 3 showing images through
the downwind road plane (

Comparison of mean emission rates using three scenarios from four
sites (

Comparisons between mean emission rates calculated from all available
transects for sites 1–4 are shown in Table 5 and site-specific details are
shown in Table 3. Relatively good agreement is found between the LES
emission retrieval and the SS and MS Gaussian approach for sites 1–4. This
indicated there is consistency in retrieved emissions from a range of
scenarios despite using different amounts of information to set up the
sources. The range of emission retrievals vary within a factor of 2 in
most cases. For sites 1–4, the average percent difference (difference from
average value) between the LES and IGM emissions (SS or MS) was

For this analysis, we have assumed the source to be constant during the time
span of the measurements (typically less than 1 h). This may not be true
for all sites and may be a driver of variability; for instance, tanks are
known to emit sporadically and Goetz et al. (2015) have shown emissions
varying over the course of a few hours. However, it is not clear that there
is a need to quantify emission variability at scales less than 1 h for
most sources as there is a practical limit to the time resolution that can
be included in inventory estimates. We thus expect any changes
in emission rate at

Other sources of uncertainty considered are source location and source
height. While well pads can be a few thousand m

Additionally, as shown in Sect. 4.1 (Fig. 9 and Table 4), inaccurate wind
data can be a potential source of error. Because the modeled

Another important consideration is the assignment of the background value to
calculate plume enhancement. For this work, the background was calculated as
the minimum value from the plume transect because the averaged 1 Hz data
generally showed a uniform background near the plumes. These criteria were
also compared to a scenario where the background was calculated from the
average of the lowest 2 % of observations in a transect with very similar
results again indicating that the background value is very stable. When
comparing samples with repeat transects, the backgrounds identified for each
transect had a median standard error of 5 ppb. When the 5 ppb tolerance is
applied to the same dataset, the median change in calculated flux was
4.4 %. This means that the background is expected to contribute an
additional

The final additional source of uncertainty investigated pertains to
stability. The stability class determines the analytical equation used to
derive the diffusion coefficients, thus affecting the emission rate. By
again comparing a theoretical case, the effect of changing the stability
class by 1 can be seen in Fig. S14. The tolerance of 1 stability class
reflects the fact that the atmosphere does not usually change multiple
stability classes rapidly at a scale of 1–3 h (i.e., a change from class
A to class E would not be feasible). While there are certainly cases where
the atmosphere can change rapidly in this time period (i.e., from class B to
D), generally a miscategorization class difference of at most 1 is expected.
For instance, neutral stability was targeted (Class D) for the

Not investigated here, but potentially very important to uncertainty, is the
effect of terrain including both nonuniform slopes and structures such as
trees. In this analysis, we have intentionally sampled sites that were
determined to be relatively flat and open. All of the sites modeled in this
study follow these criteria, even though not every site in our sample is as
simple. The geometric mean of the absolute terrain slope, defined as the
absolute value of terrain rise over the distance between sources and
observation, for all of our

Sources and magnitude of uncertainty in IGM emission estimates.

Monte Carlo inputs for each uncertainty estimate.

The sources for uncertainty and bias in the Gaussian method measurements discussed
in this analysis are summarized in Table 6. These include the uncertainty in
the Gaussian model diffusion constant by comparing to LES-calculated diffusion
(Sect. 4), uncertainty due to source location and height, and uncertainty due
to wind speed and stability class (Sect. 5.1). In addition, the LES was used
to observe bias in the Gaussian-model-derived concentration distributions (Sect. 4.4)
and the controlled release was used to evaluate bias in both the
Gaussian method and LES results (Sect. 4.3). Finally, the LES was used to determine
the optimum sampling pattern to constrain actual atmospheric variability
(Sect. 3.1 and 3.2). The largest contributor to total uncertainty is
atmospheric variability, the random error induced by insufficient averaging
of the turbulent instantaneous plume. As atmospheric variability is
impossible to separate from other sources of uncertainty, such as wind
speed, it is not surprising that it is the largest source of uncertainty. As
described in Sect. 3.1, the LES-derived atmospheric variability (defined as
the standard deviation of emissions retrieved) is expected to be

Summary of advantages and disadvantages of each technique.

Of the approaches compared in this analysis, the LES results require far
more computational and processing time. Though inputs can be estimated from
other sources (i.e., NOAA), we chose to measure meteorological variables
directly, which contributed to significantly longer measurement time. While
this should be considered best practice when producing computationally
expensive LES outputs, there are no inherent differences between inputs
needed for LES and Gaussian method approaches, and the Gaussian method approach also
benefits from on-site measurements making in-field measurement time
theoretically similar. In practice, the additional setup time for
meteorological instrumentation can increase total measurement time for sites
intended for LES to

Overall, we find LES to be a useful tool to examine the Gaussian method sampling
strategy and sources of uncertainty for mobile laboratory measurements.
Subsampling the LES output generates an optimum sampling pattern of at least
10 transects per site to obtain reliable statistics of measurement
uncertainty due to atmospheric variability, which is the largest source of
uncertainty. When sampling at distances greater than 150 m downwind of
sites, the uncertainty due to source location and height is generally less
than 20 % (for cases where source location is known within 50 m and source
height is known within 10 m). Using the LES and a controlled release, we
confirm that the Gaussian model performs well when in situ winds are
available. The NOAA-estimated winds can be a source of error, but we did not
observe a systematic difference between the NOAA and in situ winds; thus, no
sources of bias using our approach are expected on average. We note that
this result is valid for this general area, and other locations, which have
different challenges and data density, may differ. Area-specific analysis, or
on-site winds, should always be used to reduce bias. LES is therefore not
required for studies where source strength calculation is the main goal and
other complicating factors such as complex topography are not present. The
emission retrievals generally fall within a range of two. From this we use
Monte Carlo analysis to extrapolate that the 95 % confidence interval for
sites with standard sampling (

In addition, our standard sampling uncertainty range is greater than other
Gaussian method approaches with controlled releases which reported 0.28–3.6

While the uncertainty derived for mobile Gaussian plume techniques is large
compared to many other techniques discussed in Sect. 1, it is low enough to
reliably separate normal emissions from extreme emissions that are
orders of magnitude larger. Many emission sources exhibit lognormal
distributions where this condition is met, making mobile sampling a reliable
way to identify extreme emission sites. However, longer sampling time,
reliable mobile wind sampling and visualization of plume distributions are
needed to feasibly constrain this method to under 50 % for routine
measurements. In summary, to facilitate more constrained uncertainty from
other mobile-platform-based Gaussian plume emission estimates, we recommend the
following:

Sites should be isolated to reduce contamination from other sources and be accessible from thoroughfares at least 100 m away.

On-site wind measurement should be collected whenever possible.

Additional data should be collected such as photographs (used here) or IR imagery to precisely locate the sources whenever possible.

Ideally, all sites should use

For experiments where sampling frequency is at a premium, at least one site
per sampling outing should be repeated with

Uncertainty analysis should be a systematic part of the Gaussian method sampling design.

In the absence of other experiments to study measurement uncertainty (controlled releases), the repeat measurements may be a suitable approximation for the minimum expected uncertainty.

A data file containing all the emissions,
limit of detection, uncertainty estimate,
meteorology, site locations and traits including spud date, operator,
production and status is available from DataSpace at Princeton
University (

We would like to thank all members of the fieldwork team including Stephany Paredes-Mesa, Tanvir Mangat and Kira Olander. We would also like to thank Maider Llaguno Munitxa for her help with the mobile tower modeling. We thank the reviewers for their detailed and helpful comments in the review process. We thank LI-COR Biosciences for lending instrumentation used in this campaign. This work was funded by the NOAA Climate Program Office/Atmospheric Chemistry, Carbon Cycle and Climate, no. NA14OAR4310134. Edited by: Steven Brown Reviewed by: Kenneth Davis and one anonymous referee