Introduction
The combustion of natural gas in high-efficiency power cycles is cleaner and
produces less climate-warming carbon dioxide gas than the combustion of coal
(Environmental Protection Agency, 2015), which has
led to interest in natural gas as a cleaner alternative to coal for energy
generation. Advances in natural gas extraction technology have led to a
35 % increase in total natural gas production between 2005 and 2013 in the
United States (U.S. Energy Information Administration,
2015). Production is expected to increase by 45 % above 2013 levels by the
year 2040 (U.S. Energy Information Administration, 2015).
A caveat to the promise of natural gas as a lower climate impact energy
source, however, is that leaks of methane during extraction and delivery can
result in climate warming. Methane gas has high global warming potential
(GWP): much higher, for example, than carbon dioxide (CH4 has a GWP of
28 over 100 years, compared with CO2, which has GWP of 1 by definition
Myhre et al., 2013). Above a
low threshold (estimated to be ≈ 3.2 % by
Alvarez et al., 2012) leak rate from well to power plant,
the near-term climate impacts of using natural gas for power generation
become worse than coal (Alvarez et al., 2012; Hayhoe et
al., 2002). Recent system-wide analysis suggests that natural gas sector
leak rates are likely higher than inventory estimates
(Brandt et al., 2014; Zavala-Araiza et al., 2015a). To
achieve the lower climate impacts and greater economic benefits of domestic
natural gas production, it is important to find low-cost methods to detect
and reduce methane leakage (Alvarez et al., 2012).
The current industry practice for leak detection and repair (LDAR) is to
perform infrequent (annual or less for most sites) “spot” checks for
leaks, for example by visual inspection with an optical gas imaging (OGI)
camera. However, recent work has shown that methane concentrations measured
by OGI cameras can be drastically underestimated when conditions are not
ideal, for example under conditions of lower temperature values or higher
wind speeds, or when viewing distances are greater than 50 m
(Ravikumar et al., 2016). Furthermore, spot check
monitoring is inadequate for detection of leaks, given strong evidence for
intermittency of leaks
(Allen
et al., 2013, 2015a; Mitchell et al., 2015; Subramanian et al., 2015). It
has been observed that a small number of facilities leaking at very high
rates – so-called “super-emitters”
(Brandt
et al., 2014; Frankenberg et al., 2016; Rella et al., 2015; Zavala-Araiza et
al., 2015b) – can account for a majority of total emissions
(Allen et al., 2013,
2015a, b; Brandt et al., 2014). These characteristics underscore the
importance of continuous monitoring for leaks over large areas. Field
campaigns with sophisticated atmospheric sampling techniques provide
valuable snapshots of the state of natural gas development facility leaks
(e.g., Brantley et al., 2014;
Karion et al., 2013), but it would be too costly to employ such measurement
strategies for long-term continuous monitoring of most natural gas sector
facilities.
We present and test an atmospheric measurement system coupled with a
statistical inversion approach for detecting and quantifying emissions of
methane. The statistical approach is focused on limiting the occurrence of
false-positive leak detection. The measurement system used to test the
statistical approach is composed of a long-range open-path laser situated in
the center of a field of well sites and a series of retroreflectors around
the perimeter of the field to direct light back to a detector co-located
with the laser. The concentration of trace gases along the open beam path
(defined as the path between the spectrometer–detector system and a
retroreflector) is determined from the species-specific absorption of light
(Dobler
et al., 2015; Flesch et al., 2004; Groth et al., 2015; Hashmonay et al.,
1999; Levine et al., 2016). Many open-path absorption methods for
determining species concentration have been demonstrated
(Akagi
et al., 2011; Dobler et al., 2015; Flesch et al., 2004; Jones et al., 2011;
Nikodem et al., 2015; Wagner and Plusquellic, 2016; Wu et al., 2014). Here
we use a dual frequency comb spectrometer (DCS): a unique broadband,
high-resolution spectrometer that offers very high stability (low drift) and
measurement reproducibility of the trace gas measurement so that
concentrations can be compared across different conditions and times
(Coburn et al., 2018). It was recently demonstrated
that two separate dual frequency comb spectrometers stationed side by side
and measuring the same 1 km outdoor path showed methane concentration
agreement to 0.35 % over a 2-week period under ambient variations in
temperature, pressure, and stability
(Waxman et al., 2017).
In principle, the range of conditions under which two separate dual
frequency comb spectrometers should be comparable is much wider than ambient
conditions, because the concentration retrieval is largely dependent on the
quality of absorption models (which are well-defined under most conditions
experienced at Earth's surface). Previous work also demonstrates that this
method of atmospheric trace gas measurement does not require regular or
traditional calibration
(Coburn et al., n.d.; Rieker et al., 2014; Truong et al., 2016; Waxman et al.,
2017). Laboratory and initial field measurements made with the dual
frequency comb spectrometer indicate extremely high measurement precision (3 ppb or lower) over long (1 km one-way, or 2 km round trip) path lengths
(Coburn et al., n.d.; Rieker et al., 2014; Truong et al., 2016; Waxman et al.,
2017). The combination of low uncertainty and high stability enables new
opportunities for detection and sizing of even very small emissions of
methane (Coburn et al., n.d.). Furthermore, the
demonstration of sensitive methane measurements over kilometer-scale open
paths allows for monitoring methane concentrations over large areas such as
natural gas production, processing, and distribution sites. While frequency
comb measurements have previously been made in laboratory settings, the
recent work of Coburn et al. (n.d.) and the
new work shown here demonstrate the viability of dual frequency comb
spectroscopy in real-world conditions.
We use the dual frequency comb measurements in a series of synthetic data
and field data tests to demonstrate the utility of the observing system and
a novel statistical method for accurately locating one or more point sources
of methane within a large area (4+ km2) using distributed
measurements of methane concentrations and an atmospheric transport model.
Previous studies have used Gaussian plume models with atmospheric
measurements of wind conditions and constituent concentrations to detect
sources (e.g., Hirst et al., 2004), and past
studies have also shown the utility of open-path lasers for measuring
across-plume concentrations for use in the detection of emissions
(Flesch
et al., 1995; McBain and Desjardins, 2005). Here, we present a novel
statistical technique applied to source detection and quantification – with
the goal of minimizing false-positive source identification. The
source-attribution method used here is to apply a non-negative least-squares (NNLS)
fitting technique to solve for methane flux at a series of potential source
locations (e.g., pads, well heads or other components), given a set of
atmospheric observations and knowledge of atmospheric transport
(Leuning et al., 2008). The new
statistical approach, called the non-zero minimum bootstrap method (NZMB),
uses a bootstrapping of model uncertainties to produce an empirical
distribution of source strength for a given well site. Specifically, the
empirical distribution is obtained by performing multiple atmospheric
inversions (or estimates of surface fluxes using atmospheric data) using a
set of resampled atmospheric measurements. The NZMB method establishes a
criterion by which well sites or facilities are identified as having
non-zero methane emissions based on examination of the minimum value of an
ensemble of inversions. That is, a potential leak site is positively
identified as a source of methane to the atmosphere when the empirical
cumulative distribution of likely source strengths (determined with a series
of bootstrap operations) does not include a minimum threshold flux such as
zero. Similarly, a facility is identified as not leaking when the empirical
cumulative distribution of likely source strengths does include the minimum
threshold flux (that is, the minimum value of all bootstrap operations is,
for example, zero). By defining a specific null value for each potential
leak, this approach reduces the incidence of false-positive leak
identification (the incorrect attribution of a methane source to a
non-leaking facility or well), compared with the same tests that do not use
the NZMB method (the “non-bootstrap” approach). For comparison, we run the
same series of tests with the non-bootstrap approach, which approximates
emissions using a single NNLS fit.
Synthetic data tests are performed that assess the effects of increasing
measurement density (4, 8, 16, 32, and 64 beams) and the effects of
increasing model–data mismatch (that is, combined uncertainty in the ability
to simulate observations arising from measurement, transport, and other
sources). Field tests with atmospheric observation data are performed in a
3 km × 2.5 km field site located in north-central Colorado over the course of
1 day in January 2017. The meteorological conditions (wind speed, wind
direction, atmospheric stability) on this day are typical of wintertime and
annual mean conditions measured near the field site (for example, compared
with conditions at nearby weather station KCOLONGM30). Field measurements
are made along a series of three beams extending from a spectrometer in the
middle of the domain.
We define leak identification success as maximizing the incidences of leaks
found, with a minimal occurrence of false-positive source identification,
enabling quick response to leaks and avoiding costly mobilization of repair
teams due to false-positive leak identification. The ability to correctly
ascertain the absence of a leak is therefore of equal importance to the
ability to find leaks for regulatory compliance applications of this method.
With the above tests, we therefore seek to determine (1) whether methane
point source emissions can be detected and sized under conditions of
observational uncertainty (model–data mismatch) and background variation;
(2) whether the absence of a leak can be ascertained in an outdoor field
setting; (3) whether the NZMB method allows for leaks to be positively
identified under scenarios of greater simulated model–data mismatch
uncertainty, compared with the non-bootstrap method; and (4) whether a higher
number of observations increases likelihood that the NZMB and non-bootstrap
methods can positively identify leaks. The success of the synthetic and
field data tests demonstrates the potential of this observing system for
continuous monitoring applications, such as for natural gas facilities, and
for providing emission source locations and their approximate strengths. The
experiments here also demonstrate the potential for this technology to be
used for other source estimation and monitoring applications, for example
carbon sequestration.
Methods
Gaussian plume atmospheric transport model
In both the synthetic and real data tests, atmospheric transport is
simulated using a Gaussian plume model, using Pasquill–Gifford
parameterization of plume dispersion in the lateral and vertical directions
(Green
et al., 1980; Griffiths, 1994; Hanna et al., 1982). Micrometeorology in the
boundary layer is a non-trivial source of uncertainty for characterization
of atmospheric flow, and the Gaussian plume model represents a simplified
representation of atmospheric transport and dispersion. It is used to
characterize the mean state (or steady state) of source–receptor
relationships with a point source, as long as the transport time from source
to receptor is comparable to the data averaging time
(Gifford, 1976; Hirst et al., 2004). More
sophisticated plume (e.g., AERMOD) or stochastic Lagrangian dispersion
models (e.g., WindTrax) and stability parameterizations would be expected to
provide more robust representations of the wind shear and inhomogeneities in
turbulence in the atmospheric surface layer
(Flesch et al., 1995;
Perry et al., 1994; Wilson and Sawford, 1996). We select the simplified and
low-computational-cost plume model for assessment of the NZMB method as a
baseline test rather than implementing more advanced representations of
transport. Future campaigns aimed at quantification of true emissions will
benefit from an assessment of the drawbacks inherent in Gaussian plume model
characterization of atmospheric transport or use of a more sophisticated
model, particularly for measurements made at short range.
For the synthetic data tests, the choice of transport model is largely
trivial, given that the transport is considered “perfect”. Field data are
collected with a constant methane source to the atmosphere and a measurement
averaging time that is comparable to the source-to-receptor travel time,
such that the Gaussian plume model is a simplified but appropriate choice of
transport model (Gifford, 1976; Hirst et
al., 2004). Because the purpose of this study is to confirm or reject the
basic methodology and not to investigate the impacts of micrometeorological
representation on flux estimation, we find the plume model to be sufficient
as a baseline test (see Sect. 6).
Neglecting influence of background methane concentrations, Eq. (1) shows the
relationship between fluxes and atmospheric concentrations
(e.g., Leuning et al., 2008):
c=x×c/xmodeled,
where the n×1 vector c is the atmospheric concentration of the
constituent of interest, and n is the number of measurements. The vector
x is m× 1 sources of the constituent (flux units), where the size of
m is equal to the number of potential source flux locations. Here, the vector
of fluxes, x, is the emission rate of methane from each potential
source location. In the synthetic tests and field tests described here,
multiple measurements are made on each beam, such that n is always greater
than m. The value (c/x)modeled is the transport
operator matrix describing the relationship between the point source
emission and concentrations at observation points (spectrometer beams) under
different meteorological conditions, derived using the Gaussian plume model,
and commonly written as H (that convention will be followed here; see Sect. 2.5.3 for details on scaling from point source, to point
concentration, to line-averaged concentration).
Dual frequency comb spectrometer for long-range open-path methane
detection
Dual frequency comb spectrometer measurements are made by transmitting light
from the spectrometer through open air at a discrete set of wavelengths
where methane absorbs light. The light is transmitted in the direction of a
retroreflector, which can be placed 1+ km away
(Coburn
et al., n.d.; Rieker et al., 2014; Truong et al., 2016; Waxman et al.,
2017). The retroreflector directs light back toward a detector co-located
with the spectrometer. The amount of light that is absorbed by methane
yields a direct measurement of the average concentration of methane along
the open path from spectrometer to retroreflector. The measurements
presented here are part of the first campaign to measure atmospheric
concentrations with a fielded dual frequency comb spectrometer
(Coburn et al., n.d.). The temporal resolution of
measurements is related to averaging time: as averaging time increases,
measurement precision increases, until such time that atmospheric CH4
variability begins to erode measurement repeatability (see Sect. 4.1). The
spatial resolution of the measurement depends on beam length, which is
easily adjusted by moving retroreflectors closer to or further away from the
spectrometer, and beam width, which scales with telescope diameter.
Flux estimation with non-negative least-squares fitting solution
We use the NNLS algorithm in Fortran-90 to
solve for a flux rate (that is, the emission rate from each potential source
location), given atmospheric observations (synthetic or real) and
atmospheric transport influence functions (Lawson and
Hanson, 1995). This algorithm iteratively solves for the best-fit m×1 vector of
fluxes, x (see Sect. 2.1 for a description of x), given an
n×1 vector of data measurements, y, and an n×m matrix of influence
functions, H. Given H and y, the NNLS algorithm
computes a vector x (methane emission rate at each well site) that
solves the least squares problem:
Hx=y,subject tox>=0.
Uncertainties in x and y are not included in the NNLS fit;
model–data mismatch is used only in generation of the synthetic
observations and not as a control on the solution for x. The NNLS
algorithm returns the solution vector, x, and also allows for the
calculation of Hx, an n×1 vector describing the expected atmospheric
concentration given H and the solution for x.
Non-zero minimum bootstrap analysis
The non-zero minimum bootstrap analysis, or NZMB, is a statistical test of
the null hypothesis (Hypothesis0) that the source strength at a given well site is
equal to 0 kg s-1. It is used here to estimate source strengths in both
the synthetic and field data tests. Whereas bootstrapping methods and
least-squares methods are not novel techniques and have previously been
applied to problems of source strength estimation, we develop the present
methodology with the motivation to seek a solution for fluxes in which the
incidence of false-positive source attribution is limited
(Efron, 1979; Lawson and Hanson, 1995).
For each of m potential source locations, the null hypothesis
(Hypothesis0) is that there is no methane emission from that potential source
location, and the alternative hypothesis (Hypothesis1) is that there is a
(non-zero) emission from that potential source location:
Hypothesis0:xj=0(j=1,…,m),Hypothesis1:xj>0(j=1,…,m).
Given that model–data mismatch uncertainty is not zero (i.e., there is
uncertainty in the exact relationship between atmospheric observations and
surface fluxes due to transport, measurement, and other uncertainties), it is
not expected that the NNLS fit of Hx to y is exact,
although the problem is overdetermined (that is, n > m). We
therefore use the mismatch between Hx and y to create an
empirical distribution function describing the confidence interval of the
fit to the data and to accept or reject the null hypothesis claim that we
have enough evidence to claim that a particular source is not leaking. That
is, the empirical fit to the data is used to quantify uncertainties
associated with the model–data mismatch (including, for example, instrument
and measurement uncertainties, transport uncertainties, and model
uncertainties) rather than relying on a “bottom-up” estimation of those
sources of uncertainty. We rely on the assumption that model–data mismatch
uncertainty has an un-biased Gaussian distribution. Although biases in
transport or other sources of uncertainty can exist, we suggest that
investigation of that contingency is suited for future studies.
The method for employing the bootstrap analysis is as follows. We first
solve for surface-to-atmosphere fluxes of CH4, x, using NNLS,
as described in Sect. 2.3. Second, for each observation, yi (i= 1, …, n), we calculate the residual values from the fit to the
NNLS solution:
ei=yi-y^i,
where y^i (i= 1,…,n) are the individual values in
the vector Hx. The values of y^i (i= 1,…, n) are the “predicted” change in atmospheric methane given the NNLS
solution for x, or the change in atmospheric methane that is
simulated by convolving the source–receptor matrix, H, with
x.
The next step in the NZMB method is, for each observation, yi (i= 1,…, n), to generate a new estimate of that observation by using
Eq. (3) to sample from the vector of the residuals of the fit to the
atmospheric data, e (with replacement, meaning a given value can
be sampled more than once), and adding that randomly selected ei value
to the predicted observation value, y^i, to create ybi
(Efron, 1979). That is, for each observation vector, y,
we create a new vector, yb (b denotes a bootstrapped value):
ybi=y^i+ebi.
We perform this step 1000 times, resulting in 1000 vectors yb,
or 1000 different sets of observations of the form {ybi,…,ybn}, where ybi=y^i+ebi.
For the field data, we apply a moving block bootstrap
(Künsch, 1989) because residuals of
observations made nearer together in time are more likely to be
co-representative, whereas residuals of observations made further apart in
time are likely to be less representative due to changes in wind conditions
and atmospheric stability. We calculate the autocorrelation in time of the
residuals resulting from a single non-negative least-squares fit and use for
the moving block window length a value 2 times the lag time at which the
autocorrelation falls below the 95 % confidence level. As there is no time
dimension in the synthetic data case, we do not apply the moving block
bootstrap to those cases.
Next, we use NNLS to solve for x for each of the 1000 resampled
sets of observations, yielding 1000 individual solutions for x. The
final step in the NZMB method is to apply the non-zero-minimum criterion to
the 1000 bootstrap solutions for each member of x. For each
possible source location, we find the minimum value from the 1000-member
bootstrap analysis. The non-zero-minimum criterion states that if the
minimum bootstrap value for a given well location is 0 kg s-1, then the
source location is classified as having a leak rate of 0 kg s-1 (i.e.,
no leak). This criterion establishes, under the null hypothesis, whether or
not 0 (< 0 is not possible since a non-negative least-squares fit is
used) is included in the domain of the empirical cumulative distribution
function with non-zero mass, described by the 1000 solutions for each well
site in x. If zero is included in this distribution, then the null
hypothesis (x=0) cannot be rejected. Conversely, if 0 is not
included in the empirical cumulative distribution function for a given well
site (xj), then the null hypothesis can be rejected and it can be
assumed that the well site is leaking. We use a large number of bootstrap
members (1000) to ensure that the law of large numbers (LLN) is met. LLN
justifies that when the number of bootstrap operations is large, the
bootstrapped leak mean approaches the estimated leak from the sample (i.e.,
the bootstrapped leak mean is a consistent estimator of the estimated leak),
and the distribution of the bootstrapped leak approaches the probability
distribution of the source strength. Thus, we can claim that the
bootstrapped estimator is a good candidate of the estimated leak from the
NNLS and that the empirical cumulative distribution function is an
approximation of the true cumulative distribution function.
After having identified which source locations are non-zero sources to the
atmosphere (leaking), the mean leak strength is estimated as the mean of the
1000 bootstrap solutions for that source location. Uncertainty in the
strength of the true leak is calculated as the standard deviation of the
1000 bootstrap solutions at the true leak location.
This method requires little additional computational cost over the
non-bootstrap NNLS approach, because additional runs of the transport model
are not required, only additional NNLS fits using resampling of the
observations. The NZMB approach has the benefit of reducing false-positive
solutions while also gathering information regarding the parameters of the
assumed Gaussian distribution.
Synthetic data tests and results
“True” leak locations and strengths
To prepare synthetic data testing of the NZMB method, we randomly distribute
20 possible leak source locations within a theoretical 2 km × 2 km domain.
This is a reasonable approximation of well density based on high-production
regions of the western United States (average well density across the
Marcellus and Haynesville shale gas plays is 3+ wells km-2). In the
synthetic tests, therefore, m= 20. Of the 20 well sites in the domain, we
simulate a scenario in which two source locations are leaking. The “true”
leak rate at well site number 6 is 4.5 × 10-5 kg s-1 and the “true” leak
rate at well site number 19 is 3.0 × 10-5 kg s-1. The remaining 18 well
sites are assigned “true” leak rates of 0 kg s-1 (Fig. 1). The two
non-zero leak strengths are very small: roughly half the size of the
smallest leaks found by Rella et al. (2015) in a survey of oil and natural
gas well pads. The height above ground level of each leak is 1 m.
Synthetic test observation area: 2 km × 2 km domain with 20 source
locations (black dots) at randomly distributed x and y locations (position
shown on x and y axes). Of 20 point sources, well site 6 (x= 750, y= 750)
and well site 19 (x= 650, y= 1750) have non-zero source strengths (shown
on the z axis).
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Idealized meteorological conditions for synthetic data tests
The meteorological data used for synthetic data tests include many wind
directions and a variety of wind speeds during the sampling of each beam in
the domain, representing an ideal scenario for the generation of as many
independent measurements of the leak strength as possible. Leak strengths
are constant through time, such that the time dimension of the meteorology
does not need to be considered. This approach assumes that enough time has
passed for all meteorological conditions to have occurred during the
sampling of each beam, a condition that eliminates complications in
comparing synthetic cases with different beam orientations. The idealized
meteorological field applies 216 unique wind conditions to all beams: three
wind speeds (2, 3, and 6 m s-1) from 72 directions
(from 5 to 360∘, in 5∘
increments). The conditions represent a situation in which, over a long
period of time, many different wind conditions yield a variety of different
measurements downwind of emissions. Given the simple beam configuration
presented here, which is independent of potential source locations, increasing
the number of measurement conditions improves the conditioning of the
problem (Crenna et al., 2008; Flesch et al., 2009).
Measurement system configuration and synthetic observations
The “synthetic” atmospheric measurements are simulated based on the dual
frequency comb spectrometer observing system described in Sect. 2.2. The
spectrometer is located in the center of the domain, at x= 1000 m and y= 1000 m (Fig. 2). Configurations of 4, 8, 16, 32, and 64 beams per
spectrometer–detector system are tested. In all beam configurations,
retroreflectors are placed at an equal distance (1000 m) from the
spectrometer and at equal distances from neighboring retroreflectors (e.g.,
Fig. 2). The hub-and-spoke beam configuration is a simple and repeatable
pattern for comparison of different numbers of beams. The height of the
spectrometer and retroreflectors is 3 m above ground level (m a.g.l.). Figure 2 shows
beams, beam end point locations (retroreflectors), and the spectrometer in a
case with 16 beams.
Map view of synthetic tests, with 20 source locations shown as
black dots and 16 beams shown as gray lines that extend from the
spectrometer (circle at x= 1000 m and y= 1000 m) to retroreflectors
(black triangles).
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The vector of “true” atmospheric methane concentrations, c, is
simulated by combining knowledge of atmospheric transport with knowledge of
“true” sources and measurement (beam segment) locations with Eq. (1). The
influence functions describing the relationships between each element of
x and each segment of each beam path for each wind condition,
H, are created using the Gaussian plume model described in Sect. 2.1,
with neutral stability conditions (Pasquill category D). In order to
generate the synthetic measurement data, each beam path is discretized into
100 segments. For each unique wind condition, “true” source fluxes are
multiplied by H to calculate atmospheric enhancements at each of
the 100 points along the beam path. Enhancements due to leaks are calculated
independently for each segment of a beam and subsequently averaged for each
beam and for each wind condition. This value mimics the actual data output
of the spectrometer, which measures the average concentration along the beam
length.
The dimensions of n (e.g., the length of the atmospheric concentration
vector, c) in the synthetic tests vary along with the number of beams
per spectrometer–detector system and the number of meteorological
conditions. In the configuration of four beams, for example, n= 216 × 4, because each distinct meteorological condition is
applied to each beam. In the 8-beam configuration n= 216 × 8, in
the 16-beam configuration n= 216 × 16, and so on.
Perturbation of observations with noise equivalent to model–data
mismatch uncertainty
Model–data mismatch is the difference between the true atmospheric CH4
concentration, c, and the simulated or measurable atmospheric
CH4 concentration. This difference is expected to be non-zero due, for
example, to measurement uncertainty (sampling and instrumental error),
transport uncertainty (imperfect knowledge of air flow between source and
observation points), and representation error (for example, the assumption
that the measured segment of beam appropriately characterizes the
atmospheric concentration at the time and space scales that it represents in
the model). We assume here that uncertainty due to the imperfectly known
background concentration is also part of model–data mismatch uncertainty. We
simulate progressively larger levels of model–data mismatch in order to
identify differences in model capabilities to locate and size leaks between
the NZMB and non-bootstrap methods.
A range of model–data mismatch values are tested with the expectation that
both the NZMB and non-bootstrap models will be more likely to locate and
source leaks when lower model–data mismatch is added to the data. To
simulate different possible magnitudes of model–data mismatch, the simulated
true atmospheric concentrations, c, are perturbed with random
Gaussian noise with mean 0 ppb and standard deviation equal to the following
values: 0.1, 0.2, 0.3, 0.4, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5,
6, 7, 8, 9, and 10 ppb, over a 1 km path. Measurement statistical
uncertainty alone is expected to be on the order of 3 ppb or lower for a 1 km path (Rieker et al., 2014). As the results of
field tests will show, the range of model–data mismatch values tested are an
appropriate approximation of observed uncertainty (Sect. 4.4). Model–data
mismatch uncertainties are assumed to be uncorrelated, following convention
and understanding of the dual frequency comb measurement scheme. In Eq. (5),
ϵ is a vector of model–data mismatch uncertainty
corresponding to the vector, c. Both vectors are of length n (i
=1,…,n), where n is the number of observations, as described in
Sect. 2.5.3. The vector y contains the synthetic observations or
the true atmospheric concentrations perturbed with measurement noise.
yi=ci+ϵi
Field data observations
Description of field-deployed dual comb setup
The first measurements from a field-deployed dual frequency comb
spectrometer are from the NOAA/ESRL Table Mountain Test Facility, 10 km
north of Boulder, Colorado (Fig. 3; Coburn et al.,
n.d.). The spectrometer is located near the center of a large (≈ 3 × 2.5 km) flat-topped mesa that rises several meters above the surrounding
terrain (see Fig. 3). The dual frequency comb is housed inside of a trailer,
with telescope transceiver affixed to a rotating gimbal on the trailer roof
(roughly 4 m a.g.l.). The actual dual frequency comb
spectrometer is contained in a 56 × 56 × 61 cm electronics rack, and the
large trailer provides a field deployment home base. The beam transceiver
system sends light between 1620 and 1680 nm, with discrete line spacing of
0.002 nm, through a 2 in. telescope. Dual comb spectroscopy uses a large
spectral bandwidth and high spectral resolution, which allows for the
simultaneous fitting of the absorption pattern for each gas, so that
interference among gases is avoided. Background infrared light does not
affect the laser signal due to the heterodyne nature of the detection – the
detected beat signals between the comb teeth are of high frequency whereas
background signals (for example from solar radiation) are of lower
frequency. The system emits and senses approximately 28 900 individual comb
teeth (Coburn et al., n.d.; Rieker
et al., 2014). The wavelength “window” to which the instrument at Table
Mountain is tuned is ≈ 50 nm, spanning 625 individual CH4
features, 2482 CO2 features, and 133 H2O features. Intensity
feedback, triggered data acquisition, and onboard phase correction are
quasi-autonomous, enabling the system to operate continuously for any length
of time
(Coburn
et al., n.d.; Truong et al., 2016; Waxman et al., 2017).
Map view of observation test site at Table Mountain, Colorado
(upper left inset shows geographic location of test site), with two source
locations (location 1, in red, between beams 1 and 2; location 2, in green,
between beams 2 and 3) and three beams shown as white lines that extend from
the spectrometer (blue square) to retroreflectors (white triangles,
labeled 1–3).
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Leak location and strength
For the field experiments at Table Mountain, a cylinder of compressed
methane gas is placed roughly 528 m away from the spectrometer (Fig. 3) with
the gas outlet 1 m a.g.l. The methane cylinder is outfitted
with a regulator and an Alicat mass flow controller (MC-20SLPM-D). The flow
controller is set to release methane in a controlled flow of 3.1 × 10-5 kg s-1 at source location 1, between 10:08 and 16:30 on 26 January 2017.
The flow rate at source location 2 is set to 0.0 kg s-1 through the
duration of 26 January 2017. The controlled methane release point is
roughly 0.43 cm in diameter, and the velocity of gas exiting the tubing is
negligible.
The field tests are arranged so as to approximate the synthetic tests as
closely as possible: to emulate the “perfect” background condition of the
synthetic tests, the background methane concentration for each source
location is measured directly by an upwind beam
(Crenna et al., 2008; Flesch et al., 2009). Because
the background is assumed to be unique for each source location, each
inversion includes only that source location in its solution for fluxes.
That is, one inversion is performed for source location 1, and a separate
inversion is performed for fluxes at source location 2. The dimensions of
m for each test are, therefore, equal to 1, and the dimensions of n for each
test are equal to the number of measurements made downwind of the source
location.
Retroreflector locations
Three corner-cube retroreflectors are located near source locations 1 and 2
at Table Mountain (see Fig. 3). At their nearest points, the lateral
distances between beams 1 and 2 and source location 1 are 11 and 6 m,
respectively. The minimum lateral distances between leak location 2 and
beams 2 and 3 are 12 and 8 m, respectively. The horizontal distance from
the spectrometer to each retroreflector is 584, 585, and 588 m,
respectively, for retroreflectors 1, 2, and 3. All retroreflectors are
positioned 1 m a.g.l.
Meteorology at Table Mountain
Wind speed and wind direction are measured directly with a 3D Sonic
Anemometer (RM Young 81000 Ultrasonic 3D Anemometer with
manufacturer-specified accuracy of ± 0.05 m s-1) located mid-way
between the spectrometer and the retroreflectors. It is possible that local
wind circulation could lead to meteorological conditions that are not
homogenous across the Table Mountain site, which could cause the mean winds
measured at the anemometer to not perfectly represent those influencing the
plume. Measurement of the entire wind field is not practical, however, so
the point measurement is used to characterize meteorology across the site.
The suitability of the Gaussian plume model for short-range simulations
decreases under low speeds, so all data taken at wind speeds below 0.8 m s-1 were removed from this analysis (the reliability of the Gaussian
plume model erodes as wind speeds decrease below ≈1 m s-1; e.g., De Visscher, 2013).
Measurements
We test the bootstrap methodology using measurements taken over the course
of 1 day in January 2017. We test the ability of the bootstrap approach to
both disprove the null hypothesis (i.e., to correctly ascertain the presence
of a non-zero methane emission) and to prove the null hypothesis (i.e., to
correctly ascertain the absence of a leak) by gathering measurements along
beam paths that bound (1) source location 1, where methane is released in a
controlled flow rate of 3.1 × 10-5 kg s-1, and (2) source location 2, where
no methane is released. Quasi-continuous (626 Hz) data acquisition occurs
for 2 min on each beam. Time averaging over 2 min is performed to
maximize gains in measurement precision as well as to average across shorter
timescale eddy mixing events. After a measurement is taken, less than 30 s elapse while the gimbal moves to focus the beam on the next
retroreflector (“retro”) in the measurement sequence. The measurement
sequence for the time period of study on 26 January 2017 is retro 1, retro
2, retro 1, retro 3, retro 1, retro 2, and so on. A fourth retroreflector is
included in the measurement sequence (leading to a small time delay between
measurements made on retro 3 and retro 2), but data from that beam are not
analyzed here for simplicity.
In the field tests, the dimensions of n vary along with the number of
measurements taken on the beams used in the fit for the methane emission
rate vector, x. For the fit to the methane emission rate at source
location 1, all data (that is, all 2 min measurements) gathered on
retroreflectors 1 and 2 are used. For the fit to the emission rate at source
location 1, all data gathered on retroreflectors 2 and 3 are used. Upwind
measurements are used to constrain background, and downwind measurements are
used to determine source strength. The dimensions of n are therefore equal to
the number of downwind measurements. For the test at source location 1, n= 63, and for the test at source location 2, n= 30. The value of n is smaller
at source location 2 because of the sampling pattern described above.
Background CH<inline-formula><mml:math id="M176" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:math></inline-formula> estimation
To most closely approximate the synthetic data testing framework in the
field environment, we directly sample background CH4 concentrations
upwind of the leak point. The array of beams shown in Fig. 3 “sandwich”
each source location. This configuration means that under most wind
conditions (wind directions within ≈ 40∘ of
orthogonal to the beam array in either direction), one beam is situated
upwind and one beam is situated downwind of each source location. With this
method, we attempt to remove the time-varying CH4 concentration to
which enhancements from discrete near-field emissions are added. While the
Table Mountain site is relatively removed from expected anthropogenic and
biogenic methane sources, the presence of nearby small livestock and oil and
gas operations means that the background methane concentration does vary
according to wind direction and through time. The “beam sandwich”
approach, of placing beams on either side of each source location,
represents a plausible solution to future regional-scale monitoring of many
potential emitters.
Results of synthetic data tests
Synthetic source location with and without the NZMB method
We calculate solutions for x using NNLS in a single solution
without a bootstrap approach for each set of beam configurations and for
each model–data mismatch scenario in the synthetic data case. Figure 4
summarizes the findings of each test by categorizing the results into four
outcomes: two true leaks found with no false positives, one true leak found with
no false positives, zero true leaks found with no false positives, and one or
more true leaks found with one or more false positive. The top half of Fig. 4
(for the non-bootstrap method) shows that, of the five different beam
configurations tested, all result in false-positive source locations under
every model–data mismatch scenario when a non-bootstrap approach is taken.
That is, even with very low model–data mismatch (0.1 ppb) and many beam
measurement locations (64), the non-bootstrap method fails to positively
identify true leak sources without also generating false-positive results.
Non-zero solutions are found for source locations where no “true” leak
exists.
Summary of synthetic data test results. Top 5 rows show results of
non-bootstrap inversions and bottom 5 rows show results of NZMB inversions
for the 4, 8, 16, 32, and 64 beam cases. Columns indicate results for
different values of model–data mismatch added as noise to the synthetic
measurements. Color coding of cells indicates summary of model success, as
detailed by the legend.
![]()
The bottom half of Fig. 4 shows the results of the same tests, using instead
the NZMB method for locating leaks. The results show that success in leak
detection is much higher using NZMB compared with the non-bootstrap tests.
Indeed, none of the NZMB tests result in the occurrence of a false-positive
leak location, and only tests with low numbers of beams relative to the
number of source locations (four- and eight-beam cases) fail to find both of the
true leaks. The four-beam case results in positive identification of both leaks
up to a model–data mismatch threshold of 2 ppb, above which one true leak is
found. One leak is consistently found up to a threshold of 5 ppb, and above
5 ppb model–data mismatch no true leaks are identified (but no false
positives are generated either). The eight-beam case results in accurate
location of both true leaks up to a model–data mismatch threshold of 3.5 ppb, above which 1 true leak is found (with no false positives). One leak is
consistently found up to the maximum testing point of 10 ppb. In order to
reliably locate both true leaks with no false-positive results under all
model–data mismatch scenarios, 16 or more beams are needed for the set of
cases that are tested here. Alternate configurations of “true” leaks at
well sites other than 6 and 9 are not tested; however, given that
meteorological conditions are simulated equally from all directions, we
would not expect a different set of results from a different set of “true”
leaks.
Top left panel shows well site numbers (x axis) and corresponding
“true” leak rates (y axis), and remaining panels show resulting leak rate
(y axis) at each well site (x axis) from non-bootstrap least squares fit to
synthetic observations perturbed with model–data mismatch (MDM) noise shown,
for the eight-beam case. Open circles show locations and strengths of all
non-zero solutions.
![]()
Top left panel shows well site numbers (x axis) and corresponding
“true” leak rates (y axis), and remaining panels show NZMB results
(y axis) for each well site location (x axis) with synthetic observations
perturbed with model–data mismatch (MDM) noise shown, for the eight-beam case.
Light gray (black) open circles show locations and strengths of the maximum
(minimum) of 1000 bootstrap operations. Minimum values of zero are not
plotted.
![]()
A subset of the results for the eight-beam NNLS without bootstrap and the NNLS
with NZMB cases are shown in Figs. 5 and 6 (for conciseness; all results are
shown in the Supplement). It is evident from Fig. 5 that, even
with very low model–data mismatch noise (0.5 ppb), the non-bootstrap model
results in well sites other than the two true leak locations being erroneously
identified as sources of methane. It is evident from Fig. 5 that, as
model–data mismatch increases, the strength of incident false-positive
results also increases. By contrast, no false-positive leaks are identified
in the NZMB case shown in Fig. 6, at any level of model–data mismatch noise.
Above a model–data mismatch threshold of 4 ppb, only one of two true leaks
is found in the eight-beam case using NZMB. As Fig. 4 shows, 16 or more beams
are necessary to consistently find both true leaks at higher thresholds of
model–data mismatch uncertainty using the NZMB method, given the
hub-and-spoke beam placement scheme tested here. More complex placement of
beams (for example placing beams closer to known well sites) would likely
result in even better ability to locate leaks with fewer beams.
Synthetic source sizing using the NZMB method
Synthetic data tests of the new bootstrap methodology presented here show
high success in leak location, with zero incidence of false-positive leak
detections. Figure 6 shows the maximum and minimum values of 1000 bootstrap
operations for each model–data mismatch test case for the eight-beam
configuration. At low levels of model–data mismatch uncertainty (0.1–0.5 ppb), the maximum and minimum solutions bound a small range that is close to
the true leak strength. As higher levels of model–data mismatch noise are
added to observations, the maximum and minimum values diverge. However, even
as the maximum and minimum solutions diverge, most cases include the true
leak strength within the maximum and minimum bounds.
NZMB solutions for leak strength of true leaks, given 2 ppb
model–data mismatch uncertainty, for each beam configuration.
Number of
Well site 6
Well site 6, 1 SD
Well site 19
Well site 19, 1 SD
beams
mean strength
mean strength
4
4.2 × 10-5 kg s-1
0.4 × 10-5 kg s-1
2.5 × 10-5 kg s-1
0.6 × 10-5 kg s-1
8
4.5 × 10-5 kg s-1
0.4 × 10-6 kg s-1
2.0 × 10-5 kg s-1
0.3 × 10-5 kg s-1
16
4.5 × 10-5 kg s-1
0.4 × 10-6 kg s-1
2.8 × 10-5 kg s-1
0.9 × 10-6 kg s-1
32
4.4 × 10-5 kg s-1
0.3 × 10-6 kg s-1
3.0 × 10-5 kg s-1
0.8 × 10-6 kg s-1
64
4.5 × 10-5 kg s-1
0.3 × 10-6 kg s-1
3.0 × 10-5 kg s-1
0.6 × 10-6 kg s-1
True leak: 4.5 × 10-5 kg s-1
True leak: 3.0 × 10-5 kg s-1
Using the NZMB method, all beam cases (even the four-beam case) correctly
identify that both well sites 6 and 19 are emitting methane when model–data
mismatch is 2 ppb or lower (Fig. 4). At that level of model–data mismatch,
higher numbers of beams and observations tend to lead to lower standard
deviation around the mean estimated leak strength and a more accurate
estimate of true leak strength (Table 1). An exception is at well site 19,
where the eight-beam case did not perform as well as the four-beam case. It may be
that both cases were inadequate for accurately sizing leaks, and that 16
beams are necessary in a dense field of wells such as is tested here. The
failure of the eight-beam case to accurately predict the leak rate at well site
19 is also evident from histograms of bootstrap operations, shown for each
beam case with model–data mismatch of 2 ppb in Fig. 7.
Histograms of source strength, with mean ±1 standard
deviation shown with vertical lines for well site 6 (black) and well site 19
(gray), for each beam configuration, and with 2 ppb model–data mismatch
uncertainty. Note that x axes are truncated at 2 × 10-5 kg s-1 (lower
bound) and 5 × 10-5 kg s-1 (lower bound) for scale.
![]()
Histograms of the results for the 16, 32, and 64 beam cases with 10 ppb
model–data mismatch are shown in Fig. 8. It is clear from Fig. 8 that, even
with very high model–data mismatch uncertainty, simple hub-and-spoke
configurations of between 16 and 64 beams are able to locate and estimate leak
flow rates to within reasonable bounds of uncertainty.
Results of field data tests
Performance overview of field-deployed DCS
Atmospheric observations were made over the course of 1 day on 26 January 2017 at the Table Mountain site. A set of three retroreflectors
created
long-range open-path beams of ≈ 585 m (Fig 3). Spectrometer
performance in the field demonstrated no loss of precision or reliability
compared with laboratory performance, as demonstrated by
Coburn et al. (n.d.). Figure 9 shows a plot of Allan
deviations for 26 January 2017, demonstrating measurement precision of 5–6 ppb when measurements are averaged for 2 min. Precision of field
measurements is limited by repeatability of measurements and atmospheric
variability of CH4 because measurements are time averaged; the latter
is likely a dominant driver of uncertainty in this case, as will be
discussed in Sect. 4.3. The Allan deviation in Fig. 9 shows improvement of
precision with averaging time, to a minimum at ≈ 70 s,
followed by an increase that is likely due to atmospheric variability.
Histograms of source strength, with mean ± 1 standard
deviation shown with vertical lines for well site 6 (black) and well site 19
(gray), for 16, 32, and 64 beam configurations, and with 10 ppb model–data
mismatch uncertainty.
![]()
Atmospheric observations of CH<inline-formula><mml:math id="M268" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:math></inline-formula> at Table Mountain
On 26 January 2017, measurements are made throughout the day, including
during a 6.5 h controlled release of methane at source location 1. At
adjacent source location 2, no methane release is emitted. A series of three
retroreflectors is oriented such that each source region is monitored
independently from the other; one beam on either side of each source
location serves as a “background” measurement. We examine the results of
two separate inversion tests: (1) a day-long set of observations of source
location 1 (with the controlled release) that is situated between
retroreflectors 1 and 2 and (2) a day-long set of observations of
non-leaking source location 2 that is situated between retroreflectors 2 and
3. These tests are performed simultaneously, such that contamination from
source location 1 could result in background contamination for monitoring of
source location 2.
Allan deviation plot showing changes in measurement precision with
averaging time from field data collected at Table Mountain on 26 January
2017.
![]()
On 26 January 2017, mean wind speeds are 2.1 m s-1 and winds are
primarily from the east and northeast, so that retroreflector 1 is downwind
of the controlled release and retroreflector 2 is upwind of the controlled
release. Similarly, retroreflector 2 is downwind of non-leaking source
location 2 and retroreflector 3 is upwind of non-leaking source 2 (Fig. 3).
Stability classes range from B (moderately unstable) to D (neutral)
throughout the course of the day (see Supplement for a
time series of stability and detailed description of its calculation). We use
the Griffiths (1994) corrections to the
Briggs (1974) parameterizations to calculate σy and σz.
At source location 1 (Fig. 10a), during the period when the
controlled release is on (non-zero flow), the downwind retroreflector (Retro
1) shows a clear enhancement above the concentration measured on the upwind
retroreflector (Retro 2), except during the middle of the day when the winds
shift briefly to the south (Fig. 10c). The mean of all CH4
measurements along beam 1 during the period that the leak is on is 2046 ppb;
the mean CH4 measured along beam 2 during the same period is 2025 ppb.
Both retroreflectors demonstrate changes in background CH4
concentrations over the course of the day; the range in values measured on
the upwind retroreflector is 65 ppb. There may be a relationship between
ambient CH4 concentration and wind direction, as both retroreflectors
show a drastic decrease in concentration when the winds abruptly shift to
the west at 16:30 (which happens to coincide with the time the leak was
turned off).
Line-integrated atmospheric CH4 concentrations measured on
26 January 2017 along beam paths to retroreflectors 1 and 2 (a) and to
retroreflectors 2 and 3 (b), as well as wind speed and wind direction (c). Gray and
black points and left-hand axes of panels (a) and (b) show CH4
concentration. The black line and right-hand axis in panel (a) show the
flow rate at source location 1 (bounded by retroreflectors 1 and 2) and the
black line and right-hand axis in panel (b) show the flow rate at source
location 2 (bounded by retroreflectors 2 and 3). In panel (c), the black
line and left-hand axis show wind speed and the gray diamonds and right-hand
axis show wind direction (according to meteorological convention,
0∘ is north, 90∘ is east,
180∘ is south, 270∘ is west, and
360∘ is north). All data reflects 2 min averaging time.
![]()
At source location 2, no leak is released during the period of study, and
throughout the course of the day, both retroreflectors 2 and 3 measure
similar changes in atmospheric CH4 variability (Fig. 10b). The
range of measured values over the course of the entire day are 128 ppb on
beam 2 and 124 ppb on beam 3. The mean of all CH4 measurements
(throughout the course of the day) is 2016 ppb on beam 2 and 2019 ppb on
beam 3.
Background CH<inline-formula><mml:math id="M285" display="inline"><mml:msub><mml:mi/><mml:mn mathvariant="normal">4</mml:mn></mml:msub></mml:math></inline-formula> observations
The beams stationed upwind of each source location provide estimates of the
background CH4 concentration inflow for that location. After a linear
interpolation to upwind measurements has been applied, this background is
subtracted from measurements on the downwind beam to yield a measure of the
CH4 enhancement due to fluxes at the source location. Applying this
method, the mean and standard deviation of the enhancement above background
on retroreflector 1 – which is downwind of source location 1 (leak rate of
3.1 × 10-5 kg s-1) – is 17.4 ± 10.1 ppb. Applying this method to
source location 2, we find the mean and standard deviation of the
enhancement on retroreflector 2 – which is downwind of source location 2
(leak rate of 0 kg s-1) – is 3.1 ± 7.3 ppb, a value within the
range of variability expected from combined measurement and background
uncertainty.
Field-based estimates of model–data mismatch
We examine measurements at source location 2, where no leak is present, in
order to estimate model–data mismatch in the field, for comparison with the
model–data mismatch values applied in the synthetic data tests. By examining
the difference between measurements made on different retroreflectors
(retroreflectors 2 and 3) at similar points in time (within 5 min), we
obtain an approximation of the combined contributions to model–data mismatch
arising from measurement uncertainty, representation uncertainty, background
construction (the method of background estimation), and background sampling
(the method of sampling background concentrations). We find a standard
deviation of 5 ppb. This value differs from the standard deviation of the
enhancement for the entire time series (reported above in Sect. 4.3) because
it compares differences in upwind and downwind concentrations measured at
approximately the same time. For estimation of total model–data mismatch, we
add (in quadrature) an estimate of the transport uncertainty that includes
uncertainties in measurement of wind speed and wind direction, atmospheric
stability parameterization, and placement of the sonic anemometer relative
to the leak location (see Supplement for detail). Transport
uncertainty estimation is for a plume that interacts with any location along
the beam and therefore requires knowledge of the mean distance between the
leak point and each segment of the beam. The estimated transport
uncertainty, calculated in this way, is 0.8 ppb. If, for example, the wind
direction is perfectly perpendicular to the beam for the entirety of the
measurement period (which does not occur on 26 January 2017), then
the leak-to-beam distance used in the calculation should collapse to the
minimum lateral distance between the leak and the beam. Using that value
instead, transport uncertainty is 12.2 ppb. The overall value of model–data
mismatch (reflecting combined measurement, background, and transport
uncertainty), estimated in this way, is therefore 5.1 ppb with a maximum
range of 13.2 ppb, which suggests that the range of model–data mismatch
values tested in the synthetic data experiments are appropriate. The Allan
deviation in Fig. 9 shows a similar level of measurement uncertainty,
suggesting that most of the uncertainty observed in our record is captured
in this estimate of model–data mismatch, which includes effects of
atmospheric variability. Precision could be improved by averaging data over
a shorter time span (70 s), but those gains would be minimal (Fig. 9).
Controlled methane release flow rates and 1 standard deviation for
each field experiment, including local time that leak was turned on and off.
Source location 1
Source location 2
Controlled leak time on:
10:08
n/a
Controlled leak time off:
16:30
n/a
Measured mean flow rate:
3.1 × 10-5 ± 0.01 × 10-5 kg s-1
0.0 ± 0.0 kg s-1
Non-bootstrap solution:
2.4 × 10-5 kg s-1
0.5 × 10-5 kg s-1
NZMB solution:
2.6 × 10-5 ± 0.5 × 10-5 kg s-1
0.0 ± 0.0 kg s-1
n/a: not applicable.
Results of inversions using Table Mountain observations
Both the non-bootstrap and the NZMB approaches accurately predict the
presence of methane emissions at source location 1 (Table 2). The average
bootstrapped flux value is within 2σ of the true flux value measured at
the flow meter at source location 1 (Fig. 11). At source location 2, the
non-bootstrap approach falsely predicts a positive emission rate of 0.5 × 10-5 kg s-1 (Table 2) where no leak is present. The NZMB approach, by
contrast, is able to accurately predict that there is no leak present at
source location 2, because the minimum of the 1000 bootstrap solutions is
zero (Fig. 11). As the synthetic data tests also demonstrate, the NZMB
method is necessary to avoid false identification of leaking source
locations. The field data tests corroborate that the new bootstrap approach
enables higher confidence of accurate attribution of emissions to source
locations without generating “false alarms”.
Histogram of NZMB estimated source strength at source location 1,
with dashed line showing the bootstrap mean and thin dotted lines showing
±2 standard deviation. The thick black line shows the true leak
strength at source location 1 (3.1 × 10-5 kg s-1).
![]()
Conclusions
The focus of this study is to show the powerful potential of the combination
of a new statistical method with dual frequency comb spectroscopy for the
location and sizing of point source emissions. The synthetic and field tests
presented here rely on near-perfect (in the synthetic data tests) or
well-constrained (in the field data tests) background concentration
estimation. Future studies are needed to address the potential complications
of more complex background conditions and meteorological conditions under
which it is not possible to obtain sequential “upwind” and “downwind”
samples. Similarly, the tests here rely on the assumption of constant leak
rates, which may not be a realistic assumption that can be made for methane
emissions from oil and gas operations. Future work to address these
complexities will be necessary. Future studies are also needed to examine
the gains that can be made from optimization of beam configurations for
improved leak detection given variable wind and background conditions. In
particular, previous work has shown the critical impact that sensor
placement can have on the conditioning of the source–receptor relationship
matrix (H) and suggests paths forward for optimization of sensor
placement (Crenna et al., 2008; Flesch et al.,
2009). Specifically, the placement of one beam or sensor between each source
to be apportioned would be expected to lead to a lower condition number and
therefore a more reliable result (Crenna et al.,
2008; Flesch et al., 2009). Work aimed at addressing these complications is
underway, as are inversion efforts to resolve issues of leak intermittency.
A notable aspect of the micrometeorological modeling used here to
demonstrate the NZMB methodology is the simple representation of atmospheric
transport (the Gaussian plume model). The choice to use a simple model that
is familiar to the broader scientific community is intentional, but its
use belies the complex nature of turbulent mixing and dispersion in the
atmospheric surface layer. What is gained in simplicity and in providing a
baseline for the most basic performance of the methodology in a field
setting may come at the cost of recommending a model that may not ultimately
be well-suited for such an endeavor. The Gaussian plume model neglects
important aspects of atmospheric mixing such as wind shear and the height
dependence of eddy diffusivity, and better models exist for simulation of
atmospheric flow at this scale. It is assumed that more sophisticated models
of atmospheric dispersion could, therefore, lead to better flux estimation.
We suggest that future applications in field settings of the methodology
presented here consider their use. Importantly, despite its drawbacks, the
Gaussian plume model proves sufficient in the tests here for the accurate
identification (and, importantly, avoidance of misidentification) of
controlled, field-based methane leaks. Future studies of the best transport
model for the application of DCS measurements and the NZMB method for leak
detection is warranted.
The initial work presented here demonstrates the promising potential of dual
frequency comb spectroscopy for detection of leaks in the natural gas supply
chain and the valuable gains that can be provided by using the NZMB method
over the NNLS fitting technique alone.