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ACP | Articles | Volume 18, issue 24

Atmos. Chem. Phys., 18, 17895–17907, 2018

https://doi.org/10.5194/acp-18-17895-2018

© Author(s) 2018. This work is distributed under

the Creative Commons Attribution 4.0 License.

https://doi.org/10.5194/acp-18-17895-2018

© Author(s) 2018. This work is distributed under

the Creative Commons Attribution 4.0 License.

Special issue: Greenhouse gAs Uk and Global Emissions (GAUGE) project (ACP/AMT...

**Research article**
17 Dec 2018

**Research article** | 17 Dec 2018

Detecting changes in Arctic methane emissions: limitations of the inter-polar difference of atmospheric mole fractions

^{1}School of GeoSciences, University of Edinburgh, Edinburgh, UK^{2}National Oceanic and Atmospheric Administration, Earth System Research Laboratory, Boulder, Colorado, USA

^{1}School of GeoSciences, University of Edinburgh, Edinburgh, UK^{2}National Oceanic and Atmospheric Administration, Earth System Research Laboratory, Boulder, Colorado, USA

**Correspondence**: Paul I. Palmer (paul.palmer@ed.ac.uk)

**Correspondence**: Paul I. Palmer (paul.palmer@ed.ac.uk)

Abstract

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We consider the utility of the annual inter-polar difference (IPD) as a
metric for changes in Arctic emissions of methane (CH_{4}). The IPD has
been previously defined as the difference between weighted annual means of
CH_{4} mole fraction data collected at stations from the two polar
regions (defined as latitudes poleward of 53^{∘} N and 53^{∘} S,
respectively). This subtraction approach (IPD) implicitly assumes that
extra-polar CH_{4} emissions arrive within the same calendar year at
both poles. We show using a continuous version of the IPD that the metric
includes not only changes in Arctic emissions but also terms that represent
atmospheric transport of air masses from lower latitudes to the polar
regions. We show the importance of these atmospheric transport terms in
understanding the IPD using idealized numerical experiments with the TM5
global 3-D atmospheric chemistry transport model that is run from 1980 to
2010. A northern mid-latitude pulse in January 1990, which increases prior
emission distributions, arrives at the Arctic with a higher mole fraction and
≃12 months earlier than at the Antarctic. The perturbation at the
poles subsequently decays with an *e*-folding lifetime of ≃4 years.
A similarly timed pulse emitted from the tropics arrives with a higher value
at the Antarctic ≃11 months earlier than at the Arctic. This
perturbation decays with an *e*-folding lifetime of ≃7 years. These
simulations demonstrate that the assumption of symmetric transport of
extra-polar emissions to the poles is not realistic, resulting in
considerable IPD variations due to variations in emissions and atmospheric
transport. We assess how well the annual IPD can detect a constant annual
growth rate of Arctic emissions for three scenarios, 0.5 %, 1 %, and
2 %, superimposed on signals from lower latitudes, including random
noise. We find that it can take up to 16 years to detect the smallest
prescribed trend in Arctic emissions at the 95 % confidence level.
Scenarios with higher, but likely unrealistic, growth in Arctic emissions are
detected in less than a decade. We argue that a more reliable
measurement-driven approach would require data collected from all latitudes,
emphasizing the importance of maintaining a global monitoring network to
observe decadal changes in atmospheric greenhouse gases.

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Dimdore-Miles, O. B., Palmer, P. I., and Bruhwiler, L. P.: Detecting changes in Arctic methane emissions: limitations of the inter-polar difference of atmospheric mole fractions, Atmos. Chem. Phys., 18, 17895–17907, https://doi.org/10.5194/acp-18-17895-2018, 2018.

1 Introduction

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Atmospheric methane (CH_{4}) is the second most important contributor to
anthropogenic radiative forcing after carbon dioxide. Observed large-scale
variations of atmospheric CH_{4} (Nisbet et al., 2014) have evaded a
definitive explanation due to the sparseness of data
(Kirschke et al., 2013; Rigby et al., 2016; Saunois et al., 2016; Schaefer et al., 2016; Turner et al., 2016). Atmospheric
CH_{4} is determined by anthropogenic and natural sources, as well as by loss
from oxidation by the hydroxyl radical (OH) with smaller loss terms from soil
microbes and oxidation by Cl. This results in an atmospheric lifetime of
≃10 years. Anthropogenic CH_{4} sources include leakage from the
production and transport of oil and gas, coal mining, and biomass burning
associated with agricultural practices and land use change. Microbial
anthropogenic sources include ruminants, landfills, and rice cultivation. The
largest natural source is microbial emissions from wetlands, with smaller but
significant contributions from wild ruminants, termites, wildfires,
landfills, and geologic emissions (Kirschke et al., 2013; Saunois et al., 2016). Here, we
focus on our ability to quantify changes in Arctic emissions using polar
atmospheric mole fraction data.

Warming trends over the Arctic, approximately twice the global mean
(AMAP, 2015), are eventually expected to result in thawing of permafrost.
Observational evidence shows that permafrost coverage has begun to shrink
(Christensen et al., 2004; Reagan and Moridis, 2007). Arctic soils store an estimated 1700 GtC
(Tarnocai et al., 2009). As the soil organic material thaws and decomposes it is
expected that some fraction of this carbon will be released to the atmosphere
as CH_{4}, depending on soil hydrology. Current understanding is that
permafrost carbon will enter the atmosphere slowly over the next century,
reaching a cumulative emission of 130–160 PgC (Schuur et al., 2015). If only
2 % of this carbon is emitted as CH_{4}, annual Arctic emissions
could approximately double by the end of the century from current estimates
of 25 Tg CH_{4} year^{−1} inferred from
atmospheric inversions (AMAP, 2015). At present, using data from the
current observing network there is no strong evidence to suggest large-scale
changes in Arctic emissions (Sweeney et al., 2016).

The inter-polar difference (IPD) has been proposed as a sensitive indicator
of changes in Arctic emissions that can be derived directly from network
observations of atmospheric CH_{4} mole fraction. The IPD, as previously
defined (Dlugokencky et al., 2003), is the difference between weighted annual
means of CH_{4} mole fraction data collected at polar stations (those
poleward of $\pm \mathrm{53}{}^{\circ}>$ latitude) such as those from the NOAA Earth
System Research Laboratory (ESRL) network
(https://www.esrl.noaa.gov/gmd/dv/site/site_table2.php, last access:
10 December 2018). Data from individual
sites are weighted inversely by the cosine of the station latitude and by the
standard deviation of the data at a particular site.
Dlugokencky et al. (2003) reported an abrupt drop in IPD during the early
1990s. They suggested this magnitude of change was indicative of a
10 Tg CH_{4} year^{−1} reduction, which they attribute to the
collapse of fossil fuel production in Russia following the 1991 breakup of
the Soviet Union (Dlugokencky et al., 2011). In more recent work,
Dlugokencky et al. (2011) proposed that the IPD metric is potentially
sensitive to changes in Arctic emissions as small as
3 Tg CH_{4} year^{−1}, representing a value of 10 % of northern
wetland emissions. However, studies have reported little or no increase in
IPD between 1995 and 2010 (Fig. 1,
Dlugokencky et al., 2003, 2011), a period during which rising
Arctic temperatures were expected to lead to an increase in emissions
(Mauritsen, 2016; McGuire et al., 2017). In this work, we examine how
sensitive the IPD is to changing CH_{4} emissions by using model
simulations guided by results from an analytical approach.

First, we derive the continuous version of the IPD^{C} to introduce
the atmospheric transport terms that are not considered in the subtraction
approach. For our model, we have a local Arctic source (mass CH_{4} per
unit time) and an isolated inter-polar source (mass CH_{4} per unit
time) emitted at position *r* and time *t*. The IPD^{C} is given by

$$\begin{array}{}\text{(1)}& {\mathrm{IPD}}^{\mathrm{C}}\left(t\right)={\displaystyle \frac{\mathrm{1}}{\mathrm{\Delta}r}}\underset{r=\mathrm{53}}{\overset{\mathrm{90}}{\int}}c(r,t)\mathrm{d}r-{\displaystyle \frac{\mathrm{1}}{\mathrm{\Delta}r}}\underset{r=-\mathrm{90}}{\overset{-\mathrm{53}}{\int}}c(r,t)\mathrm{d}r,\end{array}$$

where Δ*r* is the graduation in latitude in the model and *c*(*r*,*t*)
denotes atmospheric CH_{4} mole fraction (ppb) at latitude *r* and time
*t* that includes influences from all other latitudes and previous times. The
mole fraction can then be described as

$$\begin{array}{}\text{(2)}& c(r,t)=\underset{{t}^{\prime}=-\mathrm{\infty}}{\overset{{t}^{\prime}=t}{\int}}\underset{{r}^{\prime}=-\mathrm{90}}{\overset{\mathrm{90}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}\mathrm{d}{r}^{\prime}\mathrm{d}{t}^{\prime},\end{array}$$

where $S({r}^{\prime},{t}^{\prime})$ denotes the surface emission fluxes
(g cm^{−2} s^{−1}); ${H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}$ denotes the fraction of emissions
from location *r*^{′} at initial time *t*^{′} that contributes to the concentration
at location *r* and a later time *t*, which includes atmospheric chemistry
and transport; and $k({r}^{\prime},{t}^{\prime})$ (cm^{3} g^{−1}) describes the conversion
between emissions and atmospheric mole fraction (parts per billion, ppb) and
takes the form $k(r,t)=\frac{{N}_{\mathrm{a}}}{{M}_{\mathrm{w}}\mathit{\rho}(r,t)}$, where
*N*_{a} and *M*_{w} denote Avogadro's constant
(molecules mole^{−1}) and the molar weight of CH_{4}
(g mole^{−1}), respectively, and *ρ*(*r*,*t*) denotes the number density of
air (molec cm^{−3}).

Our expression for IPD^{C} can be reformulated as the difference
between values determined at time *t* and a reference time *t*_{0}. The reader
is referred to Appendix A for a full derivation of the expressions
used in this introduction. Equation (3) describes the IPD
using the assumptions previously used (e.g. Dlugokencky et al., 2003):
(1) the southern polar region contains no local sources, and (2) emissions from
the northern polar region are too diffuse after transport between poles to
significantly affect mole fractions at the southern polar region.

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{\mathrm{IPD}}^{\mathrm{C}}\left(t\right)-{\mathrm{IPD}}^{\mathrm{C}}\left({t}_{\mathrm{0}}\right)=\\ {\displaystyle}& {\displaystyle \frac{\mathrm{1}}{\mathrm{\Delta}r}}\underset{{t}^{\prime}={t}_{\mathrm{0}}}{\overset{{t}^{\prime}=t}{\int}}\left(\underset{r=\mathrm{53}}{\overset{\mathrm{90}}{\int}}\right[\underset{{r}^{\prime}=\mathrm{53}}{\overset{\mathrm{90}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}\mathrm{d}{r}^{\prime}\\ {\displaystyle}& {\displaystyle}+\underset{{r}^{\prime}=-\mathrm{53}}{\overset{\mathrm{53}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}\mathrm{d}{r}^{\prime}]\mathrm{d}r\\ \text{(3)}& {\displaystyle}& {\displaystyle}-\underset{r=-\mathrm{90}}{\overset{-\mathrm{53}}{\int}}\underset{{r}^{\prime}=-\mathrm{53}}{\overset{\mathrm{53}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}\mathrm{d}{r}^{\prime}\mathrm{d}r)\mathrm{d}{t}^{\prime}\end{array}$$

The first integral in Eq. (3) represents contributions from
changes in northern polar sources between *t* and *t*_{0}; and the second and
third integral represent atmospheric transport terms that describe the
contributions from intra-polar sources to the northern and southern polar
mole fractions, respectively. To successfully isolate local Arctic emissions
of CH_{4} using the IPD these atmospheric transport terms would have to
cancel out. Taking into account that the characteristic timescale for
inter-hemispheric transport of an air mass is ≃1 year
(Holzer and Waugh, 2015) we argue that only a fortuitous set of circumstances would
allow the IPD as previously defined to isolate local northern polar sources
of CH_{4}.

In the next section, we describe the data and methods used previously to define IPD, as well as the model calculations we use to explore the importance of these atmospheric transport terms, as illustrated in Eq. (3). In Sect. 3, we report the results from our numerical experiments. We conclude in Sect. 4.

2 Data and methods

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To calculate the IPD, following Dlugokencky et al. (2011), we first group
together a subset of NOAA ESRL global monitoring measurement sites that are
located $-\mathrm{53}{}^{\circ}>$ latitude $>\mathrm{53}{}^{\circ}$
(Table 1) and assign them as the north and south polar
regions. For each polar region we calculate mean biweekly (measurements taken
every 2 weeks) mole fractions across the stations, weighted inversely by
station latitude and the standard deviation about the biweekly mean
CH_{4} mole fraction. Biweekly values of IPD are then averaged over a
calendar year to determine the annual IPD, which has been used in previous
studies.

We use biweekly CH_{4} values determined from measurements of discrete
air samples collected in flasks from the NOAA Cooperative Global Air Sampling
Network (NOAA CGASN). Air samples (flasks) are collected at the sites and
analysed for CH_{4} at NOAA ESRL in Boulder, Colorado, using a gas
chromatograph with flame 220 ionization detection. Each sample aliquot is
referenced to the WMO X2004 CH_{4} standard scale (Dlugokencky et al., 2005). Individual
measurement uncertainties are calculated based on analytical repeatability
and the uncertainty in propagating the WMO CH_{4} mole fraction standard
scale. Analytical repeatability varies between 0.8 and 2.3 ppb and has a
mean value of approximately 2 ppb averaged over the measurement record.
Uncertainty in scale propagation is based on a comparison of discrete
flask-air and continuous measurements at the MLO (Mauna Loa Observatory) and BRW observatories and
has a fixed value 0.7 ppb. These two values are added in quadrature to
estimate the total measurement uncertainty, equivalent to a ≃68 %
confidence interval.

Five northern and two southern polar stations (Table 1)
have data that cover the period discussed in previous studies (approximately
1986–2010) and a weekly resolution to calculate biweekly averages. We impute
missing data filled using a two-stage approach. We use linear interpolation
to replace missing measurements from a given week and year with the average
of the measurement values from the same week of the three preceding and
subsequent years (to provide a climatological value but preserve long-term
trends in the data). If corresponding weekly measurements for the six
neighbouring years are incomplete, we use a cubic spline interpolation. We
calculate the uncertainties on the biweekly weighted concentration means from
the polar regions using the formula for the standard error
${\mathit{\sigma}}_{\stackrel{\mathrm{\u203e}}{x}}$ of a weighted mean *μ* (Taylor, 1997),
${\mathit{\sigma}}_{\stackrel{\mathrm{\u203e}}{x}}^{\mathrm{2}}\left(\mathit{\mu}\right)=\mathrm{1}/{\sum}_{i}(\frac{\mathrm{1}}{{\mathit{\sigma}}_{i}\mathrm{cos}\left({\mathit{\varphi}}_{i}\right)}{)}^{\mathrm{2}}$, where the denominator represents
weights assigned to each station *i* as a function of biweekly mole fraction
standard deviation *σ*_{i} and the latitude *ϕ*_{i} of the station. We
propagate these errors to determine the error on the annual IPD, following
Dlugokencky et al. (2011).

We calculate the corresponding model IPD values by sampling TM5 (described below) at the time and location of each NOAA ESRL observation and processing the values as described above for the observations.

Building on the terms evaluated using our continuous IPD^{C} model
(Eq. 3) we use the TM5 atmospheric transport model
(Krol et al., 2005) to (1) examine how perturbations in inter-polar emissions are
transported to the polar regions and (2) determine the sensitivity of the
IPD to different emission distributions.

For our numerical experiments, we run the TM5 model using a horizontal
spatial resolution of 2^{∘} (latitude) and 3^{∘} (longitude),
driven by meteorological fields from the European Centre for Medium-Range
Weather Forecast (ECMWF) ERA-Interim reanalysis. Fossil fuel and agricultural
emission estimates are taken from the EDGAR3.2 inventory (Olivier et al., 2005)
with modifications (Schwietzke et al., 2016). Natural emissions are based on the
prior values used by CarbonTracker-CH_{4} (Bergamaschi et al., 2005; Bruhwiler et al., 2014). Bruhwiler et al. (2014) reported posterior CH_{4}
emission estimates for high northern latitudes that were 20 %–30 % smaller
than prior values, which we use in our current experiments. An important
consequence of our using these prior values is that the model IPD values have
a positive bias compared to values determined by CH_{4} mole fraction
measurements.

We run a suite of targeted numerical experiments to test the sensitivity of the IPD to pulsed and noisy variations from mid-latitude and tropical emission sources. In practice, both sets of experiments integrate information from both atmospheric transport terms. We also consider experiments that included Arctic emissions with different constant growth rates and realistic variations in lower latitude emissions. As a control we use a simulation with constant emissions. Appendix B includes a presentation of the time series used to calculate the IPD from our experiments.

We initialize our TM5 numerical experiments from 1980 using initial
conditions defined by the observed north–south distribution of CH_{4} in
the early 1980s. Each experiment is run from 1980 to 2010, with mole
fractions sampled at the time and location of the network observations.

Figure 1 shows that the model IPD for the control run is higher than observed values, as explained above. The model IPD also shows less variability than observed values. Variations of IPD in the early 1990s have been attributed to a rapid decline in fossil fuel production following the 1991 breakup of the Soviet Union (Dlugokencky et al., 2011). We determine the model response to changes in emissions (as described below) by subtracting the control run from the perturbed emissions runs.

To investigate the impact of a sustained continental-scale change in
emissions on the weighted polar means and the IPD metric, we run the control
experiment configuration but during the year 1990 we increase emissions by an
amount that is evenly distributed throughout the year. In the first pulse
experiment, we increase existing mid-latitude emissions over the contiguous
USA by 10 Tg CH_{4}. In the second experiment, we increase existing
tropical land sources (within $\pm \mathrm{30}{}^{\circ}$) by 20 Tg CH_{4}. We
present polar mole fraction time series produced using the control and pulsed
experiments shown in Appendix B.

To investigate the role of intra- and inter-annual variations of emission sources on the IPD we rerun the two pulse experiments but superimpose standard uniform distribution noise 𝒰(0,1) on the emissions. We conduct two runs of TM5: one with a noise function of amplitude 10 Tg on US emissions and another with a function of amplitude 20 Tg on tropical sources. These experiments help us to determine the observability of changes in mid-latitude and tropical sources at the poles and whether the IPD can isolate local Arctic emission.

To investigate the ability of IPD to detect a constant annual growth rate of Arctic emissions, we use the control experiment configuration but in three separate experiments we increase Arctic emission by 0.5 %, 1 %, and 2 % on an annual basis. Emissions are mostly limited to summer months (June–August) when the soil surface is typically not frozen.

3 Results

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Figure 2 summarizes the results from our pulsed emission experiments. The model response at both poles to the 1990 pulse peaks rapidly and then falls off approximately exponentially over several years. The northern region tracer represents the sum of local Arctic emissions and the first atmospheric transport term in Eq. (3), and the southern region tracer represents the second atmospheric transport term in that equation.

Figure 2a shows that the mid-latitude pulse of
10 Tg CH_{4} results in a larger change at the northern polar stations
(7.3 ppb peak) than at the southern polar stations (3.0 ppb peak). This
reflects the longer transport time for the pulse to reach the southern
stations during which time the pulse becomes more diffuse. More importantly,
for the interpretation of the IPD we find that the northern polar stations
experience the majority of the pulse 0.96 years before the southern polar
stations. After 1991 the pulse responses decay with *e*-folding lifetimes of
4.43 and 8.94 years in the northern and southern polar stations,
respectively. Figure 2c shows that the difference in pulse
response at the poles decays from a maximum value in 1992 with an *e*-folding
time of approximately 0.36 years.

Figure 2b shows that the peak of the 20 Tg CH_{4}
tropical pulse reaches the southern polar region 0.92 years earlier than the
northern polar region. This results in a larger change in southern polar
CH_{4} mole fractions (8.3 ppb peak) compared to corresponding values
over the northern polar regions. The earlier transit of the tropical pulse to
the southern polar region reflects that much of the prior tropical
CH_{4} fluxes that we perturb lie in the Southern Hemisphere. Responses
to the tropical pulse decay after 1992 with *e*-folding
lifetimes of 8.65 and 7.07 years for the northern and southern regions,
respectively. The significant transport delay and disparity in responses
means that an annual mean subtraction of northern and southern polar stations
(IPD) will not remove the influence of the mid-latitude pulse and isolate
local Arctic CH_{4} emissions as previously assumed.

Figure 3a shows that signal variations that we might expect from the atmospheric transport of intra- and inter-annual variation changes in emission sources can dominate the IPD signal. In response to noise superimposed on mid-latitude USA emissions, changes in biweekly IPD values have a mean value of 3.0 ppb (range −0.1–6.0 ppb). The corresponding changes in the annual IPD has a mean value of 3.0 ppb (range 0.3–5.4 ppb). The response of the biweekly IPD to noise on tropical emissions has a mean value of −2.8 ppb (range −12.8–5.6 ppb) and the corresponding response to the annual IPD has a mean value of −2.7 ppb (range −4.7–0.6 ppb). These experiments show that the IPD is susceptible to variations in inter-polar sources.

Figure 3b shows that IPD is sensitive to changes in
local Arctic CH_{4} emissions, as expected, with a near-perfect
correlation. We find only a modest response of IPD to large percentage
increases in Arctic emissions: annual increases of 0.5 %, 1 %, and
2 % in Arctic emissions result in changes of 0.09, 0.17, and
0.35 ppb year^{−1} in IPD. IPD variations that might be expected from
intra- and inter-annual variations in mid-latitude and tropical sources are
typically much larger than the signal associated with changes in local Arctic
emissions. We find that the IPD in the presence of a constant Arctic annual
growth rate and intra- and inter-annual variations in mid-latitude and tropical
emissions can detect a 0.5 % annual growth rate within 11–16 years to a
95 % confidence level (Weatherhead et al., 1998). Table 2
summarizes our results for different growth rates but generally the larger
the Arctic growth rate the shorter it takes to detect the signal, as
expected. The IPD is more susceptible to variations in northern mid-latitude
sources than tropical sources, as described above. These results represent a
best-case scenario for the IPD. In practice, there are also intra- and
inter-annual variations associated with local Arctic emissions that will complicate
the interpretation of the IPD and likely increase the time necessary to
detect a statistically significant signal.

4 Concluding remarks

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We critically assessed the inter-polar difference (IPD) as a robust metric
for changes in Arctic emissions. The IPD has been previously defined as the
difference between weighted means of atmospheric CH_{4} time series
collected in the northern and southern polar regions. A continuous version of
the IPD^{C} model includes at least two additional terms associated
with atmospheric transport. Using the TM5 atmospheric transport model we
highlighted the importance of these atmospheric transport terms. We showed
that IPD has a limited capacity to isolate changes in Arctic emissions.

We show that an inter-polar emission (here, we have evaluated emissions from mid-latitudes and the tropics) generally arrives at one pole earlier than the other pole by approximately 1 year, invalidating a key assumption of the IPD. We also show that a small amount of noise on prior mid-latitude or tropical sources that might be expected due to intra- and inter-annual source variations is not removed in the calculation of the IPD. While the IPD can detect a constant Arctic annual growth rate of emissions, any additional variation due to mid-latitude or tropical sources can delay detection of a statistically significant signal by up to 16 years.

Our study highlights the need for sustaining a spatially distributed and
intercalibrated observation network for the early detection of changes in
Arctic CH_{4} emissions. The ability to detect and quantify trends in
these emissions directly from observations is attractive, but in reality we
need to account for variations in extra-polar fluxes and differential
atmospheric transport rates to the poles. This effectively demands the use of
a model of atmospheric transport, which must be assessed using global
distributed observations.

A Bayesian inference method that integrates information from prior knowledge
and measurements is an ideal approach for quantifying changes in Arctic
CH_{4} emissions, but assumes (a) reliable characterization of model
error and (b) measurements that are sensitive to all major sources. Model
error characterization is an ongoing process. Estimating CH_{4}
emissions from atmospheric measurements is an undetermined (i.e. number of
fluxes to be estimated ≫ number of observations available) and an
ill-posed (i.e. several different solutions exist that are equally
consistent with the available measurements) inverse problem. Prior emissions
are required to regularize the inverse problem, allowing posterior fluxes to
be determined that are consistent with prior knowledge and atmospheric
CH_{4} measurements, as well as their respective uncertainties. Ground-based
measurements represent invaluable information to determine atmospheric
variations of CH_{4}, but the spatial density of these data limits the
resolution of corresponding posterior emission estimates to long temporal and
large spatial scales. Column observations from satellites represent new,
finer-scale information about atmospheric CH_{4}, but they are generally
less sensitive to surface processes than ground-based data. Daily global
observations of atmospheric CH_{4} from the latest of these satellite
instruments, TROPOMI aboard Sentinel-5P (launched in late 2017), promise to
confront current understanding about Arctic emissions of CH_{4}
described by land-surface models and bottom-up emission inventories. Passive
satellite sensors, such as TROPOMI, rely on reflected sunlight so they are
limited by cloudy scenes and by low-light conditions during boreal winter
months. Active space-borne sensors (e.g. Methane Remote Sensing Lidar
Mission, MERLIN, due for launch ≥ 2021) that employ onboard lasers to
make measurements of atmospheric CH_{4} have the potential to provide
useful observations day and night and throughout the year over the Arctic.
The sensitivity of MERLIN to projected changes in Arctic emissions of
CH_{4} is still to be determined. Another major challenge associated
with satellite observations is cross-calibrating sensors to develop
self-consistent time series that can be used to study trends over timescales
longer than the expected lifetime of a satellite instrument (nominally
<5 years). Even with access to all these data, it is clear that no simple,
robust data metric exists without integrating the effects of atmospheric
transport, but data-led analyses remain critical for underpinning knowledge
of current and future changes in Arctic CH_{4} emissions.

Data availability

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Data availability.

Mole fraction data are available at https://www.esrl.noaa.gov/gmd/dv/site/site_table2.php (NOAA, 2018). The model data are available via the NOAA anonymous FTP site: ftp://aftp.cmdl.noaa.gov/user/lori/oscar/ipd (Bruhwiler, 2018).

Appendix A: Development of the continuous IPD model

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Combining IPD(*t*) and *c*(*t*) described in Eqs. (1)
and (2) results in two integral terms that underpin the
continuous version of the IPD:

$$\begin{array}{ll}{\displaystyle}{\mathrm{IPD}}^{\mathrm{C}}\left(t\right)& {\displaystyle}\phantom{\rule{0.125em}{0ex}}=\phantom{\rule{0.125em}{0ex}}{\displaystyle \frac{\mathrm{1}}{\mathrm{\Delta}r}}\underset{{t}^{\prime}=-\mathrm{\infty}}{\overset{{t}^{\prime}=t}{\int}}\left(\underset{r=\mathrm{53}}{\overset{\mathrm{90}}{\int}}\underset{{r}^{\prime}=-\mathrm{90}}{\overset{\mathrm{90}}{\int}}k\right({r}^{\prime},{t}^{\prime}\left)S\right({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}\mathrm{d}{r}^{\prime}\mathrm{d}r\\ \text{(A1)}& {\displaystyle}& {\displaystyle}-\underset{r=-\mathrm{90}}{\overset{-\mathrm{53}}{\int}}\underset{{r}^{\prime}=-\mathrm{90}}{\overset{\mathrm{90}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}\mathrm{d}{r}^{\prime}\mathrm{d}r)\mathrm{d}{t}^{\prime}.\end{array}$$

The first integral describes contributions to CH_{4} mole fractions in
the Arctic region, including local emissions and atmospheric transport that
originate outside the Arctic emitted at an earlier time *t*^{′}. The second
integral describes contributions to Antarctic CH_{4} mole fractions.
Both terms are integrated over all previous times so they include the
influence from older sources.

We now split the first integral into contributions from local Arctic emissions and those transported from sources outside the Arctic, and we split the Antarctic term in a similar way:

$$\begin{array}{ll}{\displaystyle}{\mathrm{IPD}}^{\mathrm{C}}\left(t\right)& {\displaystyle}={\displaystyle \frac{\mathrm{1}}{\mathrm{\Delta}r}}\underset{{t}^{\prime}=-\mathrm{\infty}}{\overset{{t}^{\prime}=t}{\int}}\left(\underset{r=\mathrm{53}}{\overset{\mathrm{90}}{\int}}\right[\underset{{r}^{\prime}=\mathrm{53}}{\overset{\mathrm{90}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}\mathrm{d}{r}^{\prime}\\ {\displaystyle}& {\displaystyle}+\underset{{r}^{\prime}=-\mathrm{90}}{\overset{\mathrm{53}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}\mathrm{d}{r}^{\prime}]\mathrm{d}r\\ {\displaystyle}& {\displaystyle}-\underset{r=-\mathrm{90}}{\overset{-\mathrm{53}}{\int}}\left[\underset{{r}^{\prime}=-\mathrm{90}}{\overset{-\mathrm{53}}{\int}}k\right({r}^{\prime},{t}^{\prime}\left)S\right({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}\mathrm{d}{r}^{\prime}\\ \text{(A2)}& {\displaystyle}& {\displaystyle}+\underset{{r}^{\prime}=-\mathrm{53}}{\overset{\mathrm{90}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}\mathrm{d}{r}^{\prime}\left]\mathrm{d}r\right)\mathrm{d}{t}^{\prime}.\end{array}$$

We assume that the Antarctic region (south of latitude $-\mathrm{53}{}^{\circ}$) contains no local sources so that mole fractions are determined exclusively by atmospheric transport. This eliminates the third term and reduces the integral limits in the second integral. We also assume that atmospheric transport of Arctic sources is too diffuse by the time they arrive at the Antarctic to contribute significantly to Antarctic mole fractions, i.e. ${H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}=\mathrm{0}$ for $\mathrm{53}{}^{\circ}<{r}^{\prime}<\mathrm{90}{}^{\circ}$ and $-\mathrm{90}{}^{\circ}<r<-\mathrm{53}{}^{\circ}$. Using these assumptions (Eq. A2) now becomes

$$\begin{array}{ll}{\displaystyle}{\mathrm{IPD}}^{\mathrm{C}}\left(t\right)& {\displaystyle}={\displaystyle \frac{\mathrm{1}}{\mathrm{\Delta}r}}\underset{{t}^{\prime}=-\mathrm{\infty}}{\overset{{t}^{\prime}=t}{\int}}\left(\underset{r=\mathrm{53}}{\overset{\mathrm{90}}{\int}}\right[\underset{{r}^{\prime}=\mathrm{53}}{\overset{\mathrm{90}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}\mathrm{d}{r}^{\prime}\\ {\displaystyle}& {\displaystyle}+\underset{{r}^{\prime}=-\mathrm{53}}{\overset{\mathrm{53}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}\mathrm{d}{r}^{\prime}]\mathrm{d}r\\ \text{(A3)}& {\displaystyle}& {\displaystyle}-\underset{r=-\mathrm{90}}{\overset{-\mathrm{53}}{\int}}\underset{{r}^{\prime}=-\mathrm{53}}{\overset{\mathrm{53}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}\mathrm{d}{r}^{\prime}\mathrm{d}r)\mathrm{d}{t}^{\prime}.\end{array}$$

Equation (A3) includes three terms: (1) influence of local Arctic emissions on Arctic mole fractions; (2) an atmospheric transport term describing the influence of intra-polar sources (between latitudes $-\mathrm{53}{}^{\circ}$ and $+\mathrm{53}{}^{\circ}$) on Arctic mole fractions; and (3) an atmospheric transport term describing the influence of intra-polar sources (between latitudes $-\mathrm{53}{}^{\circ}$ and $+\mathrm{53}{}^{\circ}$) on Antarctic mole fractions.

If we now consider the change in IPD between some time *t* and a reference
time *t*_{0} we can eliminate the need to integrate over all previous times,
and instead we evaluate the integrals between *t*_{0} and *t*.

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{\mathrm{IPD}}^{\mathrm{C}}\left(t\right)-{\mathrm{IPD}}^{\mathrm{C}}\left({t}_{\mathrm{0}}\right)=\\ {\displaystyle}& {\displaystyle \frac{\mathrm{1}}{\mathrm{\Delta}r}}\underset{{t}^{\prime}=-\mathrm{\infty}}{\overset{{t}^{\prime}=t}{\int}}\left(\underset{r=\mathrm{53}}{\overset{\mathrm{90}}{\int}}\right[\underset{{r}^{\prime}=\mathrm{53}}{\overset{\mathrm{90}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}\mathrm{d}{r}^{\prime}\\ {\displaystyle}& {\displaystyle}+\underset{{r}^{\prime}=-\mathrm{53}}{\overset{\mathrm{53}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}\mathrm{d}{r}^{\prime}]\mathrm{d}r\\ {\displaystyle}& {\displaystyle}-\underset{r=-\mathrm{90}}{\overset{-\mathrm{53}}{\int}}\underset{{r}^{\prime}=-\mathrm{53}}{\overset{\mathrm{53}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}\mathrm{d}{r}^{\prime}\mathrm{d}r)\mathrm{d}{t}^{\prime}\\ {\displaystyle}& {\displaystyle}-{\displaystyle \frac{\mathrm{1}}{\mathrm{\Delta}r}}\underset{{t}^{\prime}=-\mathrm{\infty}}{\overset{{t}^{\prime}={t}_{\mathrm{0}}}{\int}}\left(\underset{r=\mathrm{53}}{\overset{\mathrm{90}}{\int}}\right[\underset{{r}^{\prime}=\mathrm{53}}{\overset{\mathrm{90}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-{t}_{\mathrm{0}}}\mathrm{d}{r}^{\prime}\\ {\displaystyle}& {\displaystyle}+\underset{{r}^{\prime}=-\mathrm{53}}{\overset{\mathrm{53}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-{t}_{\mathrm{0}}}\mathrm{d}{r}^{\prime}]\mathrm{d}r\\ \text{(A4)}& {\displaystyle}& {\displaystyle}-\underset{r=-\mathrm{90}}{\overset{-\mathrm{53}}{\int}}\underset{{r}^{\prime}=-\mathrm{53}}{\overset{\mathrm{53}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-{t}_{\mathrm{0}}}\mathrm{d}{r}^{\prime}\mathrm{d}r)\mathrm{d}{t}^{\prime}\end{array}$$

This can then be expressed as

$$\begin{array}{ll}{\displaystyle}& {\displaystyle}{\mathrm{IPD}}^{\mathrm{C}}\left(t\right)-{\mathrm{IPD}}^{\mathrm{C}}\left({t}_{\mathrm{0}}\right)=\\ {\displaystyle}& {\displaystyle \frac{\mathrm{1}}{\mathrm{\Delta}r}}\underset{{t}^{\prime}={t}_{\mathrm{0}}}{\overset{{t}^{\prime}=t}{\int}}\left(\underset{r=\mathrm{53}}{\overset{\mathrm{90}}{\int}}\right[\underset{{r}^{\prime}=\mathrm{53}}{\overset{\mathrm{90}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}\mathrm{d}{r}^{\prime}\\ {\displaystyle}& {\displaystyle}+\underset{{r}^{\prime}=-\mathrm{53}}{\overset{\mathrm{53}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}\mathrm{d}{r}^{\prime}]\mathrm{d}r\\ \text{(A5)}& {\displaystyle}& {\displaystyle}-\underset{r=-\mathrm{90}}{\overset{-\mathrm{53}}{\int}}\underset{{r}^{\prime}=-\mathrm{53}}{\overset{\mathrm{53}}{\int}}k({r}^{\prime},{t}^{\prime})S({r}^{\prime},{t}^{\prime}){H}_{{r}^{\prime}-r}^{{t}^{\prime}-t}\mathrm{d}{r}^{\prime}\mathrm{d}r)\mathrm{d}{t}^{\prime}.\end{array}$$

In this final expression, the terms that describe local Arctic emissions and
atmospheric transport are integrated between the current time *t* and some
reference time. As a result, the emission term gives a measure of changes in
Arctic emissions between *t* and *t*_{0}.

Appendix B: IPD plots

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For completeness, here we include the plots that complement the analysis
reported in the main text. Figure B1 shows the model
CH_{4} mole fraction corresponding to the weighted mean values at
northern and southern polar region used to calculate the IPD in the control
and pulsed experiments using the TM5. Figure B2 shows values
of the annual mean IPD corresponding to our numerical experiments.

Author contributions

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Author contributions.

OBDM and PIP co-led the mathematical derivation. TM5 model calculations were provided by LPB. Model analysis was led by OBD-M with contributions from LPB and PIP. PIP and OBDM co-wrote the paper with contributions from LPB.

Competing interests

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Competing interests.

The authors declare that they have no conflict of interest.

Special issue statement

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Special issue statement.

This article is part of the special issue “Greenhouse gAs Uk and Global Emissions (GAUGE) project (ACP/AMT inter-journal SI)”. It is not associated with a conference.

Acknowledgements

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Acknowledgements.

Oscar B. Dimdore-Miles was funded by a summer undergraduate project via the
NERC Greenhouse gAs Uk and Global Emissions (GAUGE) project (grant
NE/K002449/1). Paul I. Palmer gratefully acknowledges his Royal Society
Wolfson Research Merit Award. We thank NOAA/ESRL for the CH_{4} surface
mole fraction data which is provided by NOAA/ESRL PSD, Boulder, Colorado,
USA, from their website http://www.esrl.noaa.gov/psd/.

Edited by: Mathias Palm

Reviewed by: three
anonymous referees

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Short summary

The Arctic is experiencing warming trends higher than the global mean. Arctic ecosystems are a large store of carbon. As the soil organic carbon thaws and decomposes, some fraction of this store will eventually be released to the atmosphere as methane. We show that a previously used measurement-based metric to identify changes in Arctic methane emissions does not reliably quantify these changes because it neglects the effect of atmospheric transport. A better metric will combine data and models.

The Arctic is experiencing warming trends higher than the global mean. Arctic ecosystems are a...

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