Methane emissions in Canada have both anthropogenic and
natural sources. Anthropogenic emissions are estimated to be 4.1 Tg a-1
from 2010–2015 in the National Inventory Report submitted to the United
Nation's Framework Convention on Climate Change (UNFCCC). Natural emissions,
which are mostly due to boreal wetlands, are the largest methane source in
Canada and highly uncertain, on the order of ∼ 20 Tg a-1
in biosphere process models. Aircraft studies over the last several years
have provided “snapshot” emissions that conflict with inventory estimates.
Here we use surface data from the Environment and Climate Change Canada
(ECCC) in situ network and space-borne data from the Greenhouse Gases
Observing Satellite (GOSAT) to determine 2010–2015 anthropogenic and
natural methane emissions in Canada in a Bayesian inverse modelling
framework. We use GEOS-Chem to simulate anthropogenic emissions comparable
to the National Inventory and wetlands emissions using an ensemble of
WetCHARTS v1.0 scenarios in addition to other minor natural sources. We
conduct a comparative analysis of the monthly natural emissions and yearly
anthropogenic emissions optimized by surface and satellite data
independently. Mean 2010–2015 posterior emissions using ECCC surface data
are 6.0 ± 0.4 Tg a-1 for total anthropogenic and 11.6 ± 1.2 Tg a-1 for total natural emissions. These results agree with our
posterior emissions of 6.5 ± 0.7 Tg a-1 for total
anthropogenic and 11.7 ± 1.2 Tg a-1 for total natural emissions using GOSAT data.
The seasonal pattern of posterior natural emissions using either dataset
shows slower to start emissions in the spring and a less intense peak in
the summer compared to the mean of WetCHARTS scenarios. We combine ECCC and
GOSAT data to characterize limitations towards sectoral and provincial-level
inversions. We estimate energy + agriculture emissions to be 5.1 ± 1.0 Tg a-1, which is 59 % higher than the national inventory. We
attribute 39 % higher anthropogenic emissions to Western Canada than the
prior. Natural emissions are lower across Canada. Inversion results are
verified against independent aircraft data and surface data, which show
better agreement with posterior emissions. This study shows a readjustment
of the Canadian methane budget is necessary to better match atmospheric
observations with lower natural emissions partially offset by higher
anthropogenic emissions.
Introduction
Methane is a significant anthropogenically influenced greenhouse gas second
to carbon dioxide in terms of its direct radiative forcing (Myhre,
2013). The mixing ratio of methane has increased from ∼ 720 to
∼ 1800 ppb since pre-industrial times (Hartmann et al., 2013).
Present-day global methane emissions are well known to be 550 ± 60 Tg a-1 (Prather et al., 2012). However recent trends in atmospheric
methane since the 1990s are not well understood (Turner et al., 2019).
Anthropogenic methane sources include oil and gas activities, livestock,
rice cultivation, coal mines, landfills and wastewater treatment. Natural
methane emissions are dominated by wetlands but also include seeps,
termites and biomass burning (Kirschke et al., 2013). The main sink of
methane is oxidation by the hydroxyl radical (OH), resulting in a lifetime of
9.1 ± 0.9 years (Prather et al., 2012). Improving constraints on
national methane emissions is a requirement of mitigation policy (Nisbet et
al., 2020). Here we use atmospheric methane observations from the
Environment and Climate Change Canada (ECCC) surface network and satellite
observations from the Greenhouse Gas Observing Satellite (GOSAT) to estimate
Canadian methane emissions and disaggregate anthropogenic and natural
sources.
In the Government of Canada's submission to the United Nations Framework
Convention on Climate Change (UNFCCC), hereafter referred to as the National
Inventory, anthropogenic emissions are estimated to be 4.1 Tg a-1 in
2015, with 68 % of emissions originating from the Western Canadian
provinces of Alberta (42 %), Saskatchewan (17 %) and British Columbia
(9 %). Sectoral contributions over the entire country are from three
categories: energy (49 %), agriculture (29 %) and waste (22 %)
(Environment and Climate Change Canada, 2017). Natural emissions, which are
mostly due to boreal wetlands, are highly uncertain, on the order of
∼ 10–30 Tg a-1 from biosphere process modelling (Miller
et al., 2014; Bloom et al., 2017).
Atmospheric observations provide constraints on methane emissions. Studies
constraining anthropogenic and/or natural methane emissions within Canada
have included the use of surface in situ measurements (Miller et al., 2016;
Atherton et al., 2017; Ishiziwa et al., 2019), aircraft campaigns (Johnson
et al., 2017; Baray et al., 2018) and satellites (Wecht et al., 2014; Turner
et al., 2015; Maasakkers et al., 2021). These observations can determine
emissions through mass balance methods or be used in conjunction with a
chemical transport model (CTM). Bayesian inverse modelling constrains prior
knowledge of emissions based on the mismatch between modelled and observed
concentrations. This requires reliable mapping of “bottom-up” inventory
emissions for the “top-down” observational constraints to be useful (Jacob
et al., 2016). Inverse modelling has been more challenging for Canada than
the United States due to (a) the sparsity of surface stations and satellite
data (Sheng et al., 2018a), (b) anthropogenic emissions that are a factor of ∼ 10 lower
(Maasakkers et al., 2019), (c) large
spatially overlapping emissions from boreal wetlands that are highly
uncertain (Miller et al., 2014) and (d) model biases in the high-latitude
stratosphere (Patra et al., 2011), compromising the interpretation of
observed methane columns.
These observing system challenges have made Canadian methane emissions
difficult to quantify. However, studies show a consistent story across
different scales and measurement platforms. Miller et al. (2014, 2016)
determined that the North American network can successfully constrain
Canadian natural emissions and found boreal wetlands to be lower in 2008
when compared to prior fluxes in the WETCHIMP model. Aircraft campaigns over
the Alberta oil and gas sector have found higher emissions than inventories
in the Red Deer and Lloydminster regions (Johnson et al., 2017) and
unconventional oil extraction in the Athabasca Oil Sands region (Baray et
al., 2018). Atherton et al. (2017) conducted ground-based mobile
measurements of gas production in British Columbia and determined higher
emissions than reported, and Zavala-Araiza et al. (2018) conducted similar
ground-based measurements in Alberta to show a profile of super-emitters
dominating the fugitive methane profile similar to sites in the United
States. Ishiziwa et al. (2019) constrained arctic wetland fluxes to be
similar in magnitude to the mean of the WetCHARTS inventory but with better
identified seasonal and interannual variability. Satellite inversions over
North America using the GEOS-Chem CTM and data from SCIAMACHY (Wecht et al.,
2014) or GOSAT (Turner et al., 2015; Maasakkers et al., 2019) consistently
require an increase in anthropogenic emissions in Western Canada and a
decrease in natural emissions in boreal Canada to match observations, even
with the use of updated Canadian fluxes in Maasakkers et al. (2019) for
anthropogenic (Sheng et al., 2017) and wetlands (Bloom et al., 2017)
sources. Inverse modelling studies that use both in situ and satellite
observations are valuable for intercomparison and for identifying the limits
of spatial and temporal discretization that are possible (Lu et al., 2021;
Tunnicliffe et al., 2020). The Tropospheric Monitoring Instrument (TROPOMI)
launched in 2017 with a data record beginning in 2018 and is expected to
provide significant improvements in emissions monitoring through denser
observational coverage at a similar precision to GOSAT (Hu et al., 2018). It
is necessary to build a reliable historical record of Canadian methane
emissions, as anthropogenic emissions are sensitive to changes in policy and
economic activity (Rogelj et al., 2018), and natural emissions in boreal
Canada may be sensitive to climate change (Kirschke et al., 2013).
In this study we use surface observations from the ECCC greenhouse gas (GHG) monitoring
network and satellite data from GOSAT to constrain anthropogenic and natural
emissions in Canada. We use the GEOS-Chem CTM to simulate 2010–2015 methane
concentrations. The model setup includes the use of an improved bottom-up
inventory for Canadian oil and gas emissions (Sheng et al., 2017), the
WetCHARTS extended ensemble for wetland emissions (Bloom et al., 2017) and
EDGAR v4.3.2 for other anthropogenic sources. We perform an ensemble forward
model analysis which compares six wetlands scenarios to the ECCC surface
observation network to assess the influence of process model configurations
on Canadian methane. A series of Bayesian inverse analyses are performed
that use ECCC and GOSAT data independently and in a joint surface–satellite
system. We constrain monthly natural emissions and yearly total
anthropogenic emissions from 2010–2015 using ECCC and GOSAT data
independently for comparison to produce aggregated-source emissions
estimates. We test the limitations of the ECCC and GOSAT joint observation
system towards constraining emissions by inventory sector and according to
provincial boundaries. We demonstrate where the observation system succeeds
in providing strong constraints on major emissions sources and quantify the
information content of the system to understand the limitations for
resolving all minor Canadian emissions.
Data and methods
We use the GEOS-Chem CTM v12-03 (http://acmg.seas.harvard.edu/geos/, last access: 1 April 2019) to simulate methane fields from
2010–2015 on a 2∘× 2.5∘ global grid and compare them to
surface observations from the ECCC in situ GHG monitoring network and
satellite observations from GOSAT within the Canadian domain. We test for
bias in the global model representation of background methane using both
surface and aircraft in situ data at Canada's most westerly site, Estevan
Point (ESP), using global GOSAT data, and using global NOAA/HIPPO data. The
sensitivity of simulated methane in Canada to the use of different wetlands
flux parametrization is evaluated by comparing an ensemble of WetCHARTS v1.0
configurations to ECCC surface observations. The WetCHARTS ensemble mean in
addition to other GEOS-Chem prior emissions are used in the Bayesian inverse
analysis, which optimizes Canadian sources using ECCC surface data and GOSAT
satellite data independently for comparative analysis. We show the
limitations of the observing system towards subnational-level discretization
by combining ECCC and GOSAT data in a joint inversion. Here we describe the
observations, the model and the inverse analysis in further detail.
ObservationsIn situ surface observations
We use continuous measurements from eight sites in the ECCC greenhouse gas
monitoring network from 2010–2015. Figure 1 shows a map of the sites, and
Table 1 provides a descriptive list. The eight sites are Estevan Point,
British Columbia (ESP); Lac La Biche, Alberta (LLB); East Trout Lake,
Saskatchewan (ETL); Churchill, Manitoba (CHC); Fraserdale, Ontario (FRA);
Egbert, Ontario (EGB); Chibougamau, Quebec (CHM); and Sable Island, Nova
Scotia (SBL). All sites use Picarro cavity ring-down spectrometers (G1301,
G2301 or G2401) to measure dry-air mole fractions of methane with
hourly average precision better than 1 ppb. For model comparison, the
measurements are averaged over 4 h from 12:00 to 16:00 local time, when the
planetary boundary layer is well mixed. The instruments are calibrated
against World Meteorological Organization (WMO)-certified standard gases.
The westernmost site, ESP, measures methane continuously from a 40 m tower
at a lighthouse station on the west coast of Vancouver Island. ESP is
surrounded by forests to the north, east and south and the Pacific Ocean to
the west. ESP is used to evaluate boundary conditions and model bias in the
methane background as it is the least sensitive to Canadian emissions due to
prevailing westerly winds. Sites LLB and ETL are the most sensitive to
anthropogenic emissions in Western Canada. LLB measures continuously from a
50 m tower located in a region of peatlands and forest ∼ 200 km north-east of Edmonton and ∼ 230 km south of Fort McMurray. ETL
measures from a height of 105 m located ∼ 150 km north of
Prince Albert surrounded by boreal forest. The sites in the Hudson Bay
Lowlands (HBL) region, CHC and FRA, are the most sensitive to natural
wetland emissions as this area produces some of the largest methane fluxes
from wetlands in North America. CHC measures continuously from a 60 m tower
in a small port town on the western edge of Hudson Bay surrounded by flat
tundra. FRA measures from a 40 m tower and is located on the southern
perimeter of James Bay surrounded by extensive wetlands coverage. The site
CHM in Quebec is also sensitive to natural wetland emissions and is excluded
in the inverse analysis to be used to verify the posterior results. CHM is
substituted by Chapais, Quebec, ∼ 50 km away, from 2011 onwards.
The remaining Central and Atlantic Canada sites EGB and SBL are sensitive to
net outflow from Canadian sources, both natural and urban, and some
emissions from the Eastern United States. EGB is in a small rural village
∼ 80 km north of Toronto and measures from a 25 m tower. SBL
is on a remote uninhabited island 275 km ESE of Halifax, Nova Scotia, and
measures from a height of 25 m.
Descriptive list of ECCC in situ observation sites used in
the analysis.
Site codeFull name, provinceLatitudeLongitudeElevation (a.s.l.)/sampling height (a.g.l.) (m)ESPEstevan Point, British Columbia49.4∘ N126.5∘ W7/40LLBLac La Biche, Alberta55.0∘ N112.5∘ W548/50ETLEast Trout Lake, Saskatchewan54.4∘ N105.0∘ W500/105CHCChurchill, Manitoba58.7∘ N93.8∘ W16/60FRAFraserdale, Ontario49.8∘ N81.5∘ W210/40EGBEgbert, Ontario44.2∘ N79.8∘ W225/25SBLSable Island, Nova Scotia43.9∘ N60.0∘ W2/25CHMa,bChibougamau, Quebec49.7∘ N74.3∘ W383/30CHAa,bChapais, Quebec49.8∘ N75.0∘ W381/30
a Chibougamau, Quebec, is replaced by Chapais, Quebec, ∼ 50 km
away from 2011 onwards, overlapping in Fig. 1.
b Site is used to evaluate the posterior inversion results and is
not used in the inversion itself.
GOSAT satellite observations
The Greenhouse Gas Observing Satellite (GOSAT) was launched in January 2009
by the Japan Aerospace Exploration Agency (JAXA). GOSAT is in a low-Earth
polar sun-synchronous orbit with an Equator overpass around 13:00 local
time. The TANSO-FTS instrument on board GOSAT retrieves column-averaged dry-air mole fractions of methane using short-wave infrared (SWIR) solar
backscatter in the 1.65 µm absorption band (Butz et al., 2011).
Observation pixels in the default mode are 10 km in diameter separated by
260 km along the orbit track with repeated observations every 3 d. Target-mode observations provide denser spatial coverage over areas of interest.
There has been no observed degradation of GOSAT data quality since the
beginning of data collection (Kuze et al., 2016). Here we use version 7 of
the University of Leicester proxy methane retrieval over land from January
2010 to December 2015 (Parker et al., 2011, 2015; ESA CCI GHG project team,
2018). The single-observation precision of GOSAT XCH4 data is 13 ppb,
and the relative bias is 2 ppb when validated against the Total Column
Carbon Observing Network (TCCON; Buchwitz et al., 2015). Figure 1 shows the
GOSAT observations over Canada used in our analysis within the domain of
45–60∘ N latitude and 50–150∘ W longitude. The observations used have passed all quality
assurance flags for a total of 45 936 observations from 2010–2015, or
approximately ∼ 7600 observations per year. Our analysis
excludes glint data over oceans, and cloudy conditions are accounted for by
the quality assurance flags. We avoid using data above 60∘ N
latitude due to higher uncertainty in the satellite retrieval and the model
comparison (Maasakkers et al., 2019; Turner et al., 2015).
ECCC surface (a) and GOSAT satellite (b) observations used in the inverse analysis. A descriptive list of the ECCC
sites is shown in Table 1. GOSAT data shown are from a single year in 2013
and are filtered to the Canadian domain within 45–60∘ N latitude and 50–150∘ W longitude. There are
∼ 600 GOSAT observations per month in this domain with a
minimum in November–January (112–248) and maximum in July–September (872–1098); individual
months are shown in the Supplement (Fig. S1).
Forward model
We use the GEOS-Chem CTM v12-03 at 2∘× 2.5∘
grid resolution driven by 2009–2015 MERRA-2 meteorological fields from the
NASA Global Modeling and Assimilation Office (GMAO). Initial conditions from
January 2009 are from a previous GOSAT inversion by Turner et al. (2015)
which was shown to be unbiased globally when compared to surface and
aircraft data. Bottom-up anthropogenic emissions in GEOS-Chem are from the
2013 ICF Canadian oil and gas inventory (Sheng et al., 2017) and the 2012
EDGAR v4.3.2 global inventory for other Canadian and global sources and the
gridded US 2012 EPA Inventory for the United States (Maasakkers et al.,
2016). For wetlands, six configurations from the 2010–2015 extended
ensemble of WetCHARTS (Bloom et al., 2017) are used in the ensemble forward
model analysis (Sect. 3.1), and the ensemble mean is used as the prior for
the inverse analysis (Sect. 3.2–3.4). Figure 2 shows the spatial
distribution of the prior methane emissions in Canada from the major
anthropogenic and natural sources. The two largest sources are from the ICF
oil and gas inventory, (Sheng et al., 2017) and wetland emissions from the
ensemble mean of the WetCHARTS inventory (Bloom et al., 2017), with
significant emissions from livestock and waste emissions from EDGAR. Oil and
gas are 54 % of the anthropogenic total, and wetlands are 94 % of the
natural total. The prior emissions estimates in this simulation are
summarized in Table 2, which organizes emissions by Canadian source
categories and are compared to sector attribution in the National Inventory
(Environment and Climate Change Canada, 2017). Our totals for energy,
agriculture and waste are 2.4, 1.0 and 0.9 Tg a-1 respectively
compared to 2.0, 1.2 and 0.9 Tg a-1 in the National Inventory. In the
absence of a spatially disaggregated Canadian inventory for methane, we
consider these prior estimates reasonably similar for the purpose of
comparing our posterior emissions to the National Inventory; however we
cannot compare the spatial pattern of emissions, which will likely show more
discrepancies. Natural emissions are divided into wetlands, which are 14.0 Tg a-1 in the ensemble mean, and other natural sources, which are 0.8 Tg a-1 from biomass burning, seeps and termites. Each component of
other natural emissions has a separate spatially disaggregated inventory as
described in Maasakkers et al. (2019). Emissions from the United States and
the rest of the world are included in the model but not optimized in the
inversions. Loss of methane from oxidation due to OH is computed using
archived 3-D monthly fields of OH from a previous GEOS-Chem full-chemistry
simulation (Wecht et al., 2014).
Mean 2010–2015 prior estimates of Canadian methane
emissions used in GEOS-Chem arranged according to categories in the National
Inventory (Environment and Climate Change Canada, 2017).
a Emissions inputs for GEOS-Chem. These are shown for the individual
source types and summed over the categories energy, agriculture and waste.
In Canada, oil and gas are from Sheng et al. (2017); coal, livestock,
landfills, wastewater and other anthropogenic are from EDGAR v4.3.2; and
wetlands are from Bloom et al. (2017). Biomass burning is from QFED
(Darmenov and da Silva, 2013), and termite emissions are from Fung et al. (1991). Seeps and other global sources are described in Maasakkers et al. (2019).
b Emissions from the National Inventory (Environment and Climate Change
Canada, 2017) that correspond to the energy, agriculture and waste
categories. These are used in the discussion of results but are not included
in the inverse model.
Prior estimates of anthropogenic and natural methane
emissions. Colour bars are in log scale in units of kilograms of methane per squared kilometre per year (kg CH4 km-2 a-1). Most anthropogenic emissions fall under the energy category (a), which are oil and gas in the ICF inventory (Sheng et al., 2017) plus minor
emissions from coal in EDGAR 4.3.2. Livestock (b) and waste (c) are from
EDGAR. Natural emissions are primarily wetlands from the WetCHARTS inventory
(d; Bloom et al., 2017).
Inverse model methodology
We optimize emissions in the inverse analysis by minimizing the Bayesian
cost function J(x) (Rodgers, 2000).
J(x)=1/2x-xaTSa-1x-xa+1/2y-F(x)TSo-1y-F(x),
where x is the vector of emissions being optimized,
xa is the vector of prior emissions (Table 2) and F(x) is the simulation of methane concentrations corresponding to the
observation vector y of ECCC surface and/or GOSAT data.
Sa is the prior error covariance matrix, and
So is the observational error covariance matrix. The
observational error matrix includes both instrument and model transport
error. The GEOS-Chem model relating methane concentrations to emissions
F(x) is essentially linear and can be
represented by the Jacobian matrix K such that
F(x) =Kx+b, where b is the model background. The background includes initial
conditions from Turner et al. (2015) and methane from global emissions that
are held constant in the inversion. Possible bias in the background is
evaluated in detail in the Supplement Sect. S1.3 and shown to be minimal.
The K matrix is of m by n size, where n is the number of state vector
elements being optimized, and m is the number of ECCC surface and/or GOSAT
observations being used. The K matrix is constructed using the forward mode of GEOS-Chem and the tagged tracer
output for Canadian sources, which describes the sensitivity of
concentrations to emissions dy/dx in parts per billion per teragram (ppb Tg-1).
GEOS-Chem continuously simulates global emissions with a global source–sink
imbalance of +13 Tg a-1 in the budget as described in Maasakkers et
al. (2019). We show in Sect. S1.3 of the Supplement that this configuration
of the model reliably reproduces the global growth rate in atmospheric
methane with adjustments only needed for 2014 and 2015, primarily due to
differences in tropical wetland emissions (Maasakkers et al., 2019), with
reduced transport errors at 2∘× 2.5∘
resolution (Stanevich et al., 2020). This gives a well-represented
background for methane which is tested using global GOSAT and NOAA data, as
well as in situ data at Canadian background sites. We improve the model
representation of methane using bias corrections which are discussed in
Sect. S1.3 of the Supplement, and we show the consistency of the inversion
results without adjustments to the model. A high-resolution inversion over
North America over the 2010–2015 time period using the same prior has shown
adjustments to US emissions near the Canadian border are also relatively
minimal, (Maasakkers et al., 2021), so we treat US emissions as constant.
The assumption of constant US emissions is tested in Sect. S1.3.2 of the
Supplement by removing ECCC stations near the US border from the inversion,
which show consistent results. Hence, we can attribute the model–observation
mismatch (y-F(x)) using observations
limited to Canada to Canadian emissions which are optimized in the
inversion. In the main text we show three inversions with a different number
of state vector elements: (a) the monthly inversion (n=78) optimizes
monthly natural emissions in Canada and yearly anthropogenic emissions from
2010–2015; (b) the sectoral inversion (n=5) optimizes emissions according
to the major inventory categories in Table 2 individually for each year; and
(c) the provincial inversion (n=16) optimizes emissions according to
subnational boundaries, which is also repeated for each year. The monthly
inversion provides higher temporal resolution relative to the other
approaches in this study to constrain the seasonality of natural emissions,
assuming the spatial distribution is correct. The sectoral inversion
provides direct constraints on inventory categories, and the provincial
inversion provides relatively higher spatial resolution for subnational
attribution. Substituting F(x)=Kx in
Eq. (1) and subtracting the background b, the analytical solution of the cost
function dJ(x)/dx=0 yields the optimal posterior solution
x^ (Rodgers, 2000):
x^=xa+SaKTKSaKT+So-1y-Kxa.
The analytical solution provides closed-form error characterization, such
that the posterior error covariance S^ of the
posterior solution x^ is given by
S^=KTSo-1K+Sa-1-1.
The averaging kernel matrix A is used to evaluate the surface and
satellite observing systems and is given by
A=In-S^Sa-1,
where In is the identity matrix of length n corresponding to
the number of state vector elements. The averaging kernel matrix A
describes the sensitivity of the posterior solution
x^ to the true state x (A=dx^/dx). The trace of A provides
the degrees of freedom for signal (DOFS), which is the number of pieces of
information of the state vector that is gained from the inversion (DOFS ≤n). The diagonal values of A provide information on which Canadian
state vector elements can be constrained by ECCC surface and GOSAT satellite
observations above the noise, and higher DOFS closer to n correspond to
better constrained sources in total. As a further diagnostic of the
inversion, we conduct a singular value decomposition of the pre-whitened
Jacobian K=So-1/2KSa1/2
(Rodgers, 2000). The number of singular values greater than 1 is the
effective rank of K, which shows the independence of the state
vector elements and the number of pieces of information above the noise that
are resolved in the inversion (Heald et al., 2004). The comparison between
this eigenanalysis and the DOFS is discussed in the Supplement Sect. S1.4
and is used to inform the limitations of the observation system.
We construct the prior error covariance matrix Sa based on
aggregated error estimates for source categories and regions. We use 50 %
error standard deviation for the aggregated anthropogenic emissions, which
includes the Sheng et al. (2017) oil and gas inventory and other EDGAR
sources, 60 % for wetland emissions from the Bloom et al. (2017) WetCHARTS
inventory and 100 % for non-wetlands natural sources. We assume no
correlation between state vector elements so that Sa is
diagonal. Anthropogenic emissions have been shown to be spatially
uncorrelated (Maasakkers et al., 2016); however wetlands show spatial
correlation (Bloom et al., 2017). Here we optimize broadly aggregated
categories, so our method assumes the spatial pattern of each state vector
element is correct; however correlations between state vector elements in
the eigenanalysis are used to assess the limitations of source
discretization in the observing systems.
We construct the diagonal observation error matrix So, which
captures instrument and model error using the relative residual error method
(Heald et al., 2004). In this approach the vector of observed–modelled
differences Δ=yGEOS-Chem-yobservations is
calculated, and the mean observed–modelled difference Δ‾)=yGEOS-Chem-yobservations‾ is attributed
to the emissions that will be optimized. Hence, the standard deviation in
the residual error Δ′=Δ-Δ‾ represents the
observational error and is used as the diagonal elements of
So. For our Canadian inversion, we find positive
model–observation biases in the warmer months (April to September) and
negative biases in the colder months (October to March). We calculate the
relative residual error for growing and non-growing seasons separately, such
that Δ′ is partitioned into Δg′ (October to March) and
Δng′ (April to September), which is then used to calculate the
diagonal elements of So. For surface observations, the mean
observational error is 65 ppb. Since the instrument error is <1 ppb
for afternoon mean methane measurements, the observational error is entirely
attributed to transport and representation error of surface methane in the
model grid pixels. For satellite observations the mean observational error
is 16 ppb where the instrument error is 11 ppb, showing most of the
observational error is from the instrument rather than the forward model
representation of the total column. Column-averaged methane concentrations
are less sensitive to surface emissions, resulting in the lower model error
(Lu et al., 2021).
In summary, the inverse model is designed to suit the objectives of this
study, which are to (1) optimize anthropogenic and natural emissions in
Canada at the national scale, (2) compare the results of inversions using
surface and satellite observations and (3) characterize the limitations of
the observing system towards subnational-scale emissions discretization. The
spatial and temporal resolution of the inversion is limited by the precision
of GOSAT data, the precision of the model representation of surface methane
for ECCC data and the sparse coverage of both systems relative to the
smaller magnitude of Canadian emissions. This simplified approach, where
Canadian emissions are optimized using only observations in Canada, may be
sensitive to errors in the global model that are projected onto the Canadian
domain. This is minimized if errors in the regional representation of
methane, which are corrected in the inversion, are much larger than errors
in the background from the global model or if the background methane is
corrected using global observations outside of the Canadian domain. We show
an analysis of the global model alongside sensitivity tests of the
inversions in Sect. S1.3 of the Supplement, which produce consistent
results. Future studies may deploy a more sophisticated, high-resolution
inverse model that will match more sophisticated observations, which include
an expanded ECCC surface network, as well as satellites with higher density
(TROPOMI; Hu et al., 2018) or higher precision (GOSAT-2; Nakajima et al.,
2017) observations outside of the years of this analysis.
Results and discussionEvaluation of WetCHARTS extended ensemble for wetland emissions in
Canada
Wetlands are the largest methane source in Canada with uncertainties in the
magnitude, seasonality and spatial distribution of emissions. Our inverse
analysis constrains the magnitude and seasonality of emissions with
observations. Ideally, the prior emissions in the model should be the best
possible representation of emissions to reduce error in the optimization
problem (Jacob et al., 2016). Table 2 shows 2010–2015 mean wetland
emissions in Canada to be 14.0 Tg a-1 from the mean of the WetCHARTS
v1.0 inventory (Bloom et al., 2017). These emissions are more than 3
times the total of anthropogenic emissions, 4.4 Tg a-1. The much larger
signal from wetland emissions poses a difficulty for constraining
anthropogenic emissions (Miller et al., 2014). In this section, we evaluate
our use of the mean of the WetCHARTS v1.0 extended ensemble by running a
series of forward model runs using alternate ensemble members in GEOS-Chem
and comparing model output to ECCC in situ observations.
The WetCHARTS extended ensemble for 2010–2015 contains an uncertainty
dataset of 18 possible global wetlands configurations as described in Bloom
et al. (2017). These depend on three processing parameters, which are three
CH4 : C temperature-dependent respiration fractions (q10=1, 2
and 3, where 1 is the highest temperature dependency), two inundation extent
models (GLWD vs. GLOBCOVER, where GLWD corresponds to higher inundation in
Canada) and three global scaling factors for global emissions to amount to
124.5, 166 or 207.5 Tg CH4 a-1 (3×2×3=18).
We find using the scaling factors corresponding to 124.5 and 207.5 Tg CH4 a-1 within GEOS-Chem results in an imbalance in the global
budget beyond what is observed in our measurements and degrades the
representation of background methane, so we limit the extended ensemble to
six members which depend on three temperature parametrizations and two
inundation scenarios (3×2=6). Figure 3 shows the magnitude and
spatial distribution of wetland emissions in the six scenarios. The total
wetland emissions within Canada show nearly an order of magnitude difference
between ensemble members from 3.9 to 32.4 Tg a-1. Compared
to the rest of North America, boreal Canada shows the largest variability
between ensemble members, with the Southeastern United States as the second
most uncertain (Sheng et al., 2018b).
We use ECCC in situ observations to better constrain the range of wetlands
methane emissions in the ensemble members. All six configurations are used
in GEOS-Chem to produce a series of forward model runs for a subrange of
years between 2013–2015. Figure 4 shows GEOS-Chem-simulated methane
concentrations using the six WetCHARTS configurations and compares them to
four ECCC in situ measurement sites in Canada (LLB, ETL, FRA and EGB). This
subset of available data is representative of sites sensitive to both
anthropogenic and natural emissions. Most Canadian anthropogenic
emissions are from Western Canada (Fig. 2), which we use sites LLB and ETL
to evaluate (Fig. 1), and a significant amount of Canadian natural emissions
are from regions surrounding the Hudson Bay Lowlands, which we use sites
FRA and EGB to evaluate. Methane concentrations from GEOS-Chem show large
differences when compared to ECCC observations, ranging from +1050 to
-150 ppb. The boundary-condition site ESP (Fig. S3) showed a mean bias of
5.3 ppb for all of 2010–2015. Since there is no similar mismatch in the
global representation of methane, these biases up to 1050 ppb can therefore
be attributed to misrepresented local Canadian emissions plus associated
transport and representation error. Two types of biases with opposite signs
appear from this comparison. The first type is a positive summertime bias
where the modelled methane concentrations significantly exceed the
observations; this bias is more pronounced in sites FRA (Fig. 4c) and EGB
(Fig. 4d), which are in Ontario and sensitive to the Hudson Bay Lowlands.
The bias is also visible in the western sites LLB (Fig. 4a) and ETL (Fig. 4b) to a lesser extent. As we use a smaller magnitude of wetlands methane
emissions corresponding to the ensemble members in Fig. 3 (from 32.4 to 3.9 Tg a-1), this summertime bias decreases
proportionately. Therefore, we can attribute these large positive summertime
biases to growing season wetland emissions that are overestimated in the
process model configurations. The second type of bias is a year-long
negative bias that appears most in site LLB (Fig. 4a) and is magnified with
the use of lower magnitude wetland emissions. This suggests the presence of
year-round anthropogenic emissions in Western Canada that are underestimated
in the prior or that wintertime wetland emissions could also be
underestimated in WetCHARTS due to the lack of explicit soil water and
temperature dependencies. The inverse modelling results in the next section
attribute this bias to anthropogenic emissions.
Miller et al. (2016) conducted a study constraining North American boreal
wetland emissions from the WETCHIMP inventory modelled in WRF-STILT by a
comparison to observations in 2008. Their study included the use of three of
the ECCC stations described here (CHM, FRA and ETL). The model comparison to
observations in that study showed a similar pattern of modelled methane
exceeding observations in the summer and a low bias at ETL. They suggested
wetland emissions were overestimated in most model configurations and that
the wetlands bias may be masking underestimated anthropogenic emissions.
These conclusions are corroborated by the 2013–2015 comparison shown here;
we show high wetland emissions configurations in WetCHARTS produce a high
bias that exceed measured summertime methane concentrations, and the use of
lower wetlands configurations reveal a year-long low bias apparent in
Western Canada. Our results suggest the combined use of higher inundation
extent and lower temperature dependencies (GLWD and q10=3) or the
use of lower inundation extent and higher temperature dependencies
(GLOBCOVER and q10=1) best reproduce observations near the mean of
the range of emissions, although the ensemble forward model analysis is
unable to specify more detailed process model constraints.
The forward model analysis in this section is a direct evaluation of
wetlands configurations. This approach allows us to manually tune wetlands scenarios
and diagnose the sensitivity of the modelled–observed differences to the
process modelling parameters. The inverse analysis shown subsequently is a
statistical optimization that applies scaling factors to emissions based on
the same model–observation differences. The inverse analysis can be viewed
analogously as an automatic approach. These results show the challenge with
optimizing Canadian methane emissions when wetland emissions are largely
uncertain. Our approach of optimizing anthropogenic and natural emissions
simultaneously in an inversion is useful because attempting to constrain
either emissions category, anthropogenic or natural, obfuscates the analysis
on the other. We exploit the different pattern of anthropogenic and natural
emissions in time and space (Fig. 4). Natural emissions peak in the
summertime and are concentrated in boreal Canada, while anthropogenic
emissions are persistent year-round and are concentrated in Western Canada
(Fig. 2). Hence when optimizing the model–observation mismatch in a Bayesian
inverse framework, some elements of the observation vector will correspond
to high biases from summertime observations in boreal Canada, and some
elements will correspond to low biases in Western Canada. As the choice of
prior for the inversion, we use the mean of the WetCHARTS configurations
(14.0 Tg a-1) which corresponds to the middle of the range shown shaded
in red in Fig. 4. The 60 % range of uncertainty in the prior error
covariance matrix Sa appropriately excludes the extreme
scenarios in Figs. 3 and 4.
Ensemble members from the WetCHARTS v1.0 inventory (Bloom
et al., 2017) with totals for wetland methane emissions within Canada for
each configuration shown in teragrams of methane per year (Tg CH4 a-1). Ensemble members vary
according to the use of three CH4 : C q10 temperature dependencies
and two inundation extent scenarios (GLWD vs. GLOBCOVER) for 3×2=6 scenarios.
Time series of 2013–2015 modelled and observed methane
concentrations. Monthly mean methane from ECCC in situ observations (black)
are shown and compared to six GEOS-Chem simulations differing in the use of
WetCHARTS ensemble members for wetland emissions, with other emissions
corresponding to Table 2. The six configurations are labelled GCXY, where
the first digit (X=1,2,3) corresponds to the CH4 : C q10 temperature
dependency, which decreases the sensitivity of emissions to temperature with
increasing value. The second digit (Y=3,4) corresponds to the model used
for inundation extent (3 = GLWD, 4 = GLOBCOVER) where GLOBCOVER produces
lower emissions in Canada. Emissions configurations are those shown in Fig. 3 in order of magnitude from red to purple lines, with the red shading
showing the range of concentrations. Sites are LLB, Alberta (a); ETL,
Saskatchewan (b); FRA, Northern Ontario (c); and EGB, Southern Ontario (d).
Comparative analysis of inversions using ECCC in situ and GOSAT
satellite data
We optimize 2010–2015 emissions in Canada using an n=78 state vector
element inversion setup with GOSAT and ECCC data independently. Elements
1–72 of the inversion are monthly total natural emissions (wetlands +
other natural) from 2010–2015, and elements 73–78 are yearly total
anthropogenic emissions (energy + agriculture + waste) for the same
years. These categories correspond to the emissions shown in Table 2. We do
not optimize emissions according to clustered grid boxes like other
satellite inversions using GEOS-Chem (Wecht et al., 2014; Turner et al.,
2015; Maasakkers et al., 2019) and instead scale the amplitudes of these two
aggregated categories. This approach is a trade-off of time for space, due
to the limitations of the observations, giving up finer spatial resolution
for finer temporal resolution. This is useful for optimizing Canadian
methane emissions since (a) anthropogenic emissions are largely concentrated
in Western Canada and require less spatial discretization over the entire
country, and (b) natural emissions are the largest source and have an
uncertain seasonality – as shown in the previous section – and require
finer temporal discretization. The limitations of this method are that
natural emissions are very unlikely to be spatially homogenous and vary due
to hydrological differences, even at the microtopographic level (Bubier et
al., 1993). Perfectly resolving Canadian emissions sources in time and space
is challenged by the sparsity and precision of the observing system and the
model representation of the observations. We show the limitations of the
combined ECCC and GOSAT observing system towards resolving subnational
emissions in more detail in the subsequent section.
Figure 5a shows 2010–2015 posterior emissions using this 78 state
vector approach with ECCC in situ data (blue) and GOSAT satellite data
(green). Error bars are from the diagonal elements of the posterior error
covariance matrix S^. Posterior anthropogenic
emissions averaged over the 6 year period are 6.0 ± 0.4 Tg a-1
(1σ year-to-year variability) using ECCC data and 6.5 ± 0.7 Tg a-1 using GOSAT data. Posterior estimates are 36 % and 48 % higher
than the prior of 4.4 Tg a-1 for ECCC and GOSAT results, respectively.
There does not appear to be a significant year-to-year trend above the noise
for the anthropogenic emissions optimized by either dataset. The posterior
anthropogenic emissions using ECCC and GOSAT data show agreement with each
other in each year but 2011, where the GOSAT derived emissions are
statistically higher. The error from the diagonal of the posterior error
covariance matrix S^ may be overly optimistic,
particularly for GOSAT data. This is due to the observational error
covariance matrix So being treated as diagonal when
realistically there are correlations between GOSAT observations that are
difficult to quantify (Heald et al., 2004). Our results for anthropogenic
emissions show agreement with top-down aircraft estimates of methane
emissions in Alberta that are higher than bottom-up inventories (Johnson et
al., 2017; Baray et al., 2018) and previous satellite inverse modelling
studies over North America that upscale emissions in Western Canada (Turner
et al., 2015; Maasakkers et al., 2019; Maasakkers et al., 2021; Lu et al.,
2021). We show source attribution through a sectoral and subnational-scale
analysis of anthropogenic emissions in the subsequent section.
Inversion results for monthly natural emissions from 2010–2015 are also
shown in Fig. 5b. The total of posterior natural emissions
averaged over the 6-year period is 11.6 ± 1.2 Tg a-1 using ECCC
data and 11.7 ± 1.2 Tg a-1 using GOSAT data. The prior for
natural emissions is 14.8 Tg a-1 from the mean of the WetCHARTS
extended ensemble (14.0 Tg a-1) plus other natural sources (biomass burning + termites + seeps = 0.8 Tg a-1). There is some interannual
variability in the prior due to higher emissions in 2010 and 2015. Posterior
results averaged over the 6 years are 22 % lower than the prior using
ECCC data and 21 % lower using GOSAT data, with both posterior results
showing agreement with each other. These results are within the uncertainty
range of the WetCHARTS extended ensemble, and we show the magnitude of
emissions from the larger uncertainty dataset (3.9 to 32.4 Tg a-1) can
be better constrained with both ECCC and GOSAT observations.
While our results show lower natural emissions in all years, a linear fit to
the posterior annual emissions using ECCC data shows a trend of increasing
natural emissions at a rate of ∼ 0.56 Tg a-1 from 2010–2015. The posterior emissions with GOSAT data do not corroborate this
result; the overall emissions trend using GOSAT data is not robust and shows
a decreasing trend of ∼ 0.2 Tg a-1. The lack of
corroboration of trends between ECCC and GOSAT data may be reflective of the
lower overall sensitivity of total column methane to these surface fluxes
(Sheng et al., 2017; Lu et al., 2021) or the inability of this inverse
system to constrain trends sufficiently. The combined ECCC+GOSAT inversion
using this setup is consistent with the results of the individual
inversions (shown in the Supplement Fig. S11), while the
intercomparison is emphasized here, although we note the combined inversion
also does not corroborate this trend. We evaluate the possible influence of
errors in the global model on the projection of a trend onto the ECCC
inversion in Sect. S1.3.2 of the Supplement. While the mean natural
emissions over 2010–2015 show consistent results in the sensitivity tests,
the limitations of the observation system, the inversion procedure and the
timescale of the analysis limit the interpretation of trends. Poulter et al. (2017) estimated global wetland emissions using biogeochemical process
models constrained by inundation and wetlands extend data. They estimated
mean annual emissions over all of boreal North America to be 25.1 ± 11.3 Tg a-1 in 2000–2006, 26.1 ± 11.8 Tg a-1 in 2007–2012
and 27.1 ± 12.5 Tg a-1 which suggests a small increasing trend.
Observational constraints over longer timescales are necessary to
investigate the possibility of trends in Canadian natural methane emissions.
Improvements to the observation network and a better understanding of
climate sensitivity in WetCHARTS are necessary to understand how wetlands
methane emissions will evolve in future climates.
Comparative analysis of inversion results optimizing
annual total Canadian anthropogenic emissions (a) and monthly total
natural emissions (b) in an n=78 state vector element setup. The
posterior emissions determined using ECCC in situ (blue) and GOSAT satellite
(green) data are compared to the prior (grey). Error bars are from the
diagonal elements of the posterior error covariance matrix.
Figure 6 shows the 2010–2015 average seasonal pattern of natural emissions
in the prior and posterior results. The seasonality of natural methane
emissions in the prior shows a sharp peak in July, with a narrow methanogenic
growing season. The posterior emissions with ECCC data shows a peak 1 month later in
August in most years instead of July, with emissions lower than the prior in the
spring months before the peak (March to May) and similar emissions to the
prior in the autumn months after the peak (September to November). Posterior
emissions with GOSAT show a peak in July, and this corroborates the pattern of
slower to begin spring emissions and the lower intensity summer peak seen
from the ECCC inversion. The posterior results show the seasonality of
emissions is not symmetrical around the temperature peak in July. August
emissions are higher than June, September emissions are higher than May and
October emissions are higher than April. This pattern around July is present
in the prior emissions from WetCHARTS; however the inversion results
constrained by ECCC or GOSAT observations intensify the relative difference
between emissions before and after July. Miller et al. (2016) found a
similar seasonal pattern of emissions in the Hudson Bay Lowlands using an
inverse model constrained by 2007–2008 in situ data. They found a less
narrow and less intense peak of summertime emissions with higher emissions in autumn than
spring. Warwick et al. (2016) used a forward model and isotopic
measurements of δ13C-CH4 and δD-CH4 from
2005–2009 to show northern wetland emissions should peak in
August–September with a later spring kick-off and later autumn decline. This
is further corroborated by Arctic methane measurements (Thonat et al., 2017)
and high-latitude eddy covariance measurements (Peltola et al., 2019; Treat
et al., 2018; Zona et al., 2016) that show a larger contribution from the
non-growing season. Our inverse model results using ECCC and GOSAT data both
show agreement with slower to start emissions in the spring and a less
intense summertime peak for Canadian wetland emissions.
Several mechanisms have been proposed to describe a larger relative
contribution from cold-season methane emissions. Pickett-Heaps et al. (2011)
attributed a delayed spring onset in the HBL to the suppression of emissions
by snow cover. The temperature dependency in WetCHARTS is based on surface
skin temperature (Bloom et al., 2017); however subsurface soil temperatures
may continue to sustain methane emissions while the surface is below
freezing. When subsurface soil temperatures are near 0 ∘C, this
“zero curtain” period can further continue to release methane for an
extended period (Zona et al., 2016). Subsurface soils may remain unfrozen at
a depth of 40 cm, even until December (Miller et al., 2016). Alternatively,
field studies in the 1990s suggested the seasonality of emissions may be
more influenced by hydrology than temperature, with large differences
between peatlands sites (Moore et al., 1994). The WetCHARTS extended
ensemble inundation extent variable is constrained seasonally by
precipitation. While this does not directly constrain water table depth and
wetland extent, it provides an aggregate constraint on hydrological
variability (Bloom et al., 2017). We show the mean seasonal pattern of both
air temperature and precipitation from climatological measurements in
subarctic Canada are similarly asymmetrical about the July peak (Fig. S2 in
the Supplement). August is warmer and wetter than June, September is warmer
and wetter than May and October is wetter and warmer than April – with
wetness being more persistent into the autumn than air temperature. Our
inversion results showing a delayed spring start in the seasonal pattern of
natural methane emissions in Canada may suggest a lag in the response of
methane emissions to temperature and precipitation. This may be due to
lingering subsurface soil temperatures and/or more complex parametrization
necessary for hydrology.
The overall agreement between ECCC and GOSAT inversions shows robustness in
the results. While the same model, prior emissions and inversion procedure
are used for assimilating ECCC and GOSAT data, the two datasets are produced
with very different measurement methodologies (in situ vs. remote sensing)
and sample different parts of the atmosphere (surface concentrations or the
total vertical column). The posterior error intervals shown from
S^ reflect assumptions about the treatment of
observations and may insufficiently account for correlations; however the
comparative analysis provides a useful sensitivity test of the posterior
emissions since the datasets reflect different treatment of these
assumptions.
Mean 2010–2015 seasonal pattern of natural methane
emissions in teragrams per month. The annual total emissions are 14.8 (prior, grey), 11.6 ± 1.2 (posterior ECCC, blue)
and 11.7 ± 1.2 Tg a-1 (posterior GOSAT, green). The posterior
results are within the uncertainty range provided by the WetCHARTS extended
ensemble (3.9–32.4 Tg a-1 for Canada).
Joint inversions combining ECCC in situ and GOSAT satellite data
We combine the ECCC and GOSAT datasets in two policy-themed inversions: (1) optimizing emissions according to the sectors in the national inventory (n=5 state vector elements; corresponding to the categories in Table 2) and (2) optimizing emissions by provinces split into anthropogenic and natural
totals (n=16), and we show the results in Fig. 7. These inversions are
underdetermined and show the limitations of the ECCC+GOSAT observing
system towards constraining emissions in Canada with very small magnitudes.
We conduct the inversions for each year from 2010–2015 individually and
present the average from these six samples. Since these two policy
inversions use a low number of state vector elements, they are vulnerable to
both aggregation error and overfitting of the well-constrained state vector
elements and do not necessarily benefit from using a larger data vector from
all 6 years. We discuss the diagnostics and information content for these
inversions in detail in Sect. S1.4 of the Supplement. The error bars are
the 1σ standard deviation of the six yearly results and therefore
represent both noise in the inversion procedure and year-to-year differences
in the state (emissions and/or transport). Here we do not apply a weighting
factor to either dataset; the observations are treated equivalently for the
cost function in Eq. (1). While there are about 5 times more GOSAT
observations than ECCC observations for use in the analysis, and the in situ
observations have larger observational error in Sa
(due to model error), the surface measurements are much more sensitive to
surface fluxes, which offsets the weight of the larger amount of GOSAT data.
As further diagnostics, we show the inversions using GOSAT and ECCC
individually (Tables S4 and S5), which show general agreement between the
datasets. We also use a singular value decomposition eigenanalysis (Heald et
al., 2004) to evaluate the independence of the state vector elements and to
demonstrate which sectoral categories and provinces can be reliably
constrained above the noise in the system (Fig. S9 and S10 in the
Supplement).
Figure 7a shows the sectoral inversion corresponding to categories in
the National Inventory (Table 2). The prior emissions with 50 % error
estimates (60 % for wetlands) are 2.4 (energy), 1.0 (agriculture), 0.9 (waste), 14.0 (wetlands)
and 0.8 Tg a-1 (other natural). the posterior emissions are 3.6 ± 0.9 (energy), 1.5 ± 0.4 (agriculture), 0.8 ± 0.2 (waste), 9.6 ± 1.1 (wetlands) and
1.7 ± 0.9 Tg a-1 (other natural). The degrees of freedom for
signal and singular value decomposition (Fig. S9) show three to four independent
pieces of information can be retrieved, which are differentiated in the
figure by solid and hatched bars. The singular value decomposition shows
strong source signals corresponding to wetlands and energy, with
signal-to-noise ratios of ∼ 37 and ∼ 5,
respectively. These are the two largest emissions sources in Canada and show
the inverse system can successfully disentangle the major anthropogenic and
natural contributors. Emissions from waste have a signal-to-noise ratio of
∼ 2 and can be constrained despite the low magnitude of
emissions. This is likely due to waste emissions being more concentrated in
Central Canada and away from the influence of large energy and agriculture
emissions in Western Canada. Emissions from other natural sources are at the
noise limit and show a moderate correlation with wetlands, which shows that
these two sources are not completely independent. Agriculture emissions are
below the noise in the system and highly correlated with energy emissions.
This is likely due to the high spatial overlap of energy and agriculture
emissions in Western Canada. As a result of these limitations, we present
the total of energy and agriculture as 5.1 ± 1.0 Tg a-1 and the
total of wetlands and other natural as 11.3 ± 1.4 Tg a-1. Our
results for total natural and total anthropogenic emissions are consistent
with the results from the previous monthly inversion, with the added benefit
of identifying which sectors are responsible for the higher anthropogenic
emissions at the cost of lower temporal resolution. Waste emissions are
15 % lower than the prior and 14 % lower than the National Inventory.
The total for energy and agriculture is 49 % higher than the prior and
59 % higher than the total in the inventory. These results show that
energy and/or agriculture are the sectors that are responsible for the
higher anthropogenic emissions.
Joint inversions combining 2010–2015 ECCC in situ and
GOSAT satellite data showing how the combined observing system remains
limited towards resolving all Canadian sources. Inversions are done for each
year, and we present the 6-year average with error bars showing the
1σ standard deviation of the yearly results. Hatched bars indicate
sources that are not well constrained; these are defined as state vector
elements with averaging kernel sensitivities less than 0.8 which are
affected by aliasing with other sources (see Supplement Figs. S9 and S10).
Panel (a) shows the sectoral inversion according to the categories in
the National Inventory (energy, agriculture and waste) and two natural
categories (wetlands and other natural). As an example, the diagnostics in
Fig. S9 show agriculture emissions are beneath the noise and cannot be
distinguished from energy. Panel (b) shows the subnational regional
inversion according to provinces (BC British Columbia, AB Alberta, SK
Saskatchewan, MB Manitoba, ON Ontario and QC Quebec) and aggregated regions
(ATL Atlantic Canada and NOR Northern Territories) further subdivided according
to total anthropogenic and total natural emissions. The diagnostics in Fig. S10 show more than half of the regions are at or below the noise. For
anthropogenic emissions, the best constraints are on provinces AB and ON.
For natural emissions, the best constraints are on AB, SK, MB and ON.
Figure 7b shows the provincial inversion corresponding to the six
largest emitting provinces (BC British Columbia, AB Alberta, SK,
Saskatchewan, MB Manitoba, ON Ontario and QC Quebec) and two aggregated regions
(ATL Atlantic Canada and NOR Northern Territories). These regions are further
subdivided into total anthropogenic and total natural methane emissions,
with below-detection-limit anthropogenic emissions from Atlantic Canada and
Northern Territories. This inversion especially challenges the limitations
of the ECCC + GOSAT observation system, as only about 8 of 16 independent
pieces of information are retrieved. This means that half of the posterior
provincial emissions are below the noise, and we are unable to constrain
province-by-province emissions. The singular value decomposition identifies
which regions are well constrained (Fig. S10). For the anthropogenic
emissions, AB and ON are strongly constrained. For the natural emissions, AB,
ON, SK and MB are well constrained. BC shows correlation between its own
anthropogenic and natural emissions and cannot be completely disaggregated.
As a result, we group elements together in Western Canada (BC + AB + SA + MB) and Central Canada (ON + QC) for interpretation. The total for
Western Canada anthropogenic emissions is 4.7 ± 0.6 Tg a-1, which
is 42 % higher than the prior of 3.3 Tg a-1. The total for Central
Canada is 0.8 ± 0.2 Tg a-1, which is 11 % lower than the prior
of 0.9 Tg a-1.
Each of our top-down inversion results show higher total anthropogenic
emissions than bottom-up estimates. This is consistent regardless of the
observation vector incorporating ECCC data, GOSAT data or ECCC + GOSAT data.
The subnational-scale emissions are limited in their ability to provide full
characterization of minor emissions across Canada but can successfully
constrain major emissions for source attribution. The sectoral inversion
attributes higher anthropogenic emissions to energy and/or agriculture and
applies a small decrease to waste emissions. The provincial inversion
attributes higher anthropogenic emissions to Western Canada and a small
decrease to Central Canada. These results suggest that anthropogenic
emissions in Canada are underestimated primarily because of higher emissions
from Western Canada energy and/or agriculture. This interpretation is
consistent with previous satellite inverse modelling studies over North
America that apply positive scaling factors to grid box clusters in Western
Canada to match observations (Maasakkers et al., 2019; Turner et al., 2015;
Wecht et al., 2014). Aircraft studies in Alberta have also shown higher
emissions from oil and gas in Alberta than bottom-up estimates (Baray et
al., 2018; Johnson et al., 2017). Atherton et al. (2017) estimated higher
emissions from natural gas in north-eastern British Columbia using mobile
surface in situ measurements (Atherton et al., 2017). Zavala-Araiza et al. (2018) showed a significant amount of methane emissions in Alberta from
equipment leaks and venting go unreported due to current reporting
requirements, and in some regions a small number of sites may be responsible
for most methane emissions. Our inverse modelling results from 2010–2015
suggest a consistent presence of under-reported or unreported emissions
which require a policy adjustment to reporting practices.
Evaluation of inversion results with reduced major axis
(RMA) regressions using independent data. The top four panels show the
comparison to ECCC surface observations at Chapais and Chibougamau in
Quebec, Canada, and the bottom four panels show the comparison to NOAA
aircraft profiles at East Trout Lake, Saskatchewan. The agreement of
observations with prior simulated methane concentrations (blue) is compared
to posterior concentrations using optimized emissions from the monthly
inversion (green), the sectoral inversion (magenta) and the provincial
inversion (orange). The coefficient of determination (R2), slope and
mean bias are shown as metrics of agreement.
Comparison to independent aircraft and in situ data
We test the robustness of the optimized emissions from each of the three
inversions shown (monthly natural, sectoral and provincial) by a comparison to
independent measurements not used in the inversions. Prior and posterior
simulated methane concentrations are compared to measurements from NOAA ESRL
aircraft profiles at East Trout Lake, Saskatchewan (Mund et al., 2017), and
ECCC surface measurements in sites Chapais and Chibougamau in Quebec,
Canada. The surface data were averaged to daily afternoon means (12:00 to
16:00 local time) in the same manner as the surface measurements used in the
inversion. Aircraft data from the NOAA ESRL profiles coincide spatially with
the surface measurements at ETL through a joint analysis program with
Environment and Climate Change Canada and have occurred on a regular basis
approximately once a month from 2005 until present time. Aircraft
measurements reach ∼ 7000 m above the surface with samples at
multiple altitudes accomplished using a programmable multi-flask system that
is further discussed in Mund et al. (2017); however we limit the comparison
to the lowest 1 km above ground since higher altitude measurements are
mostly background. The aircraft data are not averaged; however the flights
occur around the same time in the early afternoon.
Figure 8 shows the comparison using reduced major axis (RMA) regression,
with the coefficient of determination (R2), the slope and the mean bias
shown as metrics to evaluate the agreement. Surface data in CHA, Quebec,
show better posterior agreement with observations according to all metrics
for each of the three inversions. The R2 of the prior is 0.36 and
improves to a range of 0.44–0.49 for the posterior results, the slope is
1.17 in the prior and improves to a range of 0.92–1.12 and the mean bias
(model – observations) is +16.4 ppb in the prior and improves to +13.2
and +5.6 ppb. Since this site in Quebec is particularly sensitive to the
Hudson Bay Lowlands, the agreement in all metrics suggests our posterior
emissions can better represent wetland emissions in this region. This
includes the reduced peak seasonality of natural emissions in the monthly
inversion, the reduction of wetland emissions in the sectoral inversion and
the reduction of natural emissions primarily in Central Canada in the
provincial inversion. Aircraft data in Saskatchewan show improvement in the
R2 and mean bias metrics, but the slope slightly degrades in one case.
The R2 of the prior is 0.14 and improves to a range of 0.20–0.30, and the
mean bias of the prior is +6.8 ppb and improves to +1.2 and +3.1 ppb.
The slope of the prior is 1.15, which slightly degrades to 0.83 in the
monthly inversion and improves to a range of 0.88–0.93 in the provincial
and sectoral inversions. The high-resolution aircraft measurements are more
susceptible to representation error at this 2∘× 2.5∘
grid resolution. Furthermore, the time-series comparison to surface data at
East Trout Lake (Fig. 4) shows overall lower sensitivity to summertime
wetland emissions than Fraserdale and Egbert and lower sensitivity to
anthropogenic emissions from Alberta than Lac La Biche. Hence, the modelled
methane concentrations at the aircraft measurement points are adjusted less
by the change in posterior emissions. However, improvement in the R2
and mean bias metrics shows there is still a better representation of the
variance in the data, which suggests the posterior emissions reduce bias due
to peak emission episodes.
Conclusions
We conduct a Bayesian inverse analysis to optimize anthropogenic and natural
methane emissions in Canada using 2010–2015 ECCC in situ and GOSAT
satellite observations in GEOS-Chem. Methane concentrations are simulated on
a 2∘× 2.5∘ grid using recently updated prior emissions
inventories for energy and wetland emissions in Canada. Modelled background
conditions for the Canadian domain are shown to be unbiased in the
comparison to surface in situ data at the westernmost site in Canada,
Estevan Point, with agreement within 6 ppb. A forward model analysis shows
much larger biases between -100 ppb and +1050 ppb at surface sites
throughout Canada, demonstrating the presence of misrepresented local
emissions. We show large positive biases (overestimation of emissions) in
the summertime are observed at sites sensitive to wetland emissions; these
biases are reduced by using lower magnitude wetland emissions scenarios with
lower CH4 : C temperature sensitivities or lower inundation extent. We
also show the opposite case of negative biases (underestimation of
emissions) observed year-round at sites in Western Canada. The forward model
analysis is consistent with the results of the inverse analysis that reduce
emissions from natural sources and increase emissions from anthropogenic
sources to minimize the mismatch between modelled and observed methane.
We show three approaches for using ECCC and GOSAT data towards inverse
modelling of Canadian methane emissions. These approaches differ according
to the temporal and spatial resolution of the solution. We show (1) a
relatively higher time-resolution inversion that solves for natural
emissions each month from 2010–2015 and anthropogenic emissions as yearly
totals, (2) a sectoral inversion that solves for emissions according to
categories in the National Inventory and (3) a provincial inversion that solves
for total anthropogenic and natural emissions at the subnational level. The
monthly inversion provides information on the seasonality of natural
emissions (which are ∼ 95 % wetlands) but does not provide
more depth into anthropogenic emissions beyond yearly scaling. The sectoral
inversion provides more information on the categories of anthropogenic
emissions that are misrepresented in the prior but without spatial detail.
The provincial inversion provides the highest level of spatial
discretization but is largely underdetermined due to the limitations of the
observing system towards characterizing very low magnitude emissions from
smaller contributing provinces.
Inversion results show mean 2010–2015 posterior emissions for total
anthropogenic sources in Canada are 6.0 ± 0.4 Tg a-1 using ECCC
data and 6.5 ± 0.7 Tg a-1 using GOSAT data. Annual mean natural
emissions are 11.6 ± 1.2 Tg a-1 using ECCC data and 11.7 ± 1.2 Tg a-1 using GOSAT data. Both inverse modelling estimates are
higher than the prior for anthropogenic emissions, 4.4 Tg a-1, and lower
than the prior for natural emissions, 14.8 Tg a-1. Inversion results
using both datasets show a change in the seasonal profile of natural methane
emissions, where emissions are slower to begin in the spring and show a less
intense peak in the summer. The agreement between two datasets assembled
with different measurement methodologies that sample different parts of the
atmosphere is a robust result that lends weight to our conclusions. Our
results corroborate recent studies showing a less intense and less narrow
summertime peak in North American boreal wetland emissions, with a higher
relative contribution from the cold season (Miller et al., 2016; Zona et
al., 2016; Warwick et al., 2016; Thonat et al., 2017; Treat et al., 2018;
Peltola et al., 2019). These top-down studies using atmospheric observations
show biosphere process models can better account for a more complex response
to peak surface soil temperatures.
We also conduct combined ECCC + GOSAT inversions that aim to resolve finer
resolution emissions corresponding to the sectors of the National
Inventory and corresponding to provincial boundaries. These
policy-themed inversions challenge the capabilities of the ECCC+GOSAT
observation system and show the system is not capable of resolving many
minor emissions in Canada. The degrees of freedom for signal for these
inversions are 3–4 out of 5 state vector elements for the sectoral
inversion and 8 out of 16 for the provincial inversion. The limitation of
this inverse approach towards constraining sectoral or regional-scale
emissions in Canada is due to the low magnitude of these emissions, their
overlapping nature in concentrated regions and the sparsity of data
available to distinguish them apart. Grouping correlated sectors together,
we determine 5.1 ± 1.0 Tg a-1 for energy and agriculture, which is
59 % higher than the inventory, and 0.8 ± 0.2 Tg a-1 for waste,
which is 14 % lower than the inventory. For provincial emissions, we show
Western Canada is 4.7 ± 0.6 Tg a-1, which is 42 % higher than
the prior, and Central Canada is 0.8 ± 0.2, which is 11 % lower. Both
regions show lower natural emissions. These results show that the higher
anthropogenic emissions in the posterior results can be attributed to energy
and/or agriculture primarily in Western Canada where most of Canadian
anthropogenic emissions are concentrated. Our results are consistent with
other top-down studies that show higher anthropogenic
emissions than reported in Western Canada (Wecht et al., 2014; Turner et al., 2015;
Atherton et al., 2017; Johnson et al., 2017; Baray et al., 2018; Maasakkers
et al., 2019). This may be due to oil and gas emissions that are
under-reported or unreported due to current reporting requirements
(Zavala-Araiza et al., 2018). These top-down studies show a need for policy
readjustment in reporting practices for Canadian anthropogenic methane
emissions.
This study shows the value of using complementary surface and satellite
datasets in an inverse analysis. We emphasize the value of comparative
analysis using the datasets independently versus as joint inversions, as
minor emissions are too low in magnitude for the observational precision to
distinguish finer scale discretization above the noise. The comparative
analysis has the added benefit of evaluating the datasets against each other
and the assumptions that are specific to using either surface or satellite
data. The capabilities for combining and intercomparing datasets are expected
to improve with the launch of Copernicus Sentinel-5P satellite (TROPOMI) in
2017 and continued expansions of in situ observation networks. The ability
for next-generation observations to constrain subnational-level emissions in
Canada will depend on instrument and model precision, as well as the
emissions magnitudes and spatiotemporal overlap of the targets. These
technical capabilities should be weighed alongside policy needs for improved
methane monitoring.
Data availability
GEOS-Chem is from 10.5281/zenodo.1464210 (last access: 1 April 2019; The International GEOS-Chem User Community, 2018), which includes links to all gridded prior emissions and meteorological fields used in this analysis. GOSAT satellite data are from the University of Leicester v7 proxy retrieval, available through the ESA Greenhouse Gases Climate Change Initiative: https://catalogue.ceda.ac.uk/uuid/f9154243fd8744bdaf2a59c39033e659 (last access: 1 July 2021; ESA CCI GHG project team, 2018). ECCC in situ data are available through the World Data Centre for Greenhouse Gases (WDCGG) at https://gaw.kishou.go.jp/ (last access 1 July 2021; WDCGG, 2018). NOAA/ESRL aircraft data are from the Global Monitoring Laboratory at 10.7289/V5N58JMF (last access 1 July 2021; Mund et al., 2017).
The supplement related to this article is available online at: https://doi.org/10.5194/acp-21-18101-2021-supplement.
Author contributions
SB, DJJ and RM designed the study. SB conducted the simulations and analysis
with contributions from JDM, JXS, MPS and DBAJ. AAB provided WetCHARTS
emissions and supporting data. SB and RM wrote the paper with contributions
from all authors.
Competing interests
The authors declare that they have no conflict of interest.
Disclaimer
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
Work at Harvard was supported by the NASA Carbon Monitoring System. We thank
the Japanese Aerospace Exploration Agency (JAXA), responsible for the GOSAT
instrument, and the University of Leicester for the retrieval algorithm used
in this analysis. Doug Worthy and the Climate Research Division at
Environment and Climate Change Canada are responsible for the in situ
surface measurements, and the NOAA/ESRL/GML program is responsible for the
Carbon Cycle Greenhouse Gases (CCGG) cooperative air sampling network
measurements.
Financial support
This research has been supported by the Natural Sciences and Engineering Research Council of Canada (grant nos. RGPIN-2018-05898 and 398061-201).
Review statement
This paper was edited by Patrick Jöckel and reviewed by Julia Marshall and one anonymous referee.
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