ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-16-5665-2016Separation of biospheric and fossil fuel fluxes of CO2 by
atmospheric inversion of CO2 and 14CO2 measurements: Observation System SimulationsBasuSourishsourish.basu@noaa.govhttps://orcid.org/0000-0001-8605-5894MillerJohn Bharathttps://orcid.org/0000-0001-8630-1610LehmanScottGlobal Monitoring Division, NOAA Earth System Research Laboratory, Boulder CO, USACooperative Institute for Research in Environmental Science, University of Colorado, Boulder CO, USAInstitute for Arctic and Alpine Research, University of Colorado Boulder, Boulder CO, USASourish Basu (sourish.basu@noaa.gov)10May2016169566556835January201621January201624March201612April2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://acp.copernicus.org/articles/16/5665/2016/acp-16-5665-2016.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/16/5665/2016/acp-16-5665-2016.pdf
National annual total CO2 emissions from combustion of fossil fuels
are likely known to within 5–10 % for most developed countries. However,
uncertainties are inevitably larger (by unknown amounts) for emission
estimates at regional and monthly scales, or for developing countries. Given
recent international efforts to establish emission reduction targets,
independent determination and verification of regional and national scale
fossil fuel CO2 emissions are likely to become increasingly
important. Here, we take advantage of the fact that precise measurements of
14C in CO2 provide a largely unbiased tracer for recently
added fossil-fuel-derived CO2 in the atmosphere and present an
atmospheric inversion technique to jointly assimilate observations of
CO2 and 14CO2 in order to simultaneously estimate fossil
fuel emissions and biospheric exchange fluxes of CO2. Using this
method in a set of Observation System Simulation Experiments (OSSEs), we show
that given the coverage of 14CO2 measurements available in 2010
(969 over North America, 1063 globally), we can recover the US national total
fossil fuel emission to better than 1 % for the year and to within
5 % for most months. Increasing the number of 14CO2
observations to ∼5000 per year over North America, as recently
recommended by the National Academy of Science (NAS) , we
recover monthly emissions to within 5 % for all months for the US as a
whole and also for smaller, highly emissive regions over which the specified
data coverage is relatively dense, such as for the New England states or the
NY-NJ-PA tri-state area. This result suggests that, given continued
improvement in state-of-the art transport models, a measurement program
similar in scale to that recommended by the NAS can provide for independent
verification of bottom-up inventories of fossil fuel CO2 at the
regional and national scale. In addition, we show that the dual tracer
inversion framework can detect and minimize biases in estimates of the
biospheric flux that would otherwise arise in a traditional CO2-only
inversion when prescribing fixed but inaccurate fossil fuel fluxes.
Comparative magnitudes of the annual average NEE
estimated by CarbonTracker 2013B (left) and the difference between two fossil
fuel inventories, Miller/CT and Miller/Vulcan (right). CarbonTracker is an
atmospheric inversion which estimates CO2 surface fluxes given
atmospheric CO2 measurements and “perfectly known” fossil fuel
emissions. Miller/CT is the fossil fuel emission map prescribed in
CarbonTracker 2013B, while Miller/Vulcan is a redistribution of the Miller/CT
annual total fossil fuel CO2 emission over the conterminous United
States according to the spatiotemporal pattern of the Vulcan fossil fuel
inventory . While annual total emissions over
the conterminous US for the two inventories are the same (i.e., the reds and
blues in the right figure sum to zero), over individual 1∘×1∘ grid cells their difference can be comparable to the NEE estimated
at the same location.
Introduction
The terrestrial biosphere and the oceans have taken up roughly half the
anthropogenic emissions of CO2, with the remainder contributing to
the observed increase in atmospheric CO2 concentration from
∼280 ppm in the early 1800s to ∼395 ppm in
2013 . However, while CO2 observations from sampling
networks over large, industrialized land areas will be influenced by
emissions from combustion of fossil fuels, they are often dominated by
seasonally and diurnally varying fluxes of the terrestrial biosphere. Thus,
it is nearly impossible to make use of the atmospheric CO2
observations alone as an independent constraint on the space–time patterns of
fossil fuel CO2 emissions . In addition,
conventional inversion schemes typically
prescribe fossil fuel CO2 fluxes from inventories based on economic
statistics on fossil fuel consumption and assumed combustion efficiencies
(cf. ) with an assigned uncertainty of zero. Under these
conditions, any deviation of the prescribed fossil fuel CO2 fluxes
from their true values can be expected to result in errors in the retrieved
estimates of the terrestrial biospheric exchange fluxes. In areas over which
the total carbon budget is well constrained by large number of observations,
such as the conterminous US, these “carry-over biases” may be comparable in
magnitude to the errors in the specified fossil fuel CO2 fluxes
themselves.
The assumption of perfectly well-known fossil fuel fluxes has been a
reasonable starting point since annual total fossil fuel CO2
emissions from most developed (i.e., UNFCCC Annex I and Annex II)
countries are likely known to within 5–10 % , a level
of certainty that greatly surpasses our knowledge of the annual net
terrestrial biosphere CO2 flux over those areas. However, for
developing (non-Annex) countries, fossil fuel uncertainties are likely to be
much larger. For example, estimates of Chinese emissions from fossil fuel
combustion and cement production have been revised by +17 %
and -14 % over the past 5 years alone. Moreover,
uncertainties in fossil fuel CO2 emissions are likely to be larger
(by unknown amounts) at subnational and subannual scales, even in developed
countries. To illustrate this, we show maps of the difference between two
widely used inventories of the annual fossil fuel CO2 flux over North
America along with an estimate of annual average net ecosystem exchange (NEE)
in Fig. . The inventory differences are in some cases
similar in magnitude to estimates of NEE for individual grid cells (at a
resolution of 1∘×1∘ in this example). Making matters
worse, it is frequently necessary to extrapolate emissions inventories
forward in time to correspond with the times of atmospheric observations.
Such extrapolations might reasonably account for changes in population but
will not capture changes in fossil fuel use associated with, for example,
protracted regional heat and cold waves. At the time of this writing, both
the Vulcan (http://vulcan.project.asu.edu/research.php) and EDGAR
(http://edgar.jrc.ec.europa.eu/overview.php?v=42) inventories provide
emissions estimates only up to 2008, and even the “fast track” version of
EDGAR (EDGAR v4.2 FT2010) has yet to be updated beyond 2010.
Here we take the initial steps at determining fossil fuel emissions and
evaluating our ability to reduce carry-over bias using an atmospheric top-down method and the existing and anticipated array of precise measurements of
atmospheric 14CO2, which provide for direct, precise
(∼1 ppm) and largely unbiased observational constraints on
fossil-fuel-derived CO2 in the same samples that provide the primary
CO2 observations
. Below we first
describe a new inversion framework that assimilates both CO2 and
14CO2 in a system that simultaneously optimizes both fossil fuel
and biospheric exchange fluxes of CO2. We then outline a set of
Observation System Simulation Experiments (OSSEs) designed to evaluate the
ability of the dual tracer inversion framework to separately estimate these
fluxes over the conterminous US using synthetic observations corresponding in
space and time to (a) actual observations in the NOAA ESRL Global Greenhouse
Gas Reference Network (GGRN) in 2010 (1063 14CO2 measurements
globally, of which 969 were in North America) and (b) an enhanced
observational network with 6448 14CO2 measurements globally in
2010 (5304 in North America), similar to the annual 14CO2 coverage
recently recommended by the US NAS . We use the
observational network of (b) in three additional experiments. First, we
perform an ensemble of inversions with and without 14CO2 data in
order to evaluate the degree to which the inclusion of 14CO2
observations allows us to distinguish between biospheric and fossil fuel
CO2 fluxes. We also repeat (b) without 14CO2 data in order
to quantify (by contrast to the dual tracer results) the degree to which the
dual tracer system is able to detect and minimize potential carry-over bias
in NEE that might otherwise arise from a biased fossil fuel prior. Finally we
repeat (b) but with different models of atmospheric transport to generate and
assimilate the synthetic observations, in order to evaluate the potential
impact of transport model error on our emissions estimates.
The inversion framework
Our inversion framework builds on the TM5 4DVAR
system , which has been used for estimating sources and
sinks of CH4, CO, CO2, and N2O. Here we describe modifications to the TM5 4DVAR
system that permit us to jointly assimilate the measurements of two tracers,
CO2 and 14CO2.
The atmospheric mass balances of CO2 and 14CO2 have been
presented previously by . Following those equations, we
rewrite the isotopic mass balance (Eq. 1b and c of ) in
terms of the transported and conserved quantity CΔatm, while
the carbon balance (1a) remains the same, such that
ddtC=Fbio+Foce+Ffosddt(CΔatm)=NrstdFnuc+Fcosmo+ΔfosFfos+ΔatmFoce+Fbio+Δoce-ΔatmFoceatm+Δbio-ΔatmFbioatm=NrstdFnuc+Fcosmo+ΔfosFfos+ΔatmFoce+Fbio+Focedis+Fbiodis,
where C is the atmospheric burden of CO2 and Δatm is
the isotope signature of 14CO2 in the atmosphere expressed in
Δ notation, which includes corrections for mass-dependent isotopic
fractionation between reservoirs and radioactive decay between the times of
sample collection and measurement, such that the quantity
Δ14CO2 is conserved in time (, where
Δ14C is equivalent to Δ14CO2 here).
Fbio, Foce, and Ffos are net CO2 surface
fluxes to the atmosphere from the terrestrial biosphere, oceans, and fossil
fuel burning respectively, and we set Δfos to
-1000 ‰, corresponding to a fossil fuel source devoid of
14C as a result of radioactive decay. Fnuc is the
14CO2 flux from nuclear power and reprocessing plants, and
Fcosmo is the cosmogenic production of 14CO2,
corresponding to the terms isoFnuc and isoFcosmo respectively of
. To convert these pure 14CO2 fluxes into units
of CO2 flux ×Δ (e.g., PgC ‰ yr-1), as in the
other terms on the right-hand side of Eq. (1c), we
divide by the 14C : C standard ratio, rstd=1.176×10-12, and account for mass-dependent fractionation by multiplying by N=(975/(δ13C+1000))2, where δ13C
has an assumed atmospheric value of -8 ‰. Δoce
and Δatm are the isotope signatures of the ocean and the
atmosphere respectively. In Eq. (1c) we assume
that in converting from 14C : 12C to Δ14C
all isotopic fractionation between reservoirs “drop out” of the equations,
such that we can equate the isotopic signature Δatm→x to
Δatm, and Δx→atm to Δx.
Foceatm and Fbioatm are the one-way gross ocean to
atmosphere and biosphere to atmosphere CO2 fluxes. The terms
Focedis=(Δoce-Δatm)Foceatm
and Fbiodis=(Δbio-Δatm)Fbioatm are so-called disequilibrium fluxes (where
Δbio-Δatm=Δbiodis in
). Note, finally, that an extra term involving the net ocean
and terrestrial fluxes (Foce and Fbio) appears in
Eq. (1c), compared to Eq. (1b) of ,
due to the slightly different left-hand sides (d(CΔatm)/dt vs
CdΔatm/dt) of the two equations. Their magnitudes are only
∼100 PgC ‰ yr-1 which is relatively small compared to,
for example, the fossil fuel flux of ∼10 000 PgC ‰ yr-1.
To solve Eq. (1) in an inversion, we further
separate terms in Eq. (1a) into the sum of oceanic
and terrestrial biospheric (hereafter referred to as “natural”) components and fossil fuel
components, where CO2ff denotes the CO2 in the atmosphere
accumulated due to fossil fuel burning since the beginning of the simulation
period (t0). We note here that natural in this context is a mathematical
definition of convenience, not to be confused with pre-anthropogenic. What we
refer to as the natural flux has been influenced by historical anthropogenic
emissions, land use changes and climate change.
ddtCO2nat=Foce+FbioddtCO2ff=FfosCO2ff(t=t0)=0
Our system is primarily designed to estimate fossil fuel CO2 fluxes
and NEE. However, we also solve for Focedis and Fbiodis
at a coarser temporal resolution, as explained in
Sect. . Note that Eq. (1c)
contains Δatm on both sides. However, we do not solve for a
Δatm field self-consistently within the inversion framework. On
the left-hand side, we treat CΔatm as a single tracer.
Accordingly, we convert all measured 14CO2 values to
“measurements” of CΔatm for the flux estimation. On the
right-hand side, for the term Δatm(Foce+Fbio),
we specify a Δatm that is spatially uniform and has a smooth
temporal variation based on observations from the well mixed free troposphere
at Niwot Ridge, Colorado (NWR: 40.0531∘ N, 105.5864∘ W,
http://www.esrl.noaa.gov/gmd/dv/iadv/graph.php?code=NWR&program=ccgg&type=ts),
filtered to remove possible local urban influences from the Denver-Boulder
area to the east . The error made in the inversion by using
this smoothed approximation of Δatm on the right-hand side of
Eq. (1c) is small, since it will in practice be
very close to Δatm in CΔatm and, as noted above,
the term Δatm(Foce+Fbio) is small compared to
others in the overall budget. For the disequilibrium fluxes on the right-hand
side, we solve for Focedis and Fbiodis but do not attempt
to separate those into the one-way gross CO2 fluxes and their
respective isotopic disequilibria.
The observed and modeled latitudinal gradients of
SF6, estimated as the difference between SF6 concentrations at
marine boundary layer sites of the NOAA ESRL GGRN (http://www.esrl.noaa.gov/gmd/ccgg/ggrn.php)
and the South Pole. Observations and models span 10 years from 2002 to 2011.
For each site, we account for time-dependent changes by calculating a linear trend
from observed SF6 and removing that from all three time series (observed,
TM5 EI, TM5 EIC). All observations were binned by latitude in 5∘
increments and averaged. The bottom panel shows the number of samples averaged
per latitude bin. The error bars denote ±2σ intervals, where σ
is the standard error of the mean difference with respect to the South Pole. Measured
SF6 mole fractions used here are available in the Supplement.
Modeling frameworkAtmospheric transport
We use the TM5 atmospheric tracer transport model
to simulate atmospheric tracer concentrations from surface
fluxes. TM5 can be run with convective entrainment and detrainment fluxes
determined directly from the ERA-Interim reanalysis from the European Centre
for Medium range Weather Forecasts (henceforth called TM5 EIC) or with
those fluxes computed within TM5 according to the convective scheme of
(henceforth, TM5 EI), which was the standard scheme
prior to 2014. The largest difference between TM5 EI and TM5 EIC is
in the vertical transport into the free troposphere over temperate latitudes.
For tracers with surface sources and sinks and negligible atmospheric
chemical production and loss – such as CO2 and SF6 – this
difference creates markedly different north–south (N–S) gradients at the
surface, even though the advective winds are the same. As an illustration, in Fig. we
show the average simulated N–S gradient of SF6 within the marine boundary layer for both TM5 EIC and TM5 EI,
compared to average observations from 2002 to 2011.
The 0.3 ppt N–S gradient in SF6 of TM5 EIC is very close to
the observed gradient of 0.295 ppt, whereas the 0.38 ppt N–S
gradient of TM5 EI is the farthest outlier among 16 global transport
models considered by . Moreover, in the analysis of
, most modeled N–S gradients were between
0.27 and 0.32 ppt. Thus, the difference of
0.08 ppt in the N–S gradients simulated by TM5 EI and TM5 EIC is
larger than typical inter-model differences, indicating that these two
schemes represent very different realizations of transport, at least at the
hemispheric and global scales. Since TM5 EIC delivers markedly better
agreement with the observed SF6 N–S gradient, we use TM5 EIC for both
forward simulation and inversion in all experiments, except when evaluating
the impact of transport error on estimated fluxes (for which we use TM5 EI to
assimilate synthetic observations produced by TM5 EIC, as outlined in
Sect. ).
To better resolve atmospheric transport over the domain of interest, we run
the atmospheric transport model at 1∘×1∘ resolution over
North America (20–64∘ N,
132–60∘ W), and at 3∘×2∘
resolution elsewhere. This is the same nested zoom configuration employed in
NOAA's CarbonTracker North America (carbontracker.noaa.gov).
TM5 4DVAR
The TM5 4DVAR inversion system estimates fluxes
x given observations y by minimizing the so-called cost function
J:
J=12Hx-yTR-1Hx-y+12x-x0TB-1x-x0,
where H is an atmospheric transport operator, x0 is the prior flux
before doing a data assimilation, and R and B are the
respective error covariance matrices of the model–data mismatch and the prior
flux. The TM5 variational framework for atmospheric inversion of a single
species has been described in detail previously
. In this work,
x contains the surface fluxes of the three species CO2ff
(Ffos), CO2nat (Foce and Fbio), and
CΔatm (Focedis and Fbiodis). We solve
for Fbio, Foce, and Ffos weekly, and for
Fbiodis and Focedis monthly. The prior flux error
covariance matrix is assumed to be separable in time and space, as in
B(r1,t1;r2,t2)=cov(xr1,t1,xr2,t2)=σr1,t1σr2,t2Cr(r1,r2)Ct(t1,t2),
where r and t are space and time coordinates respectively,
σr,t is the uncertainty of the prior flux at location r at
time t, and Cr(r1,r2) (or Ct(t1,t2)) is the correlation
between flux errors at locations r1 and r2 (or times t1 and
t2). No prior correlation is assumed between the five flux categories
being optimized. For each category, the temporal error correlation Ct is
assumed to be exponential, Ct(t1,t2)=e-t1-t2/T, with
T being 3 months for Foce, Ffos, and
Focedis, and 1 month for Fbio and Fbiodis.
The spatial error correlation is either
exponential, Cr(r1,r2)=e-r1-r2/L, or
regional, where the globe is subdivided into regions, and grid cells within
one region are perfectly correlated, whereas grid cells from different regions are completely uncorrelated, or
a hybrid of the first two, where the grid cell to grid cell correlation
decays exponentially within each defined region, but is zero between regions.
Spatial flux error covariance parameters of Eq. () for different categories.
a For fossil fuel CO2 flux, the “inter-prior spread” denotes
the spread between three fossil fuel inventories, CarbonTracker/Miller,
CarbonTracker/Vulcan, and ODIAC . For defining the region
boundaries across which the prior flux correlation goes to zero, we used nine
divisions of the continental United States defined by the US Census Division
(www.eia.gov/forecasts/aeo/pdf/f1.pdf), shaded in Fig. .
The rest of North America falls into a single region, while other continents,
namely South America, Europe, Africa, Asia, and Australia form five separate regions.
All ocean pixels fall in one single region, while non-optimized pixels (Greenland and Antarctica) fall into one
region.b The world's oceans are divided into the 11 TRANSCOM ocean regions .
c Outside North America, the land is divided up into nine TRANSCOM
land regions. Inside North America, the North American temperate region is
by itself, while the North American boreal region is further subdivided into
11 regions used by CarbonTracker 2013b (http://www.esrl.noaa.gov/gmd/ccgg/carbontracker/CT2013B_doc.php,
Sect. 8.1.1).
The parameters of spatial correlation for the five categories, as well as
the prior errors per grid cell (i.e., σr,t of Eq. ) are listed in
Table .
Surface fluxes are solved for at the same lateral resolution as the transport
(3∘×2∘ globally, 1∘×1∘ over North America),
to provide the inversion with flexibility to change surface fluxes where
there are more observations, and to reduce aggregation error
. This transport/flux configuration is similar to NOAA's
CarbonTracker North America, except that we solve for additive corrections to surface fluxes
per grid cell instead of multiplicative corrections to
regional surface fluxes. We focus on the year 2010, and our inversions run
from 4 July 2009 to 1 April 2011, to allow for sufficient spin up time at
the beginning and sufficient time for the fluxes at the end of 2010 to be
captured by subsequent observations.
14CO2 flux terms
Equation (1a)
and (1c) contain seven different flux terms on the
right-hand side. In the OSSE we create synthetic observations of
CΔatm by specifying and transporting “true” flux fields for
all seven terms. For the inversions, we specify prior fluxes associated with
fossil fuel CO2 emissions (Ffos) and net oceanic and
biospheric fluxes (Foce and Fbio) that differ from those
used to produce the simulated observations, and evaluate our ability to
recover true fluxes using the synthetic observations. The two different sets
(true vs. a priori) of fossil fuel CO2 and net CO2
flux terms are described in Sect. . The construction of
the isofluxes for the remaining terms is described below and is consistent
with the recent tropospheric Δ14CO2 budget and distribution
based on observations.
Gridded estimates of the 14C production flux from nuclear reactors
and fuel reprocessing plants, Fnuc, were taken from
and did not vary with time. Only the portion of this
flux estimated to be directly emitted as 14CO2 was included. The
production of 14C in the atmosphere, Fcosmo, and the
sensitivity of this production to geomagnetic latitude depend on the solar
modulation parameter Φ, a scalar which varies with time. Annual values
of Φ were calculated through 2012 based on a global array of neutron
monitor data obtained from http://nmdb.eu/ (all amplitude normalized to
count rates at Deep River, Canada,
http://neutronm.bartol.udel.edu/~pyle/bri_table.html) and the slope of
a linear regression between annual average Deep River Neutron Monitor count
rate and estimates of Φ between 1955 and 1995 from .
Then, for each year of our simulation period, we calculated the 14C
production as a function of geomagnetic latitude given the annual average
Φ of that year . This resulted in annually varying
production fields dependent on geomagnetic latitude. These production fields
were then distributed vertically over the TM5 model layers corresponding to
the stratosphere (between 150 and 3 hPa), with the mass
of 14CO2 in each layer proportional to the total mass of air in
that layer. To better match the observed 14CO2 trend at NWR, the global total cosmogenic production was scaled by
0.9 in all years.
To calculate the terrestrial disequilibrium flux term
(Δbio-Δatm)Fbioatm, we first constructed
the historical time series of atmospheric 14CO2 by compositing
overlapping time series from tree ring measurements ,
atmospheric records from Vermunt, Austria , Schauinsland,
Germany 14C, Jungfraujoch, Switzerland
14C, and more recently NWR, United States . This historical time series was convolved with the age
distribution of respired carbon derived from pulse response functions from
the Carnegie Ames Stanford Approach (CASA) biosphere model
, to obtain a monthly Δ14CO2 of respired
carbon, Δbio, for each 1∘×1∘ CASA grid
cell. Δatm was derived from filtered, monthly average
observations at NWR, to obtain
(Δbio-Δatm), and Fbioatm was determined
from the monthly total heterotrophic respiration flux for each CASA grid
cell. Monthly Fbioatm did not vary from year to year, while
Δbio and Δatm were updated monthly and from year to
year based on observed changes in atmospheric Δ14CO2.
The oceanic isotopic disequilibrium (Δoce-Δatm)
was estimated from observations of the Δ14C of surface ocean
dissolved inorganic carbon field available from World Ocean Circulation
Experiment (WOCE) for the 1980's–1990's and updated yearly through 2012
using rates of change for different ocean regions based on subsequent
observations from the Climate and Ocean Variability (CLIVAR) measurement
program (http://cdiac.ornl.gov/oceans/datmet.html) as in
. The gridded annual estimates of Δoce were
differenced from a zonally uniform surface layer Δatm field
based on filtered and seasonally smoothed observations from NWR, but with a specified increase of +10 ‰ between
20∘ N and 20∘ S. The disequilibrium flux was then
calculated by multiplying the isotopic disequilibrium by the one-way ocean to
atmosphere CO2 flux for each grid cell, which was derived from a
climatology of surface ocean pCO2 from and a
quadratic wind-speed-dependent piston velocity scaled
to a more recent analysis of the oceanic 14C inventory
.
Initial atmospheric CO2 and 14CO2 fields
Initial concentration fields of CO2 and 14CO2 for the
inversions were obtained by specifying realistic troposphere–stratosphere and
latitude gradients of Δ14CO2 and CO2 and then
propagating time-varying flux terms in Eq. (1)
through the atmosphere using TM5 EIC, starting on 1 January 2000. The three-dimensional atmospheric mole fractions of
CO2×Δ14CO2 and CO2 on 4 July 2009
were used as initial fields for the inversions. The relatively long forward
run was implemented to ensure that the simulated large-scale atmospheric
gradients were consistent with the prior fluxes.
The sites for which CO2 and
14CO2 measurements were simulated and then assimilated in our
OSSEs for two different coverage scenarios, 2010 and NRC 5000, as
described in the text.
Experimental design
Our OSSEs (Table ) are designed to evaluate the ability
of a network of 14CO2 observations – in conjunction with more
widely available CO2 observations – to constrain regional fossil
fuel CO2 and net biosphere exchange fluxes within our inversion
framework. To do this, we first create synthetic atmospheric 14CO2
and CO2 concentrations at real and projected measurement locations
based on transport of a set of true fluxes in TM5 EIC (this step is
sometimes referred to as the “nature run” for an OSSE). By true we do
not suggest that these fluxes are accurate but that they are consistent with
the synthetic observations for the purpose of conducting the OSSE. We then
assimilate the synthetic measurements in an atmospheric inversion using prior
flux estimates which differ substantially from the true fluxes. The
extent to which fluxes estimated by the inversion match the true fluxes
is a measure of the performance of our inversion framework and the network of
(synthetic) observations. An additional metric of performance is the degree
to which 14CO2 data can distinguish between NEE and fossil fuel
CO2 fluxes, measured by the posterior correlation between the two.
This metric is further discussed in Sects. and .
True fluxes
True fluxes used to simulate the observations
are those for 14CO2 described in Sect.
along with those for fossil fuel CO2 and net ocean and biosphere
exchange. For fossil fuel CO2, we use fossil fuel fluxes from
CarbonTracker 2013, redistributed within the continental US according to the
Vulcan spatiotemporal pattern. In addition, we impose scaling factors of
in order to represent the diurnal variability. True
ocean fluxes were taken from posterior fluxes of CarbonTracker 2013b,
specifically the variant which used the ocean interior inversion of
to construct prior ocean fluxes. True terrestrial
fluxes were based on the CASA Global Fire Emissions Database (GFED) 3
model . CASA GFED 3 provided
only monthly NEE fluxes; in order to represent variability at higher
frequencies we imposed daily and 3 hourly variations from SiBCASA GFED4
on the monthly fluxes.
Sampling frequency of CO2 and
14CO2 measurements at the sites of our hypothetical NRC 5000
network. Even though Fig. only displays sites over the
conterminous US and part of Canada, our NRC 5000 network also contains some
background sites such as the South Pole and Mauna Loa. The numbers below include
all sites, globally.
CO214CO2Site typeNo. of sitesSampling freq.No. of sitesSampling freq.Tower622 day-1352 week-1Flask761 week-1211 week-1Aircraft191 week-1,111 week-1,up to 16 altitudes3 altitudesCruise 21 transec month-1,––every 5∘ latitudeSynthetic observations
We simulated two sets of observations, with
distributions as shown in Fig. and
Table . The first set, which we refer to as 2010
coverage, placed a 14CO2 (or CO2) observation at each
spatiotemporal point where there was an actual 14CO2 (or
CO2) measurement between 4 July 2009 and 1 April 2011. This
resulted in a total of 1639 14CO2 and 45 330 CO2
observations over the 21 month period (1475 and 18 008 over North America,
respectively). The accuracy of the estimated surface fluxes with respect to
the true fluxes is expected to provide a measure of the performance of
the real observational network in 2010.
For the second set, which we refer to as NRC 5000, we simulated
∼500014CO2 measurements per year over North America.
In constructing the expanded, hypothetical observational network
(Fig. ) we first sought to increase measurements at
existing NOAA and NOAA-partner monitoring locations, including tall towers
and airborne and surface flask sampling locations, adding six new tall tower
sites to fill gaps in the sampling network. For CO2 we also added
shipboard samples from two monthly cruises in the Pacific Ocean.
Table lists the sampling frequencies for CO2
and 14CO2 at the different sites.
Sampling within the NRC 5000 network conformed as closely as possible to the
actual sampling protocols and periodicities at tower, flask, aircraft, and
cruise locations maintained by NOAA and its partner networks. At tower sites,
we sampled the true CO2 field twice a day at the highest intake
height, at 00:30 and 03:30 local solar time (LST) for mountaintop sites and
at 12:30 and 15:30 LST otherwise. The true 14CO2 field was
sampled on Mondays and Thursdays following the same protocol for intake
height and LST. Flask sites were sampled on Wednesdays at 13:30 LST (01:30 LST
for mountaintop sites) for both tracers. Some NOAA flask sites – such as
Ascension Island, Cold Bay (Alaska), and Guam – collect CO2 samples
less frequently. At those sites, our sampling followed the protocol for
CO2 at the other flask sites, but with sampling only every other
week. At aircraft sites, we sampled simulated CO2 at 13:30 LST, at
altitudes where actual CO2 samples are obtained (typically every 1000
to 2000 feet, to a site-dependent maximum altitude). This resulted in between
nine and twelve samples per profile, depending on the site. For
14CO2, three samples were taken per aircraft profile, distributed
between the boundary layer and the free troposphere, reflecting the actual
ongoing aircraft sampling strategy for 14CO2 (cf.
). Shipboard samples for CO2 were simulated as
samples along a transect once every 5∘ latitude, successive samples
being separated by 1 day, along NOAA Pacific Ocean and Western Pacific
cruises, which go back and forth once a month.
Prior flux specifications for OSSEs
For the inversion of synthetic observations, we
specified a set of prior fossil fuel CO2 and net biospheric and
oceanic fluxes that differed from those used to create the data. Prior fossil
fuel CO2 fluxes were taken from the EDGAR 4.2 FT2010 global inventory
(http://edgar.jrc.ec.europa.eu/overview.php?v=42FT2010). EDGAR fluxes
were available at 1∘×1∘ resolution, but had no subannual
variability and were available only through 2010. For 2011, country totals
for 2010 were scaled up according to the growth rate between 2010 and 2011
for each country from statistics compiled by BP
(http://www.bp.com/en/global/corporate/about-bp/energy-economics/statistical-review-of-world-energy/statistical-review-downloads.html).
The fossil fuel flux was optimized over weekly time steps. We imposed – but
did not optimize – an hour-of-day variability on the fossil fuel fluxes
using the diurnal (but not day of week) scaling factors of
. Prior terrestrial fluxes were from SiBCASA/GFED4,
which included NEE, fires, and biomass burning . The
fluxes were specified globally on a 1∘×1∘ grid at 3
hour time steps. The inversion optimized weekly terrestrial fluxes at the
lateral resolution of the TM5 transport model. Within each week, the prior
3 hourly variations were imposed as additive temporal patterns, but not
optimized; i.e., only the mean NEE over a week was adjusted. Prior oceanic
CO2 fluxes, also at 1∘×1∘ and 3 hourly
resolution, were taken from the ocean prior of CarbonTracker 2013b (the
variant based on ), and optimized weekly. The prior errors
assumed for the different fluxes are listed in
Table . Of the remaining four 14CO2 flux
terms described in Sect. , only the two disequilibrium
terms were optimized during the inversion, while the nuclear and cosmogenic
terms were held fixed.
Average difference between observed and
modeled aircraft profiles of SF6 at eight different sites over the
continental United States for the period 2001 to 2011 (inclusive). The error
bars denote ±2σ intervals, where σ is the standard error of
the mean difference between each model and observations. The locations of the
profiles are identified by three-letter site codes. Details for each site can
be found at http://www.esrl.noaa.gov/gmd/dv/site/site_table2.php. Atmospheric
mole fractions of SF6 were simulated using the EI and EIC variants of the
TM5 transport model. Three-dimensional initial conditions on 1 January 2000 were
based on (a) vertical gradients from the end (1 January 2006)
of a previous 6-year TM5 run (with initial conditions which included a
specified latitude gradient but no vertical gradient) and (b) the 1 January 2000
smoothed marine boundary layer latitudinal gradient derived
from SF6 observations from the NOAA ESRL GGRN. The 1 January 2006
vertical gradients were zonally averaged, scaled back to 1 January 2000 and
then added to the observed latitude gradient to create a zonally uniform but
vertically and meridionally variable field. SF6 emissions for the run
were based on the spatial emission pattern from EDGAR v4.2 scaled to match the
annual increases in SF6 emissions derived from the observed SF6
growth rate (assuming no atmospheric SF6 loss). Measured SF6 mole
fractions used here are available in the Supplement.
Transport errors
The OSSEs described above allow for an accurate
assessment of our ability to calculate fossil and biosphere fluxes given
different sets of 14CO2 and CO2 observations, in the limit
of perfectly known atmospheric transport (note, however, that the elements of
the model–data mismatch matrix R are inflated to account for expected
transport uncertainty). The performance of an inversion of real
14CO2 data will be limited not only by the observations ingested,
but also by errors in simulated atmospheric transport not adequately
represented by Re.g.,.
Thus, a more comprehensive way to estimate
the impact of transport model error is to use different transport models for
the simulation and assimilation steps . To that end,
we conducted a controlled experiment where TM5 EI was used to assimilate
synthetic data simulated by TM5 EIC. As described in
Sect. , these two model variants differ substantially
in their representations of vertical transport, which is an especially
important component of the atmospheric transport with regard to flux
estimation, since vertical transport directly influences the residence time
of air within the continental boundary layer (CBL) and therefore the
relationship between tracer flux and simulated concentrations in the CBL.
To illustrate this for our case, Fig. shows the
mismatch between modeled and measured vertical profiles of SF6 over
the continental US for both TM5 EI and EIC. We once
again consider SF6 because it is a nearly inert gas (lifetime
∼2000 years) and, like CO2ff, it has purely continental
sources linked to industrial activity overwhelmingly in the northern
midlatitudes (http://edgar.jrc.ec.europa.eu/part_SF6.php), but without
a substantial seasonal cycle, ). Thus, we expect the
vertical gradient of SF6 over the continental US to depend on the
strength of vertical mixing between the boundary layer and the free
troposphere, and any systematic differences between simulated and observed
gradients to provide an observational constraint on the representation of
vertical transport processes in the different models. As shown in
Fig. , both models display a mean offset from
observations of ∼0.04 ppt in the free troposphere, even at
Trinidad Head (THD), which is upwind of the continent. This uniform free
tropospheric offset is consistent with a 2002–2011 average offset of
∼0.04 ppt between both models and the observed SF6 at
the South Pole. Apart from the upper level offset, the SF6 gradient of
TM5 EIC is consistently and significantly closer to the observations,
suggesting that the EIC vertical transport scheme better represents the real
atmosphere. Moreover, the vertical gradient of SF6 between
850 and 400 hPa (i.e., between ∼1.5
and ∼7.1 km above sea level) for the two models differs by
an average of 0.025 ppt across all sites, which is larger than the
0.018 ppt 1σ spread across 16 modern global transport
models over midlatitude continents found by . This
suggests that TM5 EI and TM5 EIC provide substantially different realizations
of the transport not just at hemispheric scale
(Fig. ), but also at a location and scale most
relevant to an “imperfect transport” OSSE for the conterminous US
(Fig. ).
OSSE evaluation
Flux inversion OSSEs are often evaluated according
to the so-called “uncertainty reduction”, defined as the fractional
reduction between the prior and posterior flux uncertainty (e.g.,
). That metric, however, depends heavily
on the prior uncertainties prescribed, and a large uncertainty reduction
could easily arise from insufficient weighting of the prior during flux
estimation. Moreover, iterative schemes such as the variational scheme used
in TM5 4DVAR cannot estimate the full-rank posterior error covariance matrix
. Because of this limitation, we focus
here instead on the mismatch between the inversion-estimated fluxes and
true fluxes. Since prior and true fluxes differ significantly in both
space and time, the ability of our inversion to recover the true fluxes (also
referred to hereafter as the truth) should serve as a rigorous test of our observational and inversion framework.
For the “perfect transport” OSSEs, we also evaluate the posterior
correlation between Ffos and Fbio to assess the degree to
which these fluxes can be retrieved independently using (a) CO2 data
only and (b) using 14CO2 and CO2 data together.
Conventional CO2-only inversions solve Eq. (1a),
but Ffos is prescribed and not optimized. However, if we were to
solve Eq. (1a) for both Fbio+Foce and
Ffos, in a CO2-only system we would expect a large negative
correlation between the natural and fossil fuel fluxes, since under most
circumstances CO2 observations constrain the total flux and not its
components. The magnitude of this correlation would be limited in part by how
well the CO2 observations constrained the total CO2 budget
for the domain of interest; in the limiting case of a perfectly constrained
total CO2 budget, this correlation would be -1. Assimilating
14CO2 observations in order to solve both
Eq. (1a) and (1c)
simultaneously, we should expect a reduction in the magnitude of negative
correlation due to the independent information 14CO2 provides
about Ffos. The amount of reduction in the correlation between
Fbio+Foce and Ffos thus serves as an objective
metric of the ability of 14CO2 observations to separate
natural and fossil fuel CO2 fluxes within our observational
framework. In the case of the conterminous US, the natural CO2
flux is largely equivalent to Fbio, or NEE.
The evaluation of this posterior flux correlation, however, is imprecise in a
variational approach because Ffos:Fbio correlations are
derived from an approximate posterior covariance matrix as mentioned above.
To obtain a more accurate estimate of the posterior covariance (and hence
correlation) matrix, we follow the prescription of . The
posterior covariance between any two elements xi and xj of the state
vector x being estimated is
Cijapos=(xiapos-x‾iapos)(xjapos-x‾japos),
where the ensemble average is taken over an ensemble of variational
inversions, each of which starts from a different prior and assimilates a
different set of measurements, such that the probability distribution of all
the priors follows the prior covariance matrix B of
Eq. (), and the probability distribution of all the
measurements follows the model–data mismatch (covariance) matrix R of
Eq. ().
Choosing the number of inversions in the ensemble is a balancing act between
statistical robustness and computer resources. recommended
at least 50 inversions to estimate the posterior covariance matrix to within
10 %. A key assumption in their recommendation was that the mean of the
posterior estimates xapos corresponded to the analytical
solution; i.e., each individual inversion had already “reached convergence”
to within the analytical posterior error. In our case, due to the limited
number of iterations performed (40 out of the theoretically required
nstate= 4 095 000), we cannot be sure that within the ensemble, the
xapos estimates are distributed with the analytical solution
as their mean. However, in the case of our OSSEs, we know the analytical
solution, which is the true flux of Sect. . Therefore,
for evaluating the posterior covariance between Ffos and
Fbio, we perform an ensemble of inversions where the prior fluxes
are perturbations from the true flux following the statistics of B.
This approach of perturbing around a known truth to better estimate the
posterior covariance is similar to that used by, e.g., .
To be on the safe side of the recommendation of , our
ensembles contain 100 inversions each.
Performing 100 independent inversions is computationally expensive.
Therefore, we only evaluate the posterior correlation between
CO2ff and CO2nat for two scenarios, (a) the NRC
5000 scenario, and (b) the NRC 5000 scenario without 14CO2
observations. In an ideal system, for scenario (b) we expect to see large
negative correlations between the posterior natural and fossil fuel
CO2 flux, at least over large areas where the total CO2 flux
is well constrained, and in scenario (a) we expect the negative correlations
to be measurably smaller.
Nine regions defined by the US Census
Division, over which we aggregate our fossil fuel CO2 flux estimates
(www.eia.gov/forecasts/aeo/pdf/f1.pdf).
Monthly total emissions estimates for 2010
and NRC 5000 network scenarios, along with prior and true fluxes,
aggregated for the conterminous US and neighboring groups of regions identified
in Fig. . The orange band depicts the ±5% margin
around the true fluxes, and the numbers next to region names refer to the
region labels in Fig. .
Results
OSSE results are considered at scales ranging from
monthly national totals, monthly totals for regions specified in
Fig. , and for groups of neighboring regions.
Figures and compare monthly totals
of the estimated fossil fuel CO2 flux to specified true fluxes
used to create the observations and the prior fluxes used in the inversions,
for both 2010 and NRC 5000 measurement coverage. At the national
scale, the monthly fossil fuel flux over the contiguous United States is
recovered to within 5 % (orange shaded region in Fig. )
for all but 1 month for the 2010 measurement coverage, while the national,
annual total is recovered to better than 1 % (true flux = 1497.5 TgC,
estimated flux = 1497.2 TgC). For the
considerably denser measurement coverage of NRC 5000, the monthly US fossil
fuel flux is recovered to within 5 % (and usually to within 3 %) for all
months, while the national, annual total is again recovered to better than
1 % (true flux = 1497.5 TgC, estimated flux = 1506.5 TgC).
The impact of the increased coverage is more obvious
when we consider smaller regions. Over the eastern and central US, the NRC 5000 scenario always yields monthly flux estimates that are within 5 % of the
truth, and over the central US the phasing of the NRC 5000 estimate is
much closer to the truth than that for the 2010 coverage. Estimates for
the western US frequently deviate by more than 5 % from truth, even for the
NRC 5000 scenario. This is likely due to the combination of the relatively
small regional emissions and the fact that even for our case of effectively
perfect transport, the elements of the transport that carry emissions
from upwind regions to the sampling sites may be biased; indeed it appears
that both 2010 and NRC 5000 observation networks are detecting a transported
signal from a region with a larger emission signal and greater seasonality
than the western US (compared to the truth). In addition, unlike other US
regions, the western US tends to lack constraints from upwind observations
(i.e., over the Pacific), which are relatively sparse in both measurement
scenarios.
Over smaller regions (i.e. those of Fig. ), monthly
flux estimates deviate more significantly from the truth under both
coverage scenarios (Fig. ). This is expected, since
the number and distribution of observations and the information content of
the prior ultimately limit the spatiotemporal scale at which independent flux
estimates can be reliably obtained. NRC 5000 monthly flux estimates are as
good as or better than 2010 coverage estimates over almost all regions. Over
regions 1, 4, 7, and 9, the NRC 5000 monthly flux estimates are almost always
within 5 % of the true fluxes, whereas over regions 3, 5, 6, and 8 the NRC
5000 estimates sometimes fall outside the 5 % interval, but are always within
10 % of the truth. Over region 2 (Mountain US), even though the NRC 5000
flux estimates do not follow the truth closely (likely for reasons
discussed with respect to the western US above), they are closer to the
truth on average than the estimates from 2010 coverage. By contrast, the
estimates from 2010 coverage consistently fall within the 5 % error range
only over region 9 (South Atlantic US), whereas over several regions (e.g.,
3, 6, 7, and 8) its performance is significantly worse than for NRC 5000. The
good performance of the 2010 coverage over the Southern Atlantic states,
compared to other regions, may be due to the presence of a surface (tower)
sampling site at Beech Island, SC (SCT), and aircraft profiles and surface
measurements at Cape May, NJ (CMA), which are typically downwind of that
region.
Monthly total emissions estimates for 2010
and NRC 5000 network scenarios, along with prior and true fluxes for
individual regions identified in Fig. . The orange band
depicts the ±5% margin around the true fluxes, and the numbers next
to region names refer to the region labels in Fig. .
Annual total fossil fuel
CO2 emissions estimates for 2010 and NRC 5000 network
scenarios along with true and prior fluxes aggregated for the
conterminous US, individual regions and neighboring groups of regions
identified in Fig. . The orange rectangles denote the
±5% range around the true emission each region.
Posterior correlation between fossil fuel and
biospheric CO2 fluxes obtained with and without 14CO2
measurements for the NRC 5000 network scenario.
Figure shows the accuracy of estimated annual
total fossil fuel fluxes over the United States and several subregions. For
all the regions, the prior annual emission estimate is outside a 5 % margin
around the true emissions (orange rectangles). For the relatively sparse
2010 coverage scenario, the true fluxes are recovered to within 5 % for
the US, the eastern US, the central US, and two out of the nine regions of
Fig. . Under the augmented NRC 5000 coverage scenario,
annual total fossil fuel flux estimates are within 5 % of the truth for the
conterminous US and all of its subregions except one (Mountain US).
Correlation between Ffos and Fbio with and without 14CO2 observations
Over large land areas, CO2 observations constrain only the sum of
biospheric and fossil fuel CO2 fluxes; thus any attempt to separately
estimate the two based on CO2 observations alone should lead to large
negative correlations between the two flux types. Any independent information
on fossil fuel fluxes from 14CO2 observations can be expected to
result in a reduction in this negative correlation. To evaluate this, we
calculate the posterior correlation between fossil fuel and biospheric fluxes
for two scenarios, (a) an inversion using only CO2 data to estimate
both fossil fuel and biospheric CO2 fluxes, and (b) an inversion
using both CO2 and 14CO2 data for the same purpose. The
synthetic data sets in both cases are drawn from the NRC 5000 coverage
scenario. The method used to calculate the posterior correlation matrix was
outlined in Sect. . If yff and ynat
denote the fossil fuel and natural CO2 flux aggregates over some
spatiotemporal extent (e.g., North America over 2010), then the correlation
between fossil fuel and natural fluxes over that extent is
r=∑i=1Nyiff-〈yff〉yinat-〈ynat〉∑i=1Nyiff-〈yff〉2∑i=1Nyinat-〈ynat〉2,
where yi is the estimate of the spatiotemporal flux aggregate from the
ith inversion, and 〈y〉 is the mean y across all N
inversions.
Characterizing an error for r is not straightforward since r is bounded
within ±1 and does not have a normal distribution. We therefore estimate
a confidence interval of r using a bootstrap method in
which we randomly resample the 100 inversions with replacement and calculate
the correlation coefficient from that random drawing. We repeat this 50 000
times to produce a distribution of r. We report the median value of r,
and call the range between percentiles 2.5 and 97.5 the error in r
(i.e., covering 95 % of the values, analogous to ±2σ limits for a
normal distribution).
The median value of the posterior correlation r and its error range (95 %
confidence interval) for the NRC 5000 scenario with and without
14CO2 observations is plotted in Fig. for
the conterminous US and several subregions. For the inversion with only
CO2 data, we expect the correlation to be strongly negative (i.e.,
close to -1) over regions for which the total carbon budget is well
constrained by the CO2 observations, and less negative (i.e., closer
to 0) over regions with fewer observational constraints. In
Fig. this is seen, for example, for the conterminous US
(called the United States) due to the strong observational constraint posed
by the large number of CO2 observations (37 884 for the year 2010 in
the NRC 5000 coverage). Results for the eastern US also show a strong
negative correlation because of the dense coverage in the NRC 5000
network (Fig. ) for that area compared to the central
and western US. The observational constraint on the total CO2 budget
is less stringent, and hence the negative correlation weaker, over smaller
regions (such as the NY-NJ-PA tri-state area or the New England states) or
for regions for which the upwind influence is less well characterized and
the downwind area is not well sampled (such as the Pacific coast and the
western US).
Monthly net biospheric CO2 flux
estimates for the NRC 5000 network scenario with and without
14CO2 observations along with prior and true fluxes aggregated for
the conterminous and eastern US (left) and annual net biospheric and fossil
fuel fluxes for the conterminous US and groups of neighboring regions
(right). As discussed in the text, the NRC 5000 (traditional) inversion
does not optimize fossil fuel fluxes and does not assimilate 14CO2
observations. For both the inversions above, large numbers of CO2
observations in the NRC 5000 scenario drive the biosphere flux estimates
toward true fluxes, while adding 14CO2 helps to address carry-over bias arising from erroneous specification of the fossil fuel prior.
Over all regions in Fig. the addition of
14CO2 data weakens the negative correlation between fossil fuel
and biospheric CO2 flux, indicating that 14CO2 provides
information needed to partition CO2 flux components. Over all the
large regions, this reduction is significant; the 95th percentile
error bars barely overlap for the central US, and for the eastern, western,
and the conterminous US, the error bars are well separated. These represent areas
where fossil fuel and biospheric flux estimates can be separated based on
CO2 and 14CO2 observations from the NRC 5000 network.
Carry-over bias in NEE
As discussed in Sect. ,
errors in fossil fuel fluxes specified in traditional CO2-only
inversions (usually with zero prior uncertainty) may be expected to result in
spatial and temporal biases in estimated NEE, which we refer to as carry-over
bias. To evaluate the magnitude of potential carry-over bias, and the extent
to which it may be reduced by assimilating 14CO2 observations, we
compare two inversions in which the prior fossil fuel CO2 flux fields
are deliberately biased. The first is the NRC 5000 dual
CO2+14CO2 inversion already discussed. The second, referred to as NRC 5000 (traditional), is a CO2-only
inversion in which we attempt to estimate both biospheric and oceanic fluxes
of CO2 by assimilating synthetic CO2 observations from the
NRC 5000 network, but not 14CO2 observations. For both inversions,
the prior fossil fuel flux is from EDGARv4.2 FT2010 and the prior biospheric
flux is from SiBCASA, as described in Sect. . As can be
seen in Figs. , ,
and , both the annual and monthly totals for
the prior fossil fuel fluxes differ markedly from the true fossil fuel fluxes
for the US and all subregions. Using the entire conterminous US as an
example, and assuming stringent total carbon constraint based on the large
number of CO2 observations in the NRC 5000 scenario, we may
anticipate monthly carry-over biases as large as 100–200 TgC yr-1 based
on differences between true and prior fossil fuel CO2 fluxes in
winter and midsummer (e.g., 185 TgC yr-1 in January 2010,
133 TgC yr-1 in July 2010, and 176 TgC yr-1 in December 2010).
Monthly total fossil fuel CO2
emission estimates along with prior and true fluxes aggregated for the
conterminous US and neighboring groups of regions identified in
Figure , using perfect (NRC 5000) and
intentionally biased transport (NRC 5000 (EI)). As discussed in the text,
estimates for biased transport are in this case uniformly low because of
systematic differences in the vertical transport between the two model
variants.
Estimated biospheric fluxes for the two inversions are given along with
true and prior biospheric fluxes as both monthly and annual net totals in
Fig. for the conterminous US and several
subregions. In all cases, both inversion estimates (those with and without
14CO2 observations) migrate away from the specified prior
biospheric fluxes and lie close to true biospheric fluxes. This is due to
the observational constraints provided by the very large number of synthetic
CO2 measurements and the fact that even the largest potential
carry-over bias (e.g., 188 TgC yr-1 in February 2010 for the US) is
small relative to either prior or true monthly NEE, which is typically at
least an order of magnitude larger. However, we note that for regions that
are rich in both CO2 and 14CO2 observations, such as the
eastern US, we resolve differences between the cases with and without
14CO2 assimilation that are directly comparable to differences in
the underlying fossil fuel inventories. For example, the fossil fuel prior in
February 2010 over the eastern US is biased low by 154 TgC yr-1, which
results in an NEE estimate 153 TgC yr-1 higher than the truth if
14CO2 data are not assimilated, but only 78 TgC yr-1 higher
than the truth if 14CO2 data are assimilated. Similarly, in
December 2010, the fossil fuel prior over the eastern US is biased low by
163 TgC yr-1, resulting in a bias in the estimated NEE of
133 TgC yr-1 without assimilation of 14CO2 and only
9 TgC yr-1 with 14CO2 observations. These results indicate
that carry-over biases that would otherwise go unresolved can in large part
be overcome by adding observational constraints from 14CO2.
For the three US subregions in Fig. (right
panel), the annual NEE estimate with 14CO2 is closer to truth
than without. However, the reverse is true for annual NEE aggregated over the
conterminous US (i.e. the sum of the three subregions). This is due to a
cancellation between the western US (where the CO2-only NEE estimate
is too negative) and the other two regions (where the CO2-only
estimate is too positive compared to the truth).
Imperfect transport OSSE
As mentioned in Sect. , we
performed an inversion with intentionally biased transport. That is, we
simulated CO2 and 14CO2 measurements with true fluxes
in TM5 EIC, and assimilated those observations using TM5 EI. As noted in
Sect. , forward simulations of an inert tracer sourced
largely from the northern continents (SF6, which is in this respect
similar to fossil fuel CO2) produce substantially different vertical
profiles over the conterminous US for the two model versions
(Fig. ), indicating that the two models represent
meaningfully different realizations of atmospheric transport.
Figure shows the monthly fossil fuel fluxes
estimated over the United States and three of its subregions for both biased
transport (NRC 5000 (EI)) and what is effectively perfect transport (NRC
5000). For assimilation of observations using TM5 EI, the monthly flux
estimates over the conterminous United States (and over its three large-scale
subregions) no longer lie within 5 % of the true fluxes. The flux
estimates with biased transport are in this case uniformly low, consistent
with our understanding of the primary difference between EI and EIC transport
schemes involving vertical entrainment and detrainment fluxes over the
northern temperate latitudes. As seen for forward simulations in
Fig. , EIC tends to better ventilate the CBL such
that the surface signal is more efficiently transferred to the well mixed
free troposphere compared to EI (which allows more signal to build up within
the CBL). Thus, TM5 EI requires smaller surface fluxes in order to recover
the surface layer signal simulated by TM5 EIC; annual fossil fuel flux
estimates from EI transport are thus in all cases lower than the estimates
from EIC transport (Fig. ).
As outlined in Sects. and , TM5
EI and TM5 EIC differ significantly in terms of their respective vertical
transport schemes, giving rise to large differences in transported tracer
distributions at the global scale and, importantly, over the northern
midlatitude continents. TM5 EI is in particular demonstrably biased compared
to the ensemble of transport models used in most state-of-the-art global
inversions according to several metrics considered by
. Thus, while the differences between our fossil fuel
CO2 flux estimates serve as a demonstration of the potential biases
that can arise from poor or differing representations of the real transport,
they almost certainly exaggerate flux biases likely to be seen amongst models
that are well validated against observations. Conversely, our results with
effectively perfect transport serve to demonstrate that assimilation of
14CO2 along with CO2 observations has the potential to
yield direct, independent top-down observational constraints on fossil
fuel emission at subcontinental, regional scales (in our case, corresponding
to ∼250 000 km2) with uncertainties comparable to those
estimated for bottom-up inventories. Ongoing improvements in tracer
transport models along with rigorous evaluation of transported tracer
distributions against a growing network of observations, of the kind we show
for SF6 in Figs.
and , provide a clear path towards a more complete
realization of the full potential of the dual 14CO2 and
CO2 assimilation capability described in this work.
Conclusions
In this work we develop and present a new dual tracer inversion framework
that makes use of the present and anticipated networks of precise atmospheric
14CO2 measurements to simultaneously estimate fossil-fuel-derived
and biospheric fluxes of CO2. Using a set of OSSEs, we demonstrate the ability of atmospheric
CO2 and 14CO2 measurements to recover previously specified
true fossil fuel CO2 emissions over North America. As expected,
the accuracy of the flux estimates depends both on the coverage of the
measurement network and the spatiotemporal scale of analysis. We simulated
two coverage scenarios, namely the coverage of the NOAA GGRN network in 2010
(969 14CO2 measurements over North America), along with an
augmented coverage of ∼500014CO2 measurements over North
America (NRC 5000), as recently recommended by the US NAS
. With the 2010 coverage, we recover true annual total
fossil fuel emissions over the conterminous US to better than 1 % and over
several highly emissive subregions to within 5 %. For NRC 5000 coverage,
we also recover monthly emissions to within 5 % for the United States. For
all but one of nine subregions, we also recover the monthly emission to
within 5 % for at least 9 months of the year with the NRC 5000
coverage (where, for the subregion which is the exception, emissions are
small and upwind observations are sparse). For regions with a strong
constraint on the total CO2 flux based on large numbers of
CO2 observations in the NRC 5000 scenario, the anticipated
14CO2 coverage allows for detection of and substantial reduction
in biases in regional NEE that would otherwise arise from erroneous
specification of the fixed fossil fuel CO2 emission in a traditional
CO2-only inversion. Additionally, we evaluate biases in fossil fuel
CO2 flux estimates that can arise from poor representation of
atmospheric transport and suggest that the growing network of other tracer
measurements may be used to select and improve the best transport models. For
the best models, our ability to recover fossil fuel emissions over the US
should approach that of our idealized OSSEs and be comparable to that for
most bottom up fossil fuel emission inventories with estimated annual and
monthly regional uncertainties of 5–10 %. It is likely that even an inverse
model with less than optimal transport would still be able to resolve trends
in fossil fuel emissions precisely. In a future world with anticipated
national commitments to reduce CO2 emissions (e.g. Intended
Nationally Determined Contributions, or INDCs,
http://unfccc.int/focus/indc_portal/items/8766.php), such a capability
could provide for independent top-down verification of such commitments
for the US and other areas where atmospheric observing networks are or can be
established.
The Supplement related to this article is available online at doi:10.5194/acp-16-5665-2016-supplement.
Acknowledgements
We would like to thank Colm Sweeney for providing aircraft-based measurements
of SF6 and Ed Dlugokencky and Andrew Crotwell for marine boundary
layer measurements of SF6, Colin Lindsay for homogenizing global
neutron monitor data and oceanic 14CO2 data from multiple sources,
and Nicolas Bousserez for useful discussions on uncertainty quantification.
Part of this work was performed under grant NA13OAR4310075 from the NOAA
Climate Programs Office (CPO). All computations for this work were performed
on the Zeus and Theia clusters of the NOAA Research & Development High
Performance Computing System (RDHPCS).
Edited by: C. Gerbig
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