ACPAtmospheric Chemistry and PhysicsACPAtmos. Chem. Phys.1680-7324Copernicus PublicationsGöttingen, Germany10.5194/acp-18-735-2018Top-down constraints on global N2O emissions at optimal resolution: application of a new dimension reduction techniqueWellsKelley C.MilletDylan B.dbm@umn.eduhttps://orcid.org/0000-0003-3076-125XBousserezNicolasHenzeDaven K.GriffisTimothy J.ChaliyakunnelSreelekhaDlugokenckyEdward J.SaikawaErihttps://orcid.org/0000-0003-3166-8620XiangGaoPrinnRonald G.O'DohertySimonhttps://orcid.org/0000-0002-4051-6760YoungDickonhttps://orcid.org/0000-0002-6723-3138WeissRay F.https://orcid.org/0000-0001-9551-7739DuttonGeoff S.https://orcid.org/0000-0001-7777-9268ElkinsJames W.KrummelPaul B.https://orcid.org/0000-0002-4884-3678LangenfeldsRaySteeleL. PaulDepartment of Soil, Water, and Climate, University of Minnesota, St. Paul, MN, USADepartment of Mechanical Engineering, University of Colorado at Boulder, Boulder, CO, USAEarth System Research Laboratory, NOAA, Boulder, CO, USADepartment of Environmental Sciences, Emory University, Atlanta, GA, USAJoint Program on the Science and Policy of Global Change, Massachusetts Institute of Technology, Cambridge, MA, USACenter for Global Change Science, Massachusetts Institute of Technology, Cambridge, MA, USASchool of Chemistry, University of Bristol, Bristol, UKScripps Institute of Oceanography, University of California San Diego, La Jolla, CA, USACIRES, University of Colorado at Boulder, Boulder, CO, USAClimate Science Centre, CSIRO Oceans and Atmosphere, Aspendale, Victoria, AustraliaDylan B. Millet (dbm@umn.edu)22January20181827357566July201710December201717November201714August2017This work is licensed under the Creative Commons Attribution 4.0 International License. To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/This article is available from https://acp.copernicus.org/articles/18/735/2018/acp-18-735-2018.htmlThe full text article is available as a PDF file from https://acp.copernicus.org/articles/18/735/2018/acp-18-735-2018.pdf
We present top-down constraints on global monthly N2O emissions for
2011 from a multi-inversion approach and an ensemble of surface observations.
The inversions employ the GEOS-Chem adjoint and an array of aggregation
strategies to test how well current observations can constrain the spatial
distribution of global N2O emissions. The strategies include (1)
a standard 4D-Var inversion at native model resolution (4∘×5∘), (2) an inversion for six continental and three ocean regions,
and (3) a fast 4D-Var inversion based on a novel dimension reduction
technique employing randomized singular value decomposition (SVD). The
optimized global flux ranges from 15.9 TgNyr-1 (SVD-based
inversion) to 17.5–17.7 TgNyr-1 (continental-scale, standard
4D-Var inversions), with the former better capturing the extratropical
N2O background measured during the HIAPER Pole-to-Pole
Observations (HIPPO) airborne campaigns. We find that the tropics provide
a greater contribution to the global N2O flux than is predicted by the
prior bottom-up inventories, likely due to underestimated agricultural and
oceanic emissions. We infer an overestimate of natural soil emissions in the
extratropics and find that predicted emissions are seasonally biased in
northern midlatitudes. Here, optimized fluxes exhibit a springtime peak
consistent with the timing of spring fertilizer and manure application, soil
thawing, and elevated soil moisture. Finally, the inversions reveal a major
emission underestimate in the US Corn Belt in the bottom-up inventory used
here. We extensively test the impact of initial conditions on the analysis
and recommend formally optimizing the initial N2O distribution to avoid
biasing the inferred fluxes. We find that the SVD-based approach provides
a powerful framework for deriving emission information from N2O
observations: by defining the optimal resolution of the solution based on the
information content of the inversion, it provides spatial information that is
lost when aggregating to political or geographic regions, while also
providing more temporal information than a standard 4D-Var inversion.
Introduction
Nitrous oxide (N2O) is a long-lived greenhouse gas (τ∼122–131 years; Volk et al., 1997; Prather et al., 2012) with substantial
impacts on both climate and stratospheric chemistry. It has a global warming
potential far exceeding that of CO2 (265× on a 100-year
timescale; Myhre et al., 2013), and its emissions weighted by ozone depletion
potential currently exceed those of all other substances (Ravishankara
et al., 2009). The global N2O source is reasonably well constrained
(15.7 to 20.1 TgNyr-1 for years 1999–2009; Prather et al.,
2012; Saikawa et al., 2014; Thompson et al., 2014a, c) by its atmospheric
abundance and estimated lifetime. However, attribution of this source to
specific regions and sectors has been hindered by the sparse global observing
network and by the weak variability in N2O mixing ratios (e.g.,
Wells et al., 2015). Quantitative interpretation of atmospheric N2O
measurements in terms of globally resolved emissions thus first requires
a rigorous assessment of how results hinge on the modeling framework
employed. Here, we apply a hierarchy of model resolutions, including a new
method that formally defines the state vector for optimization based on the
information content of the observations, in a global inverse modeling
framework to address this need. We use this model hierarchy with a global
suite of observations to (i) quantify the spatial and seasonal distribution
of N2O emissions for 2011, (ii) examine what features of these
results are robust across model configurations, and (iii) assess the
implications for current understanding of the N2O budget and future
research needs.
The primary sources of atmospheric N2O are microbial
denitrification and nitrification, which lead to N2O production in
soils (Firestone and Davidson, 1989), ocean waters (Elkins et al., 1978;
Cohen and Gordon, 1979), and in streams, rivers, and lakes (Seitzinger and
Kroeze, 1998; Beaulieu et al., 2011). Global mean N2O mixing ratios
rose by 0.85±0.1ppbyr-1 from 2001 to 2015 (based on NOAA
surface measurements) primarily due to increased use of inorganic fertilizers
and manure (Galloway et al., 2008; Davidson, 2009; Park et al., 2012) and the
nonlinear response of N2O emissions to N inputs in some
agricultural systems (Shcherbak et al., 2014). Estimates for the global
agricultural flux range from 4.3 to 6.3 TgNyr-1 (Mosier et al.,
1998; Crutzen et al., 2008; Davidson, 2009): this includes emissions
occurring on-field (i.e., “direct” emissions from fertilized fields),
downstream (“indirect” emissions from N leaching and runoff, and from
deposition of volatilized NOx and NH3), and from
manure management. These sources are all subject to large uncertainties. For
example, by assuming a linear flux response to fertilizer application, one
can either under- or overestimate emissions depending on the application rate
(Shcherbak et al., 2014; Gerber et al., 2016). Recent work also suggests that
the indirect N2O flux could be 2.6–9 times larger than is
presently accounted for in bottom-up estimates (Griffis et al., 2013; Turner
et al., 2015b), which
would imply an underestimate of the agricultural contribution to the overall
N2O budget. Nonagricultural soils and oceans are thought to
contribute an additional 7.4–11 TgNyr-1 (Saikawa et al.,
2013) and 1.2–6.8 TgNyr-1 (Nevison et al., 1995; Jin and
Gruber, 2003; Manizza et al., 2012), respectively, to the global
N2O source. Industrial, transportation, and biomass burning
emissions also exist but are thought to be relatively minor, totaling
1.2–1.8 TgNyr-1 (Prather et al., 2001).
Because microbial nitrification and denitrification, and the subsequent
soil–atmosphere N2O flux, depend strongly on factors such as soil
moisture, temperature, physical characteristics, and N availability (e.g.,
Potter et al., 1996; Bouwman, 1998; Kim et al., 2012; Bouwman et al., 2013;
Butterbach-Bahl et al., 2013; Griffis et al., 2017), N2O emissions
can exhibit major temporal and spatial variability. For example,
Wagner-Riddle et al. (2017) found that short-duration freeze–thaw cycles can
account for 35–65 % of the annual direct N2O emissions from
seasonally frozen croplands and that neglecting this contribution would lead
to a 17–28 % underestimate of the global N2O source (direct
+ indirect) from agricultural soils. This type of variability poses a major
challenge to bottom-up and top-down efforts to quantify N2O surface
fluxes and attribute them to specific times, locations, and mechanisms. The
relatively sparse coverage of measurement sites and low atmospheric
variability (because of the long N2O lifetime, surface mixing
ratios typically vary by <10ppb on a ∼325ppb
background) compound the challenge and limit the spatial and temporal
resolution at which emission fluxes can be inferred (Wells et al., 2015). As
a result, global N2O inversions often employ some aggregation
strategy to optimize emissions for a small set of geographic regions (e.g.,
Hirsch et al., 2006; Huang et al., 2008; Saikawa et al., 2014). However, in
the past this aggregation has been done based on physical or political
boundaries rather than by formally determining the degrees of freedom (DOFs)
in the inverse system – which leads to aggregation errors and sub-optimal
results. Work on CO2 inversions has also highlighted this issue
(e.g.,
Kaminski et al., 2001) and the resulting importance of determining the proper
state vector size for optimal results (Bocquet et al., 2011).
Another key challenge is that because of the long N2O lifetime,
inaccuracies in model initial conditions can lead to large biases in the
subsequent optimized emissions (Thompson et al., 2014c). Past global
N2O inversion studies have established the initial conditions in
a variety of ways: from a forward model spinup that is then evaluated against
observations (e.g., Huang et al., 2008); by including the initial condition
as a separate adjustable parameter in the source optimization (e.g., Saikawa
et al., 2014; Thompson et al., 2014a); or from interpolation of atmospheric
observations (e.g., Wells et al., 2015). To our knowledge there has not yet
been a detailed evaluation of these different methods and their impacts on
N2O source inversions. Such information is needed to establish the
degree to which uncertainties in the initial conditions can propagate to
errors in the optimized N2O emission estimates.
In this paper, we address the above uncertainties in a quantitative way using
a multi-inversion hierarchy to derive top-down constraints on N2O
emissions for 2011. We use the adjoint of the GEOS-Chem chemical transport
model (CTM) to solve for monthly fluxes at the model grid box scale as well
as at geographically aggregated continental scales. We compare these results
with those obtained using a new dimension reduction technique based on the
singular value decomposition (SVD) of the so-called prior-preconditioned Hessian of the 4D-Var cost function
(Bousserez and Henze, 2017). This new SVD-based approach allows us to solve
for fluxes at optimal spatiotemporal resolution, as defined by the
information content of the N2O observations – thus maximizing the
DOFs for the inversion and avoiding any need for spatial aggregation based on
geography or source type. It also offers significant time savings over
standard grid-based 4D-Var approaches due to the use of efficient randomized-SVD algorithms (Halko et al., 2011). The initial conditions for the above
inversions are constructed in a variety of ways, and we use observations and
model simulations to assess their accuracy and associated impacts on
optimized N2O fluxes. We then evaluate these optimized emissions
using independent airborne measurements and interpret the results in terms of
underlying emission processes, with specific emphasis on the role of model
resolution in affecting the solution and on those features that appear most
robust (and most uncertain) across model configurations.
MethodsGEOS-Chem N2O simulation
The N2O simulation employed here, previously described by Wells
et al. (2015), is based on the GEOS-Chem CTM (www.geos-chem.org) with
GEOS-5 assimilated meteorological data from the NASA Goddard Earth Observing
System. We use a horizontal resolution of 4∘×5∘ with
47 vertical levels from the surface to 0.01 hPa as well as time steps of
30 min for transport and 60 min for emissions and chemistry. The simulation
period spans April 2010–April 2012 (the start date is selected to match the
initiation of N2O measurements at the KCMP tall tower site
discussed later).
A priori N2O emissions for anthropogenic, nonagricultural sources
(including industrial processes, transportation, residential, and wastewater
emissions) are from the Emission Database for Global Atmospheric Research
(EDGARv4.2; http://edgar.jrc.ec.europa.eu), which are provided annually
and total 1.7 TgNyr-1 for 2008. Monthly N2O
emissions from nonagricultural soils are from CLMCN-N2O as
described by Saikawa et al. (2013) and total 7.5 TgNyr-1 for
2011. These emissions have been shown to accurately capture the magnitude and
seasonality of soil emissions in the Amazon, but exhibited less skill in
reproducing the observed seasonal cycle in northern midlatitudes (based on
data from New Hampshire; Saikawa et al., 2013). The magnitude of these
emissions varies depending on the meteorological forcing dataset used;
forcings used here are from the MIT Integrated Global System Model (IGSM)
fully coupled transient 20th century climate integration (Sokolov et al.,
2009). Adding these to the annual EDGARv4.2 direct and indirect (leaching and
runoff) agricultural emissions (3.5 TgNyr-1), indirect
emissions from NOx and NH3 deposition
(0.4 TgNyr-1), and emissions from manure management
(0.2 TgNyr-1) leads to an a priori global soil N2O
source of 11.6 TgNyr-1 for 2011. Biomass burning emissions are
computed monthly based on the Global Fire Emissions Database version 3
(GFED3; van der Werf et al., 2010), totaling 0.6 TgNyr-1,
while monthly oceanic N2O emissions are from Jin and Gruber (2003)
and total 3.5 TgNyr-1. The global annual a priori
N2O flux for 2011 is then 17.4 TgNyr-1, in the range
of recent top-down estimates (16.1–18.7 TgNyr-1 for years
2006–2008; Saikawa et al., 2014; Thompson et al., 2014c). Stratospheric loss
of N2O via photolysis and reaction with O(1D) is
calculated from 3-D loss frequencies archived monthly from Global Modeling
Initiative (GMI) simulations driven by MERRA meteorological fields; the
resulting N2O lifetime is ∼127 years (note that the value
depends on the initial spatial distribution of N2O in the model).
The long N2O lifetime necessitates accurate characterization of
initial conditions to avoid biasing the optimized fluxes (e.g., Thompson
et al., 2014c). In our work, we construct six sets of initial conditions from
global N2O observations and evaluate the corresponding impacts on
the inferred fluxes. Initial condition fields are constructed based on either
data interpolation or 4D-Var optimization, with details discussed in Sect. 3.
Inversion frameworks
We employ three inversion methods with varying resolution to solve for
monthly N2O emissions over 2 years (April 2010–April 2012) based
on global surface observations. The first of these is a 4D-Var inversion that
iteratively optimizes emissions on the native model grid (here 4∘×5∘) using gradients computed with the GEOS-Chem adjoint
model. This has the advantage of avoiding any aggregation errors associated
with traditional clustering methods. However, our previous work (Wells
et al., 2015) has shown that the degrees of freedom for atmospheric
N2O inversions is typically much less than the native model grid
dimension and, furthermore, that native resolution optimizations have limited
ability to resolve any temporal (e.g., seasonal) N2O emission
biases. We therefore apply two alternate approaches to reduce the dimension
of the inverse problem: (1) a 4D-Var inversion solving for emissions on
aggregated, geographically defined land and ocean regions and (2) a 4D-Var
inversion solving for emissions on a reduced emission basis set defined using
an SVD-based information content analysis. In all three frameworks we
consider two emission sectors (terrestrial and oceanic) and optimize monthly
fluxes. We present details for each of the three frameworks in the following
sections.
Standard 4D-Var inversion
Our standard inversion is a 4D-Var optimization in which the state vector
contains scaling factors for monthly N2O emissions at 4∘×5∘. The optimal set of emission scaling factors is obtained
by minimizing the cost function, J(x), which is a scalar
containing contributions from the error-weighted model–measurement mismatch
and the departure from the a priori values:
Jx=12∑h(x)∈Ωh(x)-yTSy-1h(x)-y+12(x-xa)TSa-1(x-xa),
where x is a vector of the parameters to be optimized (in this
case, emission scaling factors), xa contains the a priori
values of those parameters, y is a set of observed
N2O mixing ratios, h(x) is a vector containing the
simulated mixing ratios at the time and location of each observation,
Sy and Sa are the observational and a priori
error covariance matrices, and Ω represents the time–space domain of
the observations.
We use a quasi-Newtonian routine (Zhu et al., 1994; Byrd et al., 1995) to
iteratively converge to min(J(x)). At each iteration, we use
the adjoint of GEOS-Chem to compute the gradient of J(x) with
respect to the emission scaling factor and employ a lower bound of zero and
an upper bound of 10 based on our earlier work (Wells et al., 2015). This
approach therefore implicitly assumes that the sign of the a priori flux
(which can be negative over the ocean) is correct for each model grid square.
The GEOS-Chem adjoint has previously been applied to a wide range of inverse
problems for atmospheric composition, including constraining sources and
sinks of long-lived greenhouse gases such as CO2 (Deng et al., 2014;
Liu et al., 2014; Deng et al., 2015; Liu et al., 2015), methane (Wecht
et al., 2014; Turner et al., 2015a), and N2O (Wells et al., 2015),
as well as aerosols and reactive trace gases (e.g., Henze et al., 2007; Kopacz
et al., 2009; Wells et al., 2014).
A priori uncertainties are assumed to be 100 % for both land and ocean
emissions, with off-diagonal terms assuming correlation length scales of 500
and 1000 km, respectively, following prior work by Thompson
et al. (2011, 2014a). Observational errors are calculated as the quadratic
sum of measurement uncertainty (∼0.4ppb for most sites; see
Sect. 2.4) and model transport uncertainty, with the latter estimated from
the 3-D model variance in N2O mixing ratios in the grid boxes
surrounding any given observation (resulting in a mean uncertainty ∼0.2ppb at the surface). The corresponding mean observational
uncertainty is ∼0.45ppb, with maximum values ∼4ppb. The solution presented here was calculated using 40
iterations, after which the cost function change per iteration is <1 %
and the total cost function reduction is ∼65 % (Fig. S2 in the
Supplement).
Continental-scale inversion
While the above approach avoids any aggregation error, the existing
observational network provides insufficient information to constrain
N2O emissions in every 4∘×5∘ model grid
square. Therefore, in an alternate inversion, we reduce the dimension of the
inverse problem by solving for emission scaling factors on six continental
(North America, South America, Europe, Africa, Asia, Oceania) and three ocean
regions (northern oceans: 30–90∘ N; tropical oceans:
30∘ S–30∘ N; and southern oceans: 30–90∘ S).
Regions are mapped in Fig. S1 in the Supplement and are similar to those used
in the TransCom N2O model intercomparison study (Thompson et al.,
2014b, c), except with one rather than two Asian regions. While this
inversion could readily be carried out analytically rather than numerically
(due to its small dimension), we instead use 4D-Var for consistency and to
impose the same scaling factor bounds (0–10) as in the standard inversion.
We thus use the GEOS-Chem adjoint to calculate the cost function gradient
(∇xJ(x)) aggregated over the nine
predefined regions. We then iteratively minimize J(x),
achieving a cost function change of <1 % per iteration (and total
reduction of ∼55 %) after 28 iterations (Fig. S2 in the
Supplement).
SVD-based inversion
As an advance over standard aggregation methods such as the one described
above, we also apply a new, efficient SVD-based information content analysis
technique that maximizes the degrees of freedom of the inverse system while
permitting us to solve for N2O fluxes in a fast iterative
framework. The method, based on synthesis and advancement of recent work in
this area (Flath et al., 2011; Bui-Thanh et al., 2012; Spantini et al., 2015)
by Bousserez and Henze (2017), uses an optimal low-rank projection of the
inverse problem that maximizes the observational constraints. Specifically,
for a given dimension k, the optimal reduced space (Spantini et al., 2015;
Bousserez and Henze, 2017) is spanned by the first k eigenvectors of the
prior-preconditioned Hessian G (Flath et al., 2011):
G≡Sa12HTSy-1HSa12=VΛVT,
where H is the tangent linear of the forward model, V is
a matrix whose columns are the eigenvectors of G, and
Λ is a diagonal matrix containing the eigenvalues of
G. The following analytical approximation can then be used:
Sopt=Sa-Sa12∑i=1kλiλi+1viviTSa12,
where Sopt is the posterior error covariance matrix,
while vi,i=1,…,k and λi,i=1,…,k are the
eigenvectors and eigenvalues of G. This expression gives, in some
sense, the lowest error rank-k approximation of Sopt
(see Bousserez and Henze, 2017, for details). The eigenvectors
vi can be interpreted as the most constrained modes in flux
space, i.e., flux patterns that are independently constrained by the
observations (Cui et al., 2014; Bousserez and Henze, 2017). These
eigenvectors of the prior-preconditioned Hessian are efficiently calculated
using a fully parallelized randomized algorithm (Halko et al., 2011), as in
Bui-Thanh et al. (2012) and Bousserez and Henze (2017). We use k=350 here,
which employs nearly all modes with eigenvalues greater than 1.0 (Fig. S3 in
the Supplement), as modes with eigenvalues below this threshold are informed
mainly by the prior.
From Sopt we can obtain the inversion averaging kernel (AK),
which gives a measure of how well emissions are constrained in a given
location, as follows:
AK=I-SoptSa,
where I is the identity matrix and Sa is the a priori
error covariance matrix. Optimized solutions in areas where the diagonal of
AK is close to 1.0 are well constrained by the observations. The
trace of the averaging kernel gives the total degrees of freedom, i.e., the
number of independent pieces of information that can be obtained in the
inversion framework.
The posterior mean estimate of x can also be directly
calculated from analytical formulas using the eigenvectors of G
(Spantini et al., 2015; Bouserez and Henze, 2017). However, to impose
a positivity constraint on the emissions, we rely here on the variational
minimization framework as in the standard 4D-Var case. In order to leverage
the use of the optimal basis set, we project both the cost function and its
gradient onto the principal modes to obtain a reduced analytical formulation.
The analytical expression for the reduced cost function (derivation presented
in Appendix A) is
Jx≈12x-xaTSa-12∑i=1kviviTSa-12x-xa+12hxa-yTSy-1h(xa-y)+12x-xaTSa-12∑i=1kλiviviTSa-12x-xa+12hxa-yTSy-12∑i=1kλi12wiviTSa-12x-xa+12x-xaTSa-12∑i=1kλi12viwiTSy-12hxa-y,
while the analytical approximation for the cost function gradient is
∇Jx≈Sa-12∑i=1kviviTSa-12x-xa+Sa-12∑i=1kλiviviTSa-12x-xa+Sa-12∑i=1kλi12viwiTSy-12hxa-y,
where k=350 is the number of modes retained in the approximation. Here,
h(xa) are the model mixing ratios
corresponding to the a priori emissions and wi are the
eigenvectors in observation space:
wi=1λiSy-12HSa12vi.
Because the cost function and gradient depend only on the a priori
model–measurement difference, the a priori and observational error
covariances, and the eigenvectors of G (which are computed only
once), this iterative inversion offers significant time savings, particularly
for models with a low level of parallelization. Monthly N2O
emission scaling factors for the 2-year analysis window are derived in
approximately 6 h vs. over 100 h for the standard and continental-scale
inversions, and nearly all the computation time in the former case is spent
on calculating the eigenvectors of G. The solution for the SVD-based
inversion (with a projected cost function change of <1 % per
iteration) is obtained after 60 iterations (Fig. S2 in the Supplement). The
full cost function reduction (calculated from a forward model run) is
∼25 % for this solution, whereas we achieve the minimum in the
full cost function at a much earlier iteration (see Fig. S2 in the
Supplement). The divergence in the behavior of the projected and full cost
function after this point may suggest that the weaker modes included here are
not as well approximated by the randomized-SVD calculation as the dominant
modes. An objective criteria for determining the error in the randomized SVD
is the subject of a work in progress.
Global surface observing network for
atmospheric N2O. Shown are surface discrete measurement locations
for the NOAA Carbon Cycle and Greenhouse Gases (CCGG) network, the
Commonwealth Scientific and Industrial Research Organisation (CSIRO) network,
the National Institute of Water and Atmospheric Research (NIWA) network, and
the Environment Canada (EC) network, as well as semi-continuous measurement
locations in the NOAA Chromatograph for Atmospheric Trace Species (CATS)
network, the Advanced Global Atmospheric Gases Experiment (AGAGE) network,
and the KCMP tall tower site. Also shown are flight tracks from the HIPPO IV
and V deployments.
Impact of initial conditions on
a 2-year (April 2010–April 2012) N2O simulation and inversion.
Shown are timelines of the model–measurement residuals for a 2-year
forward model simulation initialized using each of the six initial conditions
listed in Table 1. The solid line represents the mean and the dashed lines
represent the standard deviation about the mean for Northern Hemisphere (red) and Southern
Hemisphere sites (green). The final 2011 a posteriori global flux for each
simulation derived using a standard 4D-Var inversion is noted at the bottom
of each panel.
The six initial conditions (for 1 April 2010) tested for
N2O, including the time range of observations used, observation
sites included, interpolation or optimization method used, and length of
spinup.
Test nameObservational time rangeSitesEstimation methodSpinupMarZonal1–31 Mar 2010AllZonal average, linear interpOne monthAprZonal25 Mar–7 Apr 2010AllZonal average, linear interpNoneAprKriging25 Mar–7 Apr 2010AllKrigingNoneAprOpt1 Apr–31 May 2010All4D-VarNoneFebOpt1 Feb–31 Mar 2010All4D-VarTwo monthsRemoteOpt1 Jan–30 Jun 2010Remotea4D-VarThree months
a Remote sites include NOAA CCGG sites AZR, CBA,
CGO, CHR, CRZ, DRP, GIC, GMI, HBA, ICE, IZO, MID, MLO, PSA, SEY, SHM, SUM,
SYO, as well as ship-based measurements taken in the Pacific (POC).
(a) Left panels: 2011 annual
N2O emissions for the a priori database and a posteriori results
for each of the inversion frameworks used here (standard 4D-Var,
continental-scale inversion, SVD-based inversion). Global fluxes are shown
inset in each map. Right panels: annual posterior emission increments
relative to the a priori database for each inversion framework. (b)
2011 annual N2O flux over six continental and three oceanic regions
for the a priori database (black) and the a posteriori median from the three
inversion frameworks (red). Error bars denote the range of a posteriori
values for each region.
A posteriori evaluation of N2O
inversion results using HIPPO data (not themselves used in the inversion).
Shown are mean vertical profiles of the model–measurement difference for
HIPPO IV (a), 14 June–11 July 2011 and HIPPO V
(b), 9 August–9 September 2011 as a function of latitude. A priori
results are shown in black and a posteriori results in red (standard 4D-Var
inversion), green (continental-scale inversion), and gold (SVD-based inversion).
Atmospheric N2O observations
Atmospheric N2O observations used in our analysis include a global
ensemble of surface measurements as well as airborne data from the HIAPER
Pole-to-Pole Observations (HIPPO) campaigns (Wofsy, 2011). Because we found
in our prior work that the surface dataset provides the strongest constraint
on the spatial distribution of N2O emissions (Wells et al., 2015),
we employ these in the inversion and reserve the airborne data for
a posteriori evaluation.
Figure 1 shows a map of the surface measurement sites used in this study. The
surface measurements consist primarily of discrete air-filled flasks from
NOAA's Cooperative Global Air Sampling Network (CCGG) program (Dlugokencky
et al., 1994); we also include flask-based air samples from the Commonwealth
Scientific and Industrial Research Organisation (CSIRO) network, the
Environment Canada (EC) network, and a National Institute of Water and
Atmospheric research (NIWA) site. We assume a measurement uncertainty of
0.4 ppb at all flask sampling sites based on recommendations from the
data providers. In addition to the flask-based air samples, we use
high-frequency N2O measurements (discrete hourly or hourly
averaged) from the NOAA Chromatograph for Atmospheric Trace Species (CATS)
network (Hall et al., 2007), the Advanced Global Atmospheric Gases Experiment
(AGAGE) network (Prinn et al., 2000), and the University of Minnesota tall
tower (KCMP tall tower; Griffis et al., 2013; Chen et al., 2016). The hourly
measurement uncertainty at these sites is approximately 0.3, 0.6, and
1 ppb, respectively.
Small calibration offsets between measurement networks can significantly
impact N2O inversions due to its low ambient variability relative
to background mixing ratios. To address this, we adjust here the AGAGE and EC
data to the same NOAA 2006A scale used by the NOAA CCGG, CATS, CSIRO, NIWA,
and KCMP measurements. For AGAGE, we calculate an adjustment factor based on
co-located CCGG flask-based air samples taken within 15 min of an in situ
measurement at five sites: CGO (Cape Grim, Australia), MHD (Mace Head,
Ireland), RPB (Ragged Point, Barbados), SMO (Tutuila, American Samoa), and
THD (Trinidad Head, California). The mean CCGG : AGAGE ratio at these sites
from 2010 to 2012 is 1.00037, and we apply this adjustment to all AGAGE data.
For EC, we calculate an adjustment factor based on co-located NOAA
flask-based air measurements at ALT (Alert, Nunavut, Canada). The mean NOAA : EC
ratio during our analysis period is 1.00017, and we use this adjustment
factor across the EC network. While calibration-scale offsets can be
concentration and time dependent, our relatively short (2-year) analysis
window avoids the need for any temporally resolved measurement adjustments.
Prior to our analysis we also screen for outliers by omitting any
measurements more than 2 standard deviations (calculated on a running basis with a 30-day
time window for flask-based air measurements and a 24 h time window for in
situ observations) away from its nearest neighbor.
For a posteriori evaluation of the inverse modeling results we employ
airborne measurements from the HIPPO campaigns (Wofsy, 2011), which featured
pole-to-pole sampling and regular vertical profiling from approximately 300
to 8500 m altitude, with some profiles extending to
14 000 m. Figure 1 shows flight tracks for the two deployments
occurring during our simulation period and used here: HIPPO IV
(June–July 2011) and HIPPO V (August–September 2011). The aircraft payload
included high-frequency N2O measurements by quantum cascade laser
spectroscopy (Kort et al., 2011). To ensure calibration consistency we
apply an offset adjustment to these data for each deployment based on
concurrent flask-based air samples, which are anchored to the NOAA 2006A
scale.
Inversion sensitivity to initial conditions for N2O
Because of the ∼127-year atmospheric lifetime for N2O, any
bias in the model initial conditions can persist throughout the analysis
period and lead to substantial errors in top-down emission estimates
(Thompson et al., 2014c). In this section, we evaluate six alternate
approaches to generating initial N2O mass fields for the start date
of our inversions (1 April 2010), their impact on the derived fluxes, and
their overall suitability for inverse modeling.
The six treatments are summarized in Table 1. Three involve interpolation of
surface observations from the NOAA, AGAGE, CSIRO, EC, and NIWA networks for
alternate time windows (MarZonal, AprZonal, AprKriging), two involve 4D-Var
adjoint optimization of the initial mass field based on those same
observations plus those from KCMP tall tower (AprOpt, FebOpt), and one
involves optimization of the initial mass field based on observations from
remote sites (RemoteOpt). Interpolation of observations offers the advantage
of avoiding any model information that may bias the initial state, whereas
a 4D-Var optimization of the initial conditions allows us to exploit
subsequent atmospheric transport to inform the initial state in locations
without N2O observations. The first three approaches employ either
linear interpolation of zonally averaged surface measurements or kriging, and
use observations from March 2010 (with subsequent 1-month model spinup) or
from 25 March to 7 April 2010 (with no subsequent spinup). In each case, the
resulting surface mixing ratios of N2O (mapped in Fig. S4 in the
Supplement) are assigned to all vertical levels in the troposphere; initial
N2O mixing ratios above 100 hPa are based on interpolated
mean profiles from the EOS Aura Microwave Limb Sounder (MLS; Lambert et al.,
2007). Where necessary, N2O mixing ratios above the tropopause but
below 100 hPa are linearly interpolated between the tropospheric and
MLS values.
The three tests in which the initial conditions are optimized by 4D-Var use
a time window of February–March 2010, April–May 2010, or January–June 2010
to solve for the initial N2O mass field on 1 April 2010. Two of
these assimilate all surface observations while one employs only data from
remote sites. Below, we evaluate each of the six initial condition treatments
against observations at the beginning of the simulation period (1–7
April 2010) and perform a standard 4D-Var optimization of N2O
emissions to quantify the sensitivity of the inferred fluxes to the selected
initial conditions.
Initial bias statistics for each of the six initial conditions with
respect to observations at all sites, Northern Hemisphere sites, and Southern
Hemisphere sites. Statistics are calculated for the first week of the
simulation (1–7 April 2010).
Bias: Northern Bias: Southern Bias: all sites (ppb) Hemisphere sites (ppb) Hemisphere sites (ppb) Test name25thMedian75th25thMedian75th25thMedian75thMarZonal-0.210.300.710.110.460.86-0.66-0.36-0.15AprZonal-0.130.200.62-0.030.320.73-0.38-0.120.10AprKriging-0.290.060.42-0.310.020.39-0.200.140.49AprOpt-0.210.010.21-0.220.010.20-0.210.010.22FebOpt-0.290.060.48-0.42-0.030.37-0.160.140.39RemoteOpt-0.48-0.140.22-0.44-0.090.33-0.58-0.30-0.04
Table 2 shows initial bias statistics with respect to all surface
observations and by hemisphere for each initial condition treatment. Of the
interpolation approaches, the MarZonal setup has the poorest performance,
with an overly strong interhemispheric gradient (the model is biased high in
the Northern Hemisphere and low in the Southern Hemisphere) and the largest
initial model–measurement bias at all sites. In this case, the 1-month model
spinup, meant to smooth out any artificial N2O gradients from the
interpolation, is counterproductive as it allows model emission biases to
accumulate prior to the inversion. The interpolation methods without
subsequent spinup (AprZonal, AprKriging) perform better in terms of initial
model–measurement bias – in the global mean and in each individual
hemisphere. We see the same general behavior when using 4D-Var to optimize the
initial conditions, with the no-spinup AprOpt approach providing the lowest
initial model–measurement bias (and least spread in bias) across all of the
six methods tested. Using only data from remote sites (RemoteOpt) in the
initial field optimization leads to a negative model bias, on average, in
both hemispheres.
The bias statistics above can only test the realism of the initial
N2O fields in those locations where there are observations, but say
nothing about any potential bias in the large majority of model grid squares
that lack observations. However,
by carrying out a full forward model run based on each of those initial conditions, we can exploit
atmospheric transport to more fully assess the fidelity of the initial
N2O mass field based on the evolution of model–measurement biases
at the various observation sites.
Figure 2 shows monthly-mean model–measurement residuals (averaged for
Northern and Southern Hemisphere sites) for a full 2-year forward
simulation using the a priori emissions for each of the above initial mass
fields. While most of the initial conditions exhibit minimal bias at the
start of the simulation, some develop large biases over time. As a result,
the corresponding a posteriori global flux obtained in a 4D-Var source
inversion (values shown inset in Fig. 2) varies considerably depending on the
initial N2O field, with the flux adjustment even changing sign:
a posteriori values range from 16.1 to 21.4 TgNyr-1, i.e., from
a ∼7 % reduction to a 23 % increase in the prior flux. We see
in Fig. 2 that the direction of the global flux adjustment corresponds to the
trend in the model–measurement residuals. For example, with the MarZonal
initial conditions, a significant negative trend in the residuals drives
a global flux increase relative to the a priori, despite the fact that this
case exhibits a positive mean bias with respect to the observations at the
outset (Table 2). Such a trend in the model–measurement residuals could
theoretically arise from the accumulation of model source–sink errors over
the course of the simulation. However, our a priori flux and lifetime are
broadly consistent with independent observational constraints (Prather
et al., 2012), whereas an annual N2O source of 20+ Tg N would
yield a higher-than-observed atmospheric growth rate. A biased initial mass
field is thus the more tenable explanation for the negative model–measurement
residual trend.
Overall, the three simulations using initial conditions optimized by 4D-Var
yield a relatively small trend in the model–measurement N2O
residuals, as does the AprZonal simulation, arguing for a more realistic
initial N2O distribution in these cases. While the a posteriori
flux between them varies, differences are less than 10 % of the a priori
flux. Because the AprOpt initial conditions exhibit the lowest initial bias,
along with the lack of a trend in the residual timeline, we choose this
method to construct the initial conditions for the N2O inversions
presented here. Likewise, for future work on N2O and other
long-lived species, we recommend constructing the initial conditions by
4D-Var assimilation of observations at the outset of the inversion period.
Because they are used for initial condition optimization, the April–May 2010
surface observations are excluded from the subsequent source inversions.
2011 N2O emissions (TgNyr-1) over six
continental and three oceanic regions for the a priori database and
a posteriori results for the three inversion frameworks used here.
A posteriori emissions A prioriStandard 4D-VarContinental-SVD-basedRegionemissionsinversionscale inversioninversionNorth America1.611.301.781.24South America3.093.683.583.28Europe1.701.050.570.43Africa2.652.972.922.85Asia4.184.474.593.81Oceania0.760.790.640.84Northern oceans (30–90∘ N)0.660.520.070.15Tropical oceans (30∘ S–30∘ N)2.032.192.992.70Southern oceans (30–90∘ S)0.790.700.390.53Global17.417.717.515.9Inversion evaluation and results
Figure 3 shows maps of our derived annual a posteriori N2O
emissions from the standard, continental-scale, and SVD-based inversion for
2011, along with bar charts of the 2011 annual flux for the nine regions
considered in the continental-scale inversion (numerical values listed in
Table 3). A priori emissions, along with a posteriori emission increments
(a posteriori–a priori difference) are also included for comparison. We focus
on 2011 results to minimize any residual bias from the initial conditions.
Focusing on 2011 also excludes the last 3 months of the inversion window
when the adjoint forcing weakens due to the long lifetime of N2O
(Wells et al., 2015).
The optimized global fluxes, listed inset in each map in Fig. 3, range from
15.9 TgNyr-1 for the SVD-based inversion to
17.5–17.7 TgNyr-1 for the standard and continental-scale
inversions, with some similar spatial patterns and some discrepancies that we
explore further in Sect. 4.3. The SVD-based global flux agrees well with that
implied by the N2O lifetime and global burden for 2010 (15.7±1.1TgNyr-1; Prather et al., 2012). It also gives a better
comparison to HIPPO IV and V measurements in the southern extratropics and to
HIPPO V in the northern extratropics (see below). However, all three
a posteriori global annual fluxes are close to or within the range of recent
inverse studies (16.1–18.7 TgNyr-1). Below we evaluate our
inversion results using aircraft observations before interpreting
them in terms of the information they provide on N2O emission
processes.
A posteriori evaluation of N2O emissions
We apply the HIPPO IV and V airborne measurements described in Sect. 2.3 (and
mapped in Fig. 1) to evaluate the a posteriori fluxes from our different
inversion methods and assess which method yields the most realistic
depiction of true N2O fluxes. Figure 4 shows average vertical
profiles of the model–measurement N2O difference for these
deployments in the a priori and the three inverse estimates as a function of
latitude. Initially, the model vertical profile is biased high throughout the
troposphere in the northern mid-to-high latitudes; this bias is larger during
HIPPO V than HIPPO IV due to a seasonal bias in model emissions that is
further discussed in Sect. 4.4. In the southern mid-to-high latitudes the
model is also biased high through most of the troposphere. In most cases in
Fig. 4 we see that the model–measurement difference trends negative with
height in the troposphere, which may reflect a model underestimate of the
convective transport of N2O emissions (Kort et al., 2011). Large
biases above 400 hPa in HIPPO IV (30–90∘ N) and HIPPO V
(30–90∘ S) are driven by high-latitude observations in which the
aircraft is sampling below the model tropopause but above the actual
tropopause and highlight the difficulty in modeling the N2O
vertical profile at these altitudes.
All three inversions significantly reduce the 30–90∘ N bias seen
for both HIPPO campaigns; the SVD-based approach provides the fullest
correction during HIPPO V, while slightly overcorrecting the HIPPO IV bias.
However, the high bias from 30 to 90∘ S is only reduced in the
SVD-based inversion despite the fact that the continental-scale inversion
has the lowest a posteriori emissions in this latitude range (Table 3). The
lower global flux obtained with the SVD-based approach (Fig. 3 and Table 3)
is thus the reason for this correction, implying that the global annual
a priori flux (from all sources combined) may be too high. We note that
a slight low bias does emerge in the tropics in the SVD-based approach, where
observational constraints are low.
Averaging kernel diagonal values for April 2011 in the SVD-based
inversion, calculated from Eq. ().
Averaging kernel
The information from the randomized-SVD algorithm can be used to directly
calculate the inversion AK and posterior error via
Eqs. () and (), giving valuable information on the spatial
distribution of emission constraints provided by the N2O observing
network. Figure 5 shows the diagonal of the AK for N2O emissions in
April 2011 (results for other months are very similar). AK diagonal values
near 1.0 indicate emission locations that are well constrained by
observations, while AK diagonal values close to 0 indicate emission locations
that lack a direct constraint.
AK diagonal values for monthly N2O emissions are highest in the USA
and Europe, where the observational coverage is most extensive, with values up
to 0.7 in locations where hourly observations are available. Weaker
constraints are achieved in East Asia and some tropical and Australian grid
boxes, with AK values ranging from 0.01 to 0.4. AK values throughout most of
the Tropics, Southern Hemisphere, Canada, and northern Asia reveal almost no
direct observational constraints on monthly emissions in these regions.
The number of pieces of information that can be independently resolved (DOFs)
in any inversion can be determined from the trace of the AK. Here, the DOFs
are ∼315 for the full 2-year inversion. A key advantage of the
SVD-based approach is that it solves for only those spatiotemporal flux
patterns that can be constrained by the observations: i.e., the dimension of
the solution is consistent with the DOFs of the inversion. In contrast,
the standard inversion attempts to resolve 79 466 free variables, ∼250× more than can legitimately be constrained, while the
continental-scale inversion yields fewer pieces of information (216) than are
obtainable. The latter point confirms that the observations can in fact
resolve some finer-scale spatial and temporal information on N2O
emissions in the regions where AK values are highest.
Regional annual N2O emissions
In this section we interpret the inversion results by region in terms of
their implications for present understanding of N2O emission
processes. We focus on the spatial information obtained from the standard and
SVD-based inversions and on those features that are most robust across these
inversion frameworks.
North America
A posteriori emissions from North America range from 1.24 to
1.78 TgNyr-1, with a slight increase (11 %) inferred
relative to the a priori inventory for the continental-scale inversion vs.
a 20–23 % decrease for the standard and SVD-based inversion. The latter
values are quite close to a recent estimate from Saikawa et al. (2014) for
2008 (1.2±0.2TgNyr-1). Both the standard and SVD-based
inversions call for a large increase (2–3×) in emissions from the US
Corn Belt (Fig. 3), one of the most intensively managed agricultural regions
of the world. The magnitude of this upward adjustment supports emission
underestimates previously found for this region (Kort et al., 2008; Miller
et al., 2012; Griffis et al., 2013), which have been attributed to
underrepresentation of indirect N2O emissions following leaching
and runoff from agricultural soils (Turner et al., 2015b; Chen et al., 2016).
However, other processes could also contribute, such as freeze–thaw
emissions or direct emissions after spring fertilizer application. The timing
of these processes, and that of peak stream flow, corresponds to the dominant
modes of ambient N2O variability observed in this region (Griffis
et al., 2017). Finally, we find that emissions decrease relative to the
a priori estimate in the western USA and Canada (in both the standard and SVD
inversions), where natural soil emissions may be too high in the
CLMCN-N2O inventory (Saikawa et al., 2014) used here, and where
recent work argues that direct agricultural emissions are overestimated using
a standard linear emission model (Gerber et al., 2016).
South America
A posteriori emissions from South America range from
3.28 to 3.68 TgNyr-1, increasing 6–19 % over the a priori.
These values are 40–60 % larger than the median inferred by Thompson
et al. (2014c) for 2006–2008 (2.33 TgNyr-1); however, due to
weak observational constraints (Fig. 5) we find that the results here are
quite sensitive to the inversion framework used. For example, including fewer
modes in the SVD-based solution yields an even higher a posteriori flux in
this region, and the spatial distribution of emissions differs substantially
between the standard and SVD-based solutions. Saikawa et al. (2014) do note
a large recent increase in nitrogen fertilizer consumption over this region
(49 % from 1995 to 2008), which may help explain the larger a posteriori
flux seen here, although N fertilizer use in this region was only 7 % of
the global total in 2011 (International Fertilizer Association, 2016).
Europe
All three inversions point to a significant model overestimate of European
N2O emissions, with a posteriori fluxes that are 38 % (standard
inversion; optimized flux 1.05 TgNyr-1) to 75 % (SVD-based
inversion; optimized flux 0.43 TgNyr-1) lower than the
a priori. These optimized fluxes are in better agreement with the other
top-down flux estimates for Europe (both for 2006) of
1.19 TgNyr-1 (Corazza et al., 2011) and 0.93±0.12TgNyr-1 (Saikawa et al., 2014). The European source
derived in the SVD-based and continental-scale inversions
(0.43–0.57 TgNyr-1) represents ∼3 % of the global
flux found in each case, which agrees with the result from Huang
et al. (2008). We find the largest emission reductions over western and
central Europe, suggesting an overestimate of soil and nonagricultural
anthropogenic sources in the EDGARv4.2 inventory used here. While
nonagricultural anthropogenic sources make up only ∼10 % of the
global a priori N2O flux, they comprise ∼30 % of the
European a priori model emissions. Based on the spatial distribution of the
adjustments derived in the inversions, we find that both of these sources
(soils, nonagricultural anthropogenic) have a comparable high bias (from
40 to 70 % as indicated by the standard and SVD-based inversions,
respectively) in the a priori inventories over Europe.
Africa
Annual emissions from Africa range from 2.85 to 2.97 TgNyr-1 in
all three inversions, an 8–12 % increase from the prior flux. Our
a posteriori values are closer to the median optimized African flux found by
Thompson et al. (2014c) for 2006–2008 (3.36 TgNyr-1) than is
the a priori; however, the lack of direct observational constraints for this
region (Fig. 5) prevents any definitive conclusion. As in South America, the
SVD-based result here is quite sensitive to the number of modes used, with
emission increments differing in sign for some months. The spatial
distribution between the standard and SVD-based solutions also differs, with
the former preserving the a priori distribution and the latter placing more
of the flux in equatorial Africa.
Asia
Over Asia the a posteriori flux ranges from 3.82 TgNyr-1
(9 % decrease from the a priori) to 4.59 TgNyr-1 (10 %
increase). The full-dimensional and SVD-based inversions both call for
a reduction in model emissions for northern China and Russia and an increase
to the south. Consistent a posteriori spatial patterns emerge in the latter
region, with large emission increases over the prior for the Indo-Gangetic
Plain of India, Southeast Asia, and eastern China. Our flux estimates
are towards the higher end of the wide range of estimates for
North and South Asia (2.87–4.48 TgNyr-1) reported by
Thompson et al. (2014c) for 2006–2008; that study concludes that
observational constraints are low in this region, which is generally
consistent with our findings (Fig. 5). Saikawa et al. (2014) find that
agricultural N2O emissions are increasing in South Asia, and that
is consistent with our higher flux for 2011 compared to the Thompson
et al. (2014c) median value for 2006–2008. Of the total global N fertilizer
consumption, 58 % occurred in South and East Asia in 2011 (International Fertilizer
Association, 2016); it is possible that direct on-field N2O
emissions here are underestimated with N inputs exceeding crop demands
(Shcherbak et al., 2014). Indeed, a recent bottom-up estimate derives
a direct emission response for China that is 42 % larger than the global
average (Gerber et al., 2016). Over northern Asia our results point to an
overestimate of natural soil emissions (as this is the dominant regional
source in the model); a similar overestimate was inferred by Saikawa
et al. (2014).
Oceania
The emission estimates for Oceania range from 0.64 TgNyr-1
(16 % decrease from the prior) to 0.84 TgNyr-1 (10 %
increase). Observational constraints are low in this region (outside of Cape
Grim, where a measurement site exists; Fig. 5) and results depend strongly on
the a priori. The weak emission reduction in the continental-scale inversion
(Table 3) could also reflect a model overestimate of the southern ocean
source, as the sparse observations make it difficult to separate land vs.
ocean emissions here.
Ocean emissions
We obtain an annual flux ranging from 0.07 to 0.52 TgNyr-1 for
northern oceans (30–90∘ N), 2.19 to 2.99 TgNyr-1 for
tropical oceans (30∘ S–30∘ N), and
0.39 to 0.70 TgNyr-1 for southern oceans (30–90∘ S).
In all cases, our results indicate an emission increase for tropical ocean
emissions (of 9–47 %) and a decrease for northern (20–90 %) and
southern (11–51 %) oceans relative to the a priori Jin and Gruber (2003)
inventory. The wide range of values reflects the limited degree to which the
surface observing network can constrain ocean emissions. However, the
standard and SVD-based inversions both point to a model overestimate in the
North Atlantic where downwind observations in Europe have some power to
resolve monthly emissions.
The direction of the oceanic emission changes is consistent with the findings
of Thompson et al. (2014c); however, our oceanic fluxes are lower than
obtained in that study (1.08, 3.66, and 1.20 TgNyr-1 for
northern, tropical, and southern oceans, respectively). Compared to Thompson
et al. (2014c), results obtained here (3.38–3.45 TgNyr-1) are
closer to the most recent best estimate of the oceanic source derived from
observations of the air–sea N2O gradient (2.4±0.8TgNyr-1; Buitenhuis et al., 2017), albeit still higher.
We find that ocean emissions make up ∼20 % of the global
N2O flux (in both the a priori and a posteriori estimates), lower
than found in some inverse studies (31–38 %; Saikawa et al., 2014;
Thompson et al., 2014c) but consistent with Huang et al. (2008) (∼23 %).
Summary of regional-scale results
Among the most robust spatial features of our results across all the
inversion frameworks employed is an increase in annual N2O
emissions over the a priori in the tropics (particularly 0–30∘ N)
and a decrease at higher latitudes for both ocean and terrestrial sources.
While the total Asian flux differs between the full-dimensional and SVD-based
inversion, both solutions indicate a model overestimate in northern Asia and
an underestimate in Southeast Asia. Furthermore, while the inversions
disagree on whether the a priori emissions are too high or too low over North
America as a whole, both the full-dimensional and SVD-based inversions
increase the prior N2O emissions over the US Corn Belt and reduce
them over the western USA and Canada. This suggests that while the a priori
emissions may be too high in northern mid-to-high latitudes overall (which we
attribute to overly high natural soil emissions in the model, as well as
nonagricultural anthropogenic emissions in regions such as Europe, and
a possible overestimate of direct emissions in drier regions), they are
underestimated for fertilized agricultural soils in the US Corn Belt and
likely also in Asia.
Seasonality of N2O emissionsA priori seasonality
Figure 2 shows that the a priori model bias in atmospheric N2O
varies strongly as a function of season in the Northern Hemisphere, implying
a corresponding seasonal bias in the bottom-up emissions driving the model.
Because the EDGARv4.2 emissions used here are annual, the seasonality in our
prior emissions over land is dominated by the natural soil source. Here, we
compare the temporal constraints afforded by the different inversions,
focusing again on the most robust features across the inversions, after first
examining the seasonality differences between modeled and measured
N2O mixing ratios.
Two-year timelines of monthly-averaged
a priori modeled and measured N2O mixing ratios, and the resulting
model–measurement residuals, for individual measurement sites as a function
of latitude. The solid black line in the top panels shows results for the
KCMP tall tower site in MN, USA.
Figure 6 shows 2-year timelines of monthly-averaged a priori modeled and
measured N2O mixing ratios along with the corresponding
model–measurement residual for all surface measurement sites. The modeled
N2O from 30 to 90∘ N is characterized by
a November–December peak and a May–June minimum. This is out of phase with
the measurements, which have a minimum around August–September and a peak in
February–March. Several other CTMs in a recent intercomparison (Thompson
et al., 2014b, c) likewise produce a seasonal minimum that is too early
compared to observations, which that study suggests may reflect an
overestimate of the impact of N2O-depleted stratospheric air on
surface mixing ratios. Our previous work indicates that surface N2O
mixing ratios are not sensitive to biases in the magnitude of the
stratospheric sink on the timescale of our inversion (Wells et al., 2015),
while Thompson et al. (2011) find that errors in modeled
stratosphere–troposphere exchange can bias inferred regional emissions by up
to 25 %, particularly over the North Atlantic and Europe. We thus focus
here on inferred seasonal changes that are significantly larger than 25 %
and most robust to any potential errors in modeled stratosphere–troposphere
exchange.
Measured mixing ratios at the KCMP tall tower site in Minnesota are
significantly higher than other Northern Hemisphere sites. As a result, it is
one of the few sites where negative model–measurement residuals persist
through most of the 2-year inversion period. Located in an agricultural
region composed mainly of drained lands, the low model bias is consistent
with previous findings of a missing or strongly underestimated agricultural
N2O source tied to indirect emissions (Griffis et al., 2013; Chen
et al., 2016).
Monthly N2O emissions for 2011
over six continental and three oceanic regions. Shown is the a priori
database (black) and a posteriori results for the standard 4D-Var inversion
(red), the continental-scale inversion (green), and the SVD-based inversion
(gold).
Seasonality of N2O inversion results
Figure 7 contains 2011 timelines of the monthly a priori and a posteriori
emissions for the three inversion methods over the same continental and ocean
regions considered above. Both North American and European a posteriori
emissions are characterized by a shift from a summertime (June–July) to
springtime peak in emissions (March–April), with the North American results
exhibiting separate spring and summer peaks (plus an October enhancement in
the SVD-based inversion). The a posteriori seasonality over Asia is nearly
reversed from the a priori, with dual emission peaks in spring (March–May)
and fall (September–October). This double maximum is consistent with past
work and coincides with the approximate start and end times of the Asian
monsoon (Thompson et al., 2014c). Over South America and Africa we find that
the a posteriori seasonality depends more strongly on the inversion method
used, reflecting the low observational constraints in these regions (Fig. 5).
Tropical ocean emissions increase primarily during summer and fall when
emissions are at their peak, though the magnitude varies across inversion
frameworks. Emissions decrease strongly for the northern oceans (though they
were not large to begin with) for the continental and SVD-based inversions,
but with no shift in seasonality. Seasonal emission adjustments are small
over the southern oceans and Oceania, where constraints are weak.
The shift toward earlier springtime emissions in the Northern Hemisphere is
one robust feature across our inversions. Thompson et al. (2014c) arrived at
the same finding and argued that it reflects the dependence of N2O
emissions on soil moisture and temperature, as drier soils later in summer
may limit N2O fluxes. However, other factors are also likely to
contribute. Emissions associated with freeze–thaw cycles can lead to
elevated springtime N2O fluxes at these middle to high latitudes
(e.g., Wagner-Riddle et al., 2017), while higher springtime emissions are also
consistent with the timing of fertilizer application and indirect
N2O emissions due to leaching and runoff when streamflow is at its
peak (Chen et al., 2016; Griffis et al., 2017). The separate spring and
summer emission peaks seen over North America in 2011 may reflect the
respective influences of indirect and direct emissions, which have been shown
(Chen et al., 2016) to peak earlier (indirect emissions) and later (direct
emissions) in the growing season. Fall fertilizer application is also common
in the US Corn Belt – more than one-third of corn farmers in Minnesota do
their main N application during this time (Beirman et al., 2012) – which
could explain the October peak in the SVD-based results and provide a source
of nitrogen that would be released in the early spring thaw and subsequent
runoff period.
We see in Fig. 7 that the seasonal adjustments are larger in the continental
and SVD-based inversion than the standard 4D-Var, particularly in regions
where direct observational constraints are low. In our previous work (Wells
et al., 2015) we highlighted the difficulty in correcting seasonal biases
when solving for monthly N2O emissions on a grid box scale. The
SVD-based approach thus provides a major advantage in this context by
reducing the dimensions of the inverse problem and allowing us to better
resolve temporal features that inform our understanding of N2O
emission processes.
Conclusions and implications for the N2O budget
In this paper we employed three inversion frameworks to derive top-down
constraints on global monthly N2O emissions for 2011. The inverse
frameworks included (1) a standard 4D-Var inversion at 4∘×5∘, (2) a 4D-Var inversion solving for fluxes on six continental and
three ocean regions, and (3) a fast 4D-Var inversion based on a new dimension
reduction technique using efficient randomized-SVD algorithms. The latter
technique is an advance over typical aggregation schemes: it defines the
optimal resolution of the solution according to the information afforded by
the observations, maximizes the DOFs of the inverse system, and offers
major time savings compared to other iterative inversion methods.
Over many regions, our inversion results are broadly consistent with other
recent inversion studies, though the range of derived flux values and
seasonalities from poorly observed regions highlights the ill-posed nature of
the inverse problem for N2O. Based on the most robust features
across our three different inversion frameworks, we can draw the following
conclusions about the global N2O budget and underlying emission
processes:
The global annual N2O flux is likely somewhat high in the bottom-up
inventory used here, as the lower value (15.9 TgNyr-1) derived
in the SVD-based inversion gives a better representation of the N2O
background in the extratropics while also being more consistent with the
current best estimate from a 0-D consideration of the global burden and
lifetime of N2O (Prather et al., 2012).
Our inversion results indicate that a greater fraction of the global
N2O flux is emitted from the tropics than the a priori inventories
would suggest. This points to an overestimate of natural soil (and perhaps
industrial/residential) emissions in the Northern Hemisphere and to an
underestimate of agricultural (and likely oceanic) emissions in the tropics.
The former hypothesis would be consistent with the 2-fold reduction in the
industrial N2O source for EDGAR versions subsequent to that used
here.
In the northern hemispheric midlatitudes, N2O emissions peak in the
springtime (March–April). This seasonality is supported by other recent
studies and corresponds to the period of higher soil moisture, peak
streamflow, thawing of frozen soils, and the timing of fertilizer
application.
We find that N2O emissions from agricultural soils are
underestimated in the US Corn Belt and likely also in Asia. We attribute this
to an underestimate of indirect agricultural emissions due to leaching and
runoff, freeze–thaw emissions in early spring, and the direct on-field
source when N inputs exceed crop demands. Annual emissions over the US Corn
Belt are underestimated by 2–3× in the a priori inventories; the
standard and SVD-based inversions used here both increase emissions from this
region throughout the growing period (March–September).
Based on our analysis of alternate initial conditions for atmospheric
N2O, and their corresponding effects on derived fluxes, we
recommend formally optimizing the initial mass field (either alone or in
tandem with the emissions optimization) rather than interpolating
N2O observations or using an unconstrained model spinup. The
impacts can be substantial: for the sensitivity tests used here, a posteriori
global fluxes ranged by ∼25 % (16.1–21.4 TgNyr-1)
across different treatments of the initial N2O mass.
Finally, the SVD-based inverse approach used here offers a powerful framework
for maximizing the emission information derived from atmospheric observations
of N2O in an efficient, timely manner, particularly for models with
a low level of parallelization. The approach provides valuable
spatially resolved information that is lost when solving for fluxes over
ad hoc continental-scale regions, while also providing a much stronger
ability to resolve broad temporal features than is possible with a standard
4D-Var inversion at the model grid resolution. Such information is key to
furthering our understanding of N2O emission processes based on
top-down analyses.
The N2O version of the GEOS-Chem adjoint code is available via the
GEOS-Chem adjoint repository. Instructions for obtaining access to the code
can be found at http://wiki.seas.harvard.edu/geos-chem/index.php/GEOS-Chem_Adjoint.
N2O measurements used in this work are available from
NOAA ESRL/GMD (http://www.esrl.noaa.gov/gmd/dv/data/) and the World
Data Centre for Greenhouse Gases (http://ds.data.jma.go.jp/gmd/wdcgg/)
or by contacting the principle investigators of the individual measurement
stations.
Proof for cost function projection formula
Jx=12hx-yTSy-1h(x-y)+12x-xaTSa-1x-xa,
and
hx=hxa+H(x-xa).
Therefore,
hx-yTSy-1h(x-y)=hxa+Hx-xa-yTSy-1(hxa+H(x-xa)-y)=hxa+Sy12Sy-12HSa12Sa-12x-xa-yT×Sy-1hxa+Sy12Sy-12HSa12Sa-12x-xa-y.
Then we develop
Sy-12HSa12=∑i=1nλi12wiviT, where
n is the dimension of the state vector, and project the control variable
onto the optimal basis
{Sa12vi,i=1,…,k} using the
projector π=Sa12∑i=1kviviTSa-12,
which yields
hx-yTSy-1h(x-y)≈hxa-yTSy-1h(xa-y)+x-xaTSa-12∑i=1kλiviviTSa-12x-xa+hxa-yTSy-12∑i=1kλi12wiviTSa-12x-xa+x-xaTSa-12∑i=1kλi12viwiTSy-12hxa-y,
and
x-xaTSa-1x-xa≈x-xaTSa-12∑i=1kviviTSa-12x-xa.
Inserting Eqs. (A4) and (A5) in Eq. (A1), one obtains
Jx≈12x-xaTSa-12∑i=1kviviTSa-12x-xa+12hxa-yTSy-1h(xa-y)+12x-xaTSa-12∑i=1kλiviviTSa-12x-xa+12hxa-yTSy-12∑i=1kλi12wiviTSa-12x-xa+12x-xaTSa-12∑i=1kλi12viwiTSy-12hxa-y.
Differentiating Eq. (A6), one obtains
∇Jx≈Sa-12∑i=1kviviTSa-12x-xa+Sa-12∑i=1kλiviviTSa-12x-xa+Sa-12∑i=1kλi12viwiTSy-12hxa-y.
The Supplement related to this article is available online at https://doi.org/10.5194/acp-18-735-2018-supplement.
The authors declare that they have no conflict of
interest.
Acknowledgements
This work was supported by NOAA (grant no. NA13OAR4310086 and NA13OAR4310081)
and the Minnesota Supercomputing Institute. The KCMP measurements were made
with support from the USDA (grant no. 2013-67019-21364). We thank E. Kort and
S. Wofsy for providing the HIPPO N2O measurements. We thank
Environment Canada for providing data from the Alert, Churchill, Estevan
Point, East Trout Lake, Fraserdale, and Sable Island Sites. We thank
R. Martin and S. Nichol for providing data from the Arrival Heights NIWA
station. We thank J. Muhle and C. Harth (UCSD-SIO), P. Fraser (CSIRO),
R. Wang (GaTech), and other members of the AGAGE team for providing AGAGE
data. The AGAGE Mace Head, Trinidad Head, Cape Matatula, Ragged Point, and
Cape Grim stations are supported by NASA grants to the Massachusetts
Institute of Technology and Scripps Institution of Oceanography, the
Department of Energy and Climate Change (DECC, UK) contract to the University
of Bristol, and CSIRO and the Australian Bureau of Meteorology. We thank
C. Adam Schlosser for work on the MIT IGSM.
Edited by: Annmarie Carlton Reviewed by: two anonymous
referees
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