We present a method to derive atmospheric-observation-based estimates of carbon dioxide (CO2) fluxes
at the national scale, demonstrated using data from a network of surface
tall-tower sites across the UK and Ireland over the period 2013–2014. The
inversion is carried out using simulations from a Lagrangian chemical
transport model and an innovative hierarchical Bayesian Markov chain Monte
Carlo (MCMC) framework, which addresses some of the traditional problems
faced by inverse modelling studies, such as subjectivity in the
specification of model and prior uncertainties. Biospheric fluxes related to
gross primary productivity and terrestrial ecosystem respiration are solved
separately in the inversion and then combined a posteriori to determine net
ecosystem exchange of CO2. Two different models, Data
Assimilation Linked Ecosystem Carbon (DALEC) and Joint UK Land Environment Simulator (JULES),
provide prior estimates for these fluxes. We carry out separate inversions
to assess the impact of these different priors on the posterior flux
estimates and evaluate the differences between the prior and posterior
estimates in terms of missing model components. The Numerical Atmospheric
dispersion Modelling Environment (NAME) is used to relate fluxes to the
measurements taken across the regional network. Posterior CO2 estimates
from the two inversions agree within estimated uncertainties, despite large
differences in the prior fluxes from the different models. With our method,
averaging results from 2013 and 2014, we find a total annual net biospheric
flux for the UK of 8±79 Tg CO2 yr-1 (DALEC prior) and
64±85 Tg CO2 yr-1 (JULES prior), where negative values represent an
uptake of CO2. These biospheric CO2 estimates show that annual UK
biospheric sources and sinks are roughly in balance. These annual mean
estimates consistently indicate a greater net release of CO2 than the
prior estimates, which show much more pronounced uptake in summer months.
Introduction
There are significant uncertainties in the magnitude and spatiotemporal
distribution of global carbon dioxide (CO2) fluxes to and from the
atmosphere, particularly those due to terrestrial ecosystems
(Le Quéré et al., 2018). Reliable methods for quantifying carbon budgets
at policy-relevant scales (i.e. national or subnational) will be important
to accurately and transparently evaluate each country's progress towards
achieving their Nationally Determined Contributions (NDCs) made following
the Paris Agreement (UNFCCC, 2015).
Regional terrestrial carbon fluxes can be estimated using a range of
observational, computational and inventory-based methods. These include
bottom-up approaches such as the upscaling of direct flux measurements
made using eddy covariance or chamber systems (Baldocchi and Wilson, 2001) and models of
atmosphere–biosphere CO2 exchange. Flux measurements are important for
understanding the small-scale processes responsible for carbon fluxes.
However, they are relatively localised estimates (metres to hectares), which
are challenging to scale up to national levels. Biosphere models and land
surface models can be used to estimate carbon fluxes using coupled
representations of biogeophysical and biogeochemical processes, driven by
observations of meteorology and ecosystem parameters (Potter,
1999; Clark et al., 2011; Bloom et al., 2016). Such models describe
processes to varying degrees of complexity, with poorly described errors, and
are driven by observational data at differing temporal and spatial
resolutions; hence predictions of biogenic greenhouse gas (GHG) fluxes have
poorly quantified biases and can vary significantly between models (Todd-Brown
et al., 2013; Atkin et al., 2015).
Atmospheric inverse modelling is a top-down approach that provides an
alternative to the bottom-up approaches. Inversions have been used to
indirectly estimate country-scale (e.g. Matross et al., 2006; Schuh et al., 2010; Meesters et al., 2012) and
continental (e.g. Gerbig et al., 2003; Peters et al., 2010; Rivier et al., 2010) biospheric
CO2 budgets using atmospheric mole fraction observations, where the
contribution of anthropogenic fluxes to the observations has been removed.
In this approach, a model of atmospheric transport relates spatiotemporally
resolved surface fluxes of biospheric CO2 to atmospheric measurements
of CO2 mole fractions. Biospheric fluxes derived from bottom-up
approaches are often used as prior estimates in the inversion. Since
atmospheric observations are sensitive to fluxes spanning tens to hundreds
of kilometres (Gerbig et al., 2009), inverse methods
are a valuable tool for examining national fluxes and evaluating estimates
of surface exchange of CO2 at larger spatial scales. However, errors in
atmospheric transport, unknown uncertainties related to the prior fluxes and
issues surrounding the underdetermined nature of the problem are all
limitations of this approach.
The United Kingdom (UK) government has set legally binding targets to curb
GHG emissions in an attempt to prevent dangerous levels of
climate change. The Climate Change Act 2008 (UK government,
2008) commits the UK to 80 % cuts in GHG emissions, from 1990 levels, by
2050. To support this legislation, a continuous and automated measurement
network has been established (Stanley et al., 2018; Stavert
et al., 2018) with the goal of providing estimates of GHG emissions using
methods that are complementary to those used to compile the UK's bottom-up
emissions inventory, reported annually to the United Nations Framework
Convention on Climate Change (UNFCCC). Previous studies have used data from
the UK Deriving Emissions related to Climate Change (UK-DECC) network to
infer emissions of methane, nitrous oxide and HFC-134a from the UK (Manning
et al., 2011; Ganesan et al., 2015; Say et al., 2016). These studies found
varying levels of agreement with bottom-up inventory methods, where
estimates of GHG emissions are made using reported statistics from various
sectors (e.g. road transport, power generation). Here we use the DECC
network and two additional sites from the Greenhouse gAs Uk and Global
Emissions (GAUGE) programme (Palmer et
al., 2018) to estimate biospheric fluxes of CO2. Whilst anthropogenic
emissions, which are the remit of the UK inventory, are not estimated in
this study, these biospheric estimates represent the first step towards a
framework for estimating the complete UK CO2 budget.
Atmospheric inverse modelling of GHGs using Bayesian methods presents some
known challenges. Robust uncertainty quantification in Bayesian frameworks
can be difficult as they require that uncertainties in the prior flux
estimate, and uncertainties in the atmospheric transport model's ability to
simulate the data, are well characterised. In practice, this is rarely the
case because, for example, uncertainties related to the atmospheric
transport model are poorly understood and uncertainties related to
biospheric flux estimates from models are largely unknown. Various studies
have investigated the use of data-driven uncertainty estimation (Michalak,
2004; Berchet et al., 2013; Ganesan et al., 2014; Kountouris et al., 2018b).
Inversions are also known to suffer from aggregation errors. One type of
aggregation error arises from the way in which areas of the flux domain are
grouped together to decrease the number of unknowns, because usually there
are not sufficient data to solve for fluxes in each model grid cell
(Kaminski et al., 2001). Furthermore, for reasons
of mathematical and computational convenience, Gaussian probability density
functions (PDFs) are commonly used to describe prior knowledge
(e.g. Miller et al., 2014). However, Gaussian
assumptions can lead to unphysical solutions in the case of atmospheric GHG
emissions or uptake processes, as they permit both positive and negative solutions.
CO2 presents further complications over other GHGs in that
atmosphere–biosphere CO2 exchange has a diurnal flux cycle that is
significantly larger than the net flux and has strong, spatially varying
surface sources and sinks. Gerbig et al. (2003) was one of the first to develop an analysis framework for
regional-scale CO2 flux inversions. The study sets out the need to explicitly
simulate the diurnal cycle of biospheric fluxes and highlights the
importance of high spatial and temporal resolution data when addressing the
unique problems of representation and aggregation errors caused by the
highly varying nature of CO2 fluxes in both space and time. Inverse
modelling studies of CO2 flux typically assume that anthropogenic
fluxes are “fixed” in the inversion (e.g. Meesters et al., 2012; Kountouris et al., 2018a). This is based on the
assumption that uncertainties in anthropogenic fluxes are low compared to
those of the biospheric fluxes. However, it has been suggested that this may
not necessarily be the case (Peylin et al., 2011).
Here we outline a framework for evaluating the net biospheric CO2
exchange (net ecosystem exchange, NEE) from a small- to medium-sized country
(the UK covers an area of around 250 000 km2) using the high-resolution
regional, Lagrangian transport model, the Numerical Atmospheric dispersion
Modelling Environment (NAME, Jones et al., 2006). To address
many of the problems outlined above, we use an adapted form of a
hierarchical Bayesian, trans-dimensional Markov chain Monte Carlo (MCMC)
inversion (Rigby et al., 2011; Ganesan et al., 2014; Lunt et al., 2016). In the hierarchical
Bayesian framework presented in Ganesan et al. (2014),
“hyperparameters” that define the prior flux and
model–data “mismatch”
uncertainty PDFs are included in the inversion, which is solved using a
Metropolis–Hastings MCMC algorithm (e.g. Rigby et
al., 2011). This hierarchical approach has been shown to lead to more robust
posterior uncertainty quantification in Bayesian frameworks where prior
uncertainties are not well characterised (Ganesan et al., 2014).
Lunt et al. (2016) built on this method,
developing a “trans-dimensional” framework that accounted for the
uncertainty in the definition of basis functions (the way in which flux grid
cells are aggregated) and allowed this to propagate through to the posterior estimate.
Gross primary productivity (GPP) and terrestrial ecosystem respiration (TER)
estimates from the Joint UK Land Environment Simulator (JULES) and Data
Assimilation Linked Ecosystem Carbon (DALEC) models are used as prior flux
constraints. JULES is a state-of-the-art physically based, process-driven
model that estimates the energy, water and carbon fluxes at the
land–atmosphere boundary and uses a variety of observation-derived products
describing physical parameters as inputs (Best
et al., 2011; Clark et al., 2011). DALEC, on the other hand, is a simplified
terrestrial C-cycle model which is calibrated independently at each location
retrieving both process parameters and initial conditions using the carbon
data model framework (CARDAMOM) model–data fusion system. CARDAMOM ingests
satellite-based remotely sensed estimates of the state of terrestrial
ecosystems (Bloom and Williams, 2015; Bloom et al., 2016; Smallman et al., 2017).
Below, we first describe our approach for modelling biospheric CO2
fluxes, including several novel aspects compared to previous work in this
area. We then investigate the impact of using two different models that
simulate biospheric fluxes (JULES and DALEC) within our proposed inverse
framework and discuss the discrepancies between the prior and posterior flux estimates.
Method
The main components of a regional atmospheric inverse modelling framework
are the atmospheric CO2 mole fraction data themselves, a model of
atmospheric transport including a set of boundary conditions at the edge of
the regional domain and some initial information or “first guess” of
regional CO2 fluxes. These components are combined in an inversion
set-up with a mechanism for dealing with uncertainties in the inputs. To
make the problem computationally manageable, the regional domain is often
decomposed into a number of basis functions, describing a spatial grouping
of grid cells within which fluxes are scaled up or down. The selection of
these basis functions constitutes a further key element of the atmospheric
inverse problem.
Site location and measurements
This study focuses on the years 2013 and 2014. During this period,
atmospheric CO2 mole fractions were continuously measured at six sites
across the UK and Republic of Ireland (see Table 1 for site information and
Fig. 1 for the location of the sites). Four of these sites originally formed
the UK-DECC network and are described in Stanley et al. (2018), whilst two were
developed under the GAUGE programme and are described in Stavert et al. (2018). The site at Mace Head, Republic of
Ireland, is a coastal, 10 m a.g.l. (above ground level), station situated
primarily to measure concentrations of background air arriving at the site
from the Atlantic Ocean. The Laboratoire des Sciences du Climat et de
l'Environnement (LSCE) is responsible for making CO2 measurements at
this site from a 23 m a.g.l. inlet (see Vardag et
al., 2014, for a full site description). All of the UK sites are tall-tower
stations (with inlets ranging from 42 to 248 m a.g.l.), designed to measure
elevated GHG mole fractions as air is transported over the
surface in the UK and Europe.
Mean annual NAME footprint for 2014, for each of the six sites. MHD: Mace
Head; RGL: Ridge Hill; HFD: Heathfield; TAC: Tacolneston; BSD: Bilsdale;
TTA: Angus. WAO shows the location of the Weybourne Atmospheric Observatory,
where data have been used to validate the results but have not been included in
the inversion (the mean footprint from this station is not plotted).
Continuous CO2 measurements are made at all stations using cavity
ring-down spectrometers (CRDS: Picarro G2301 or G2401). CRDS data are
corrected for daily linear instrumental drift using standard gases and for
instrumental non-linearity using calibration gases, spanning a range of
above and below ambient mole fractions, on a monthly basis (Stanley et al., 2018). Calibration and
standard gases are of natural composition and calibrated at the GasLab, Max
Planck Institute for Biogeochemistry, Jena, or the World Calibration Centre
for CO2 at Empa, linking them to the World Meteorological
Organisation (WMO) X2007 scale (Stanley et
al., 2018; Stavert et al., 2018). At sites with multiple inlets,
measurements are taken for the same length of time at each inlet, each hour.
This means that measurements at each height at Bilsdale and Tacolneston
(with three inlets) are taken continuously for roughly 20 min every hour,
and at Heathfield and Ridge Hill (with two inlets) measurements are taken
continuously for roughly 30 min at each inlet every hour. For the
purposes of the inverse modelling carried out in this study, the continuous
CRDS data are used from the highest inlets and averaged to a 2 h time
resolution. Further information about the instruments, measurement protocol
and uncertainty estimates can be found in Stanley et al. (2018) and Stavert et al. (2018).
Atmospheric transport model
In this work we use a Lagrangian particle dispersion model (LPDM), NAME,
which tracks thousands of particles back in time from observation locations.
The model determines the locations where air masses interacted with the
surface and therefore where surface CO2 sources and sinks could
contribute to a CO2 concentration measurement. The model provides a
gridded sensitivity of each mole fraction observation to the potential flux
from each grid cell and this is often referred to as the “footprint” of a
particular observation (for further details, see e.g. Manning et al., 2011).
Measurement site information. The location of sites is also shown in
Fig. 1. * Weybourne data were used for validation of the results only and
were not included in the inversions. LSCE – Laboratoire des Sciences du Climat et
de l'Environnement; DECC – Deriving Emissions related to Climate Change;
GAUGE – Greenhouse gAs Uk and Global Emissions; UEA – University of East Anglia.
SiteSiteLocationInletNetworkcodeheight(m a.g.l.)Mace HeadMHD53.327∘ N, 9.904∘ W24LSCERidge HillRGL51.998∘ N, 2.540∘ W90DECCTacolnestonTAC52.518∘ N, 1.139∘ E185DECCHeathfieldHFD50.977∘ N, 0.231∘ E100GAUGEBilsdaleBSD54.359∘ N, 1.150∘ W248GAUGEAngusTTA56.555∘ N, 2.986∘ W222DECCWeybourne*WAO52.950∘ N, 1.122∘ E10UEA
At each 2-hourly measurement time step, the model releases 20 000 particles,
which are tracked back in time for 30 days, so that by the end of
this period the majority of particles will have left the model domain
(Fig. S1 in the Supplement). Since most CO2 flux to the atmosphere occurs at the surface, we
record the instances where the particles are in the lowest 40m of the
atmosphere and assume that this represents the sensitivity of observed mole
fractions to surface fluxes in the inversion domain. The domain used to
calculate atmospheric transport covers most of Europe, the east coast of
North and Central America, and North Africa (10.729–79.057∘ N
and 97.9∘ W–39.38∘ E). The spatial resolution of the meteorological analysis dataset
used to drive the model, from the Met Office Unified Model (Cullen, 1993), was
0.233∘ by 0.352∘ (roughly 25 km by 25 km over the UK).
In many previous inverse modelling studies using LPDMs (e.g. Manning
et al., 2011; Thompson and Stohl, 2014; Steinkamp et al., 2017) the
footprint is assumed to be equal to the integrated air history over the
duration of the simulation (e.g. 30 days, as in Fig. 1). Based on the
assumption that fluxes have not changed substantially during the 30-day
period, the integrated footprint can be multiplied by the prior flux and
summed over all the grid cells in the domain to create a time series of
modelled mole fractions at each measurement site. However, many CO2
inverse modelling studies using other LPDMs have disaggregated footprints
back in time, capturing changes in surface sensitivity on timescales shorter
than the duration of the simulation, thereby attempting to account for
diurnal variation in CO2 fluxes (Denning
et al., 1996; Gerbig et al., 2003; Gourdji et al., 2010). Thus far, a
disaggregation such as this has not been used in NAME simulations, so we
describe our method here.
In our simulations, we determined the footprint for 2-hourly average periods
back in time for the first 24 h before the observation and then
replaced the first 24 h of integrated sensitivities with these
time-disaggregated footprints. Mole fractions were simulated by multiplying
these footprints by biospheric flux estimates for the corresponding time, so
that the variability in the source or sink of CO2 was represented in
the modelled observations. This is demonstrated in Eq. (1), which yields the
modelled mole fraction, yt, for one 2-hourly measurement time step,
t, at one measurement site.
yt=∑i=012∑j=0nfpt-i,j×qt-i,j+∑j=0nfpremainderj×qmonthj
Here i denotes the number of 2 h periods back in time before the particle
release at time t; j represents the grid cell where n is the maximum
number of grid cells; fpt-i,j is one grid cell of the two-dimensional
time-disaggregated footprint for that time; qt-i,j is one grid cell of
the two-dimensional, 2-hourly flux field corresponding to the time the
particles were interacting with the surface; fpremainder is the
remaining 29-day footprint; and qmonth is the monthly average flux. The
choice of 24 h disaggregation balanced considerations of computational
efficiency and simulation accuracy. For certain months and sites we carried
out a set of tests to determine how sensitive our simulated mole fractions
and inversion results were when footprints were disaggregated for the first
12 or 72 h prior to each measurement (Fig. S2; Table S1 in the Supplement). Assuming
that the 72 h simulations were the most accurate, we found little
degradation in performance by using only 48 or 24 h disaggregation, when
compared to the other uncertainties in the system (e.g. differences between
fluxes derived using the 24, 48 and 72 h simulations were smaller than
the 90 % confidence interval). However, when only 12 h was used (or
fully integrated footprints), the modelled diurnal cycle was out of phase
with the observations.
Data selection and model uncertainty
LPDMs are known to perform poorly under certain meteorological conditions.
In particular, it is often assumed that model–data mismatch should be
smallest during periods when the boundary layer is relatively well mixed. A
common approach is to only include daytime data in the inversion
(e.g. Meesters et al., 2012; Steinkamp et al., 2017; Kountouris et al., 2018a) or
separate morning and afternoon averages (e.g. Matross et al., 2006). To make use
of as much high-frequency-measurement information as possible, we use a
filter based on two metrics to remove times of high atmospheric stability
and/or stagnant conditions. The first metric is based on calculating the
ratio of the NAME footprint magnitude in the 25 grid boxes in the immediate
vicinity of the measurement station to the total for all of the grid boxes
in the domain. A high ratio indicates times when a significant fraction of
air influencing the observation point originates from very local sources,
which may not be resolved by the model (Lunt et al., 2016). The second metric is
based on the modelled lapse rate at each site, which is a measure of
atmospheric stability. A high lapse rate suggests very stable conditions,
which would be conducive for significant local influence. Thresholds for
each of these criteria were chosen to preserve as much data as possible,
whilst retaining only points that the model was (somewhat subjectively)
found to resolve well. In practice, the filter retained many more daytime
than night-time points (see Fig. S3 for an analysis of the data removed in 2014)
and inversion results were mostly similar to when only daytime data
were used; however, differences were seen in some months when stagnant
conditions occurred for several daytime periods (Fig. S4).
Model uncertainty (or model–data mismatch) has a measurement uncertainty
component and a component that takes into account the ability of the model
to represent real atmospheric conditions. The measurement uncertainty was
assumed to be equal to the standard deviation of the measurements over the
2 h period to give an estimate of measurement repeatability and a measure
of the sub-model-timescale variability in the observations. The 2-hourly
measurement uncertainty was then averaged over the month to ensure that
measurements of high concentrations were not de-weighted, as they are more
likely to have greater variability and therefore a larger standard
deviation. Monthly average measurement uncertainty is around 0.9 ppm. The
measurement uncertainty is combined with a range of prior values for model
uncertainty (as this is a poorly constrained quantity), and together the
model–measurement
uncertainty is one of the hyper-parameters solved in the
inversion (further explained in Sect. 2.4.1).
Specifications for different prior and fixed fluxes.
Spatial resolutionTemporal resolutionBiogenic fluxes JULES0.25∘× 0.25∘2-hourlyDALEC25 km × 25 km (1∘× 1∘ outside the UK)2-hourlyAnthropogenic fluxes NAEI (UK)1 km × 1 km2-hourlyEDGAR (outside UK)0.1∘× 0.1∘Yearly (using 2010)Ocean fluxes4∘× 5∘Monthly (climatology)
Prior UK fluxes in 2014. (a–c) Comparison of JULES (blue)
and DALEC (orange) monthly fluxes and minimum and maximum daily values for TER,
GPP and NEE respectively. (d) Monthly anthropogenic fluxes and minimum
and maximum daily values from the NAEI inventory within the UK. (e) Monthly
coastal ocean net fluxes from the Takahashi et al. (2009) ocean CO2 flux product.
Boundary conditions
The footprints from the LPDM only take into consideration the influence on
the observations of sources intercepted within the model domain. Therefore,
an estimate of the mole fraction at the boundary must be made and
incorporated into the simulated mole fractions. To estimate spatial and
temporal gradients in these boundary conditions we use the global Eulerian
Model for OZone And Related chemical Tracers (MOZART, Emmons et al.,
2010). The model was run using GEOS-5 meteorology (Rienecker et al., 2011) and
global biospheric fluxes from the NASA-CASA biosphere model (Potter, 1999), global ocean fluxes from
Takahashi et al. (2009) and global anthropogenic fluxes from the Emission Database for Global
Atmospheric Research (EDGAR, EC-JRC/PBL, 2011). When
particles leave the NAME model domain, we record the time and location of
the exit point. We then use MOZART to find the concentration of CO2 at
these locations to serve as prior boundary conditions. The global MOZART
initial mole fraction field for January 2014 was scaled before commencing
the 2014 MOZART run to match the surface South Pole value to the mean NOAA
January 2014 flask value (Dlugokencky et al.,
2018). This scaling factor was also applied to any pre-January 2014 MOZART
output to prevent any discontinuities in the boundary mole fraction
fields. The mole fraction at each domain edge (N, E, S, W) is then scaled up
or down during the inversion to account for uncertainties in the MOZART
boundary conditions (Lunt et al., 2016). A
sensitivity test where 1 ppm is added or taken away from the mole fractions
at the domain edges indicates that in June a ±1 ppm change translates to
a 1 %–3 % change in the inversion result and in December a ±1 ppm change
translates to a 7 %–11 % change in the inversion result. These changes are
substantially smaller than the posterior uncertainty.
Prior information
In this work, we used model analyses to provide prior information about
biospheric fluxes. Two models (DALEC and JULES) were used to assess how much
influence the choice of biospheric prior has on the outcome of the
inversion. The NAME model was used to simulate the contribution of
anthropogenic and oceanic fluxes to the data, and this contribution was
removed from the observations prior to the inversion. The fluxes used for
this calculation are described below. The spatial and temporal resolution of
the prior information and fixed fluxes are summarised in Table 2 and
emissions from each source over the UK are shown in Fig. 2.
In a synthetic data study in which biospheric CO2 was inferred,
Tolk et al. (2011) found that separately
solving for positive fluxes (autotrophic and heterotrophic respiration
combined, TER) and negative fluxes (GPP) in atmospheric inversions provided
a better fit to the atmospheric mole fraction data than inversions that
scaled NEE only. Equation (2) describes the relationship between these three variables:
NEE=TER-GPP.
This separation has been applied in various studies demonstrating model
set-ups with synthetic data, for example geostatistical approaches
(Göckede et al., 2010), ensemble Kalman filter methods (Zupanski et al., 2007;
Lokupitiya et al., 2008) and Bayesian methods (Schuh
et al., 2009). However, this separation is not routinely used in CO2
inversions, as there are only a limited number of real data studies where it
has been implemented (e.g. Gerbig et al., 2003; Matross et al., 2006; Schuh et
al., 2010; Meesters et al., 2012).
In this inversion, we separately solved for TER and GPP and then combined
them a posteriori to determine NEE. Similarly to the studies cited above, we
find closer agreement with the data than if NEE were scaled directly.
Furthermore, we note that, if only one factor is used to scale both TER and
GPP, it is impossible for the inversion to respond to a prior that has, for
example, too strong a sink but a source of the correct magnitude. To
demonstrate this, we have carried out a synthetic test (Fig. S5) in which we
have investigated the ability of our inversion system to solve for a
true flux, created using the DALEC prior fluxes and NAME simulations, in
an inversion that used the JULES fluxes as the prior. Figure S5a shows
that monthly posterior fluxes for the inversion where GPP and TER are
separated agree with the true flux within estimated uncertainties in 16
out of 24 months. In contrast, whilst the posterior fluxes for the inversion
where NEE is scaled has changed significantly from the prior, it is not in
agreement with the true flux except in July 2013 and August and
September 2014. The posterior diurnal cycles of GPP, TER and NEE, which are
shown as an average for June 2014 in Fig. S5b and c, highlight
the differences in diurnal cycle between the two models. The inversion that
can adjust the two sources separately leads to higher night-time fluxes,
which are closer to the true flux than the prior. On the other hand, the
inversion where NEE is scaled can only stretch or shrink the diurnal cycle
in one direction, increasing both the daytime sink and night-time source, or
decreasing them, together. In this case, they have decreased, which does
bring the net June 2014 flux in Fig. S5a closer to the true June 2014
flux but cannot go far enough to reconcile these monthly fluxes.
Given the results of our synthetic test, separating GPP and TER in the
inversion appears to be an important improvement on scaling NEE directly and
it is what we have implemented here. However, in addition to the main
inversions presented in this paper, where GPP and TER are separated, we have
carried out two further inversions for JULES and DALEC where only NEE is
scaled. The results of these additional inversions are discussed in Sect. 4.1.
DALEC biospheric fluxes
DALEC is a simplified terrestrial C-cycle model (Smallman et al., 2017) that uses
location-specific ensembles of process parameters and initial conditions
retrieved using the CARDAMOM model–data fusion approach (Bloom et al., 2016). CARDAMOM uses a Bayesian approach
within a Metropolis–Hastings MCMC algorithm to compare model states and flux
estimates against observational information to determine the likelihood of
potential parameter sets guiding the parameterisation processes at the pixel
scale. DALEC simulates the ecosystem carbon balance, including uptake of
CO2 via photosynthesis, CO2 loss via respiration, mortality and
decomposition processes, and carbon flows between ecosystem pools
(non-structural carbohydrates, foliage, fine roots, wood, fine litter,
coarse woody debris and soil organic matter). GPP, or photosynthesis, is
estimated using the aggregated canopy model (ACM; Williams et al., 1997) while autotrophic
respiration is estimated as a fixed fraction of GPP. Canopy phenology is
determined by a growing season index (GSI) model as a function of
temperature, day length and vapour pressure deficit (proxy for water stress).
Mortality and decomposition processes follow first-order kinetic equations
(i.e. a daily fractional loss of the C stock in question). The decomposition
parameters are modified based on an exponential temperature sensitivity
parameter. The current version of DALEC used here does not include a
representation of the water cycle; rather, water stress is parameterised
through a sensitivity to high vapour pressure deficit as part of the GSI
phenology model. Comprehensive descriptions of CARDAMOM can be found in
Bloom et al. (2016) and DALEC in Smallman et al. (2017).
DALEC estimates carbon fluxes at a weekly time step and 25 km × 25 km
spatial resolution. The weekly time step information was downscaled to
2-hourly intervals, assuming that each day repeated throughout each week.
Downscaling of GPP fluxes was assumed to be distributed through the daylight
period based on intensity of incoming shortwave radiation. Respiration
fluxes were downscaled across the full diurnal cycle assuming exponential
temperature sensitivity (code for downscaling is available from the authors on request).
Observation-derived information used in the current analysis comes from
satellite-based remotely sensed time series of leaf area index (LAI) (MODIS;
MOD15A2 LAI-8 day version 5, http://lpdaac.usgs.gov/, last access: 2 April 2019), a prior estimate
of above-ground biomass (Thurner et al., 2014) and a prior
estimate of soil organic matter (Hiederer and Köchy, 2012).
Meteorological drivers were taken from the ERA-Interim reanalysis. Ecosystem
disturbance due to forest clearances was imposed using Global Forest Watch
information (Hansen et al., 2013).
CARDAMOM-DALEC differs from typical land surface models in using these data
to generate probabilistic model parameterisations and initial conditions
estimates for each pixel, with no a priori assumptions about plant
functional types, nor steady states.
JULES biospheric fluxes
JULES is a process-driven land surface model that estimates the
energy, water and carbon fluxes at the land–atmosphere boundary (Best
et al., 2011; Clark et al., 2011). We used JULES version 4.6 driven with the
WATCH Forcing Data methodology applied to ERA-Interim reanalysis data (WFDEI)
meteorology (Weedon et al., 2014), which were
interpolated to a 0.25∘× 0.25∘ grid (Schellekens et al., 2017). We
prescribed the land cover for nine surface types and the vegetation phenology
for five plant functional types (PFTs) using MODIS monthly LAI climatology and
fixed MODIS land cover and canopy height data (Berry,
et al., 2009). The soil thermal and hydrology physics are described using
the JULES implementation of the Brooks and Corey formulation (Marthews et al., 2015) with the
soil properties sourced from the Harmonized World Soil Database
(FAO/IIASA/ISRIC/ISS-CAS/JRC, 2009). Soil carbon was calculated
as the equilibrium balance between litter fall and soil respiration for the
period 1990–2000 using the formulation of Mariscal (2015). The
full JULES configuration and science options are available for download from
the Met Office science repository (https://code.metoffice.gov.uk/trac/roses-u/browser/a/x/0/9/1/trunk?rev=75249, last access: 2 April 2019).
Anthropogenic fluxes
Estimates of fluxes due to anthropogenic activity within the UK were
obtained from the National Atmospheric Emissions Inventory (NAEI,
http://naei.beis.gov.uk, last access: 2 April 2019). The NAEI provides a yearly estimate of emissions,
which we have disaggregated into a 2-hourly product, based on temporal
patterns in activity data, varying on diurnal, weekly and seasonal scales.
The inventory emissions were disaggregated according to the UNECE/CORINAIR
Selected Nomenclature for sources of Air Pollution (SNAP) sectors
(UNECE/EMEP, 2001). Figure 2d shows the seasonal and
diurnal cycle for this inventory, summed over the UK, for 2014. Outside the
UK, anthropogenic emissions come from EDGAR v4.2 FT2010 inventory data
for 2010 (EC-JRC/PBL, 2011). This is a fixed 2-D map that is used
throughout the inversion period. Within the UK, the NAEI and EDGAR fluxes
differ by around 15 % (540 Tg yr-1 for EDGAR, 460 Tg yr-1
for NAEI). We do not find that our derived UK fluxes are significantly
affected by perturbations of this magnitude applied to anthropogenic
emissions outside the UK.
Ocean fluxes
Ocean flux estimates are from Takahashi et al. (2009).
They are based on a climatology of surface ocean pCO2 constructed using
measurements taken between 1970 and 2008. The monthly UK coastal ocean flux
(defined as the UK's exclusive economic zone) from this product is plotted
in Fig. 2e. Since the oceanic flux component is small, the comparatively
low temporal and spatial resolution of these flux estimates does not
significantly impact the inversion results.
Like many atmospheric inverse methods, our framework is based on traditional
Bayesian statistics, given by Eq. (3):
ρ(x|y)=ρ(y|x)ρ(x)ρ(y),
where y is a vector containing the observations and
x is a vector of the parameters to be estimated (such as
the flux and boundary condition scaling). The traditional Bayesian approach
requires that decisions about the form of the prior PDF, ρ(x),
and likelihood function, ρ(y|x), are made a priori. These predefined decisions have the
potential to strongly influence the form of the posterior PDF in an
inversion (Ganesan et al., 2014).
Instead, we introduce a second level to the traditional Bayes equation
to account for the fact that initial parameter uncertainty estimates are
themselves uncertain. This is known as a “hierarchical” Bayes framework
where additional parameters, known as hyper-parameters, are used to describe
the uncertainties in the prior and the model.
Alongside the additional hyper-parameters θ, we also
introduce an additional term, k, that describes the size of the inversion
grid, following the trans-dimensional inversion approach described in
Lunt et al. (2016). In this approach, the
number of basis functions to be solved is not fixed a priori and hence
x has an unknown length. The number of unknowns is itself a
parameter to be solved for in the inversion, with the uncertainty in this
term propagating through to the posterior parameter estimates, more fully
accounting for the uncertainties that are only tacitly implied within a
traditional Bayesian approach. The full trans-dimensional hierarchical
Bayesian equation that is solved in our inversion thus becomes
ρ(x,θ,k|y)∝ρ(y|x,θ,k)ρ(x|θ,k)ρ(k)ρ(θ),
where θ is a set of hyper-parameters describing the uncertainty
on x (σx), the model–measurement error (σy)
and the correlation timescale in the model–measurement covariance matrix (τ).
These hyper-parameters are summarised in Table 3 along with the
prior PDFs used to describe them in this inversion set-up.
Probability density functions (PDFs) for parameter and hyper-parameter
scaling factors. Mean and standard deviation in the fourth and fifth columns relate
to log-normal PDFs; lower bound and upper bound relate to uniform PDFs.
ParameterPDFMean/Standardlowerdeviation/boundupper boundPrior uncertainty GPPxGPPLog-normal11σxGPPUniform0.11.5TERxTERLog-normal11σxTERUniform0.11.5Boundary conditionsxBCLog-normal11σxBCUniform0.010.05Model–measurement representation uncertainty Standard deviationσyUniform0.9 ppm45 ppmCorrelation timescaleτUniform1 h120 h
In this study, we have adapted the trans-dimensional method to keep a fixed
set of regional basis functions (described in Sect. 2.4.3) but allow the
inversions to have a variable time rather than space dimension. We perform our
inversion calculations over 1 month at a time, but with the
trans-dimensional case in time we find multiple scaling factors for each fixed
region over the course of the inversion, down to a minimum daily resolution.
Therefore, in this case k in Eq. (4) is more specifically the unknown number
of time periods resolved in the inversion, which is important because
CO2 fluxes vary strongly in time and have high uncertainty in their
temporal variation.
In general, there is no analytical solution to our hierarchical Bayesian
equation, so we approximate the posterior solution using a reversible jump
Metropolis–Hastings MCMC algorithm (Metropolis
et al., 1953; Green, 1995; Tarantola, 2005; Lunt et al., 2016). The
algorithm explores the possible values for each parameter by making a new
proposal for a parameter value at each step of a chain of possible
values. Proposals are accepted or rejected based on a comparison between the
current and proposed state's fit to the data (likelihood ratio),
deviation from the prior PDF (prior ratio) and a term governing the
probability of generating the proposed state versus the reverse proposal
(proposal ratio). More favourable parameter values or model states are
always accepted; however, less favourable parameter values or model states
can be randomly accepted in order to fully explore the full posterior PDF.
The algorithm had a burn-in period of 5×104 iterations and was
then run for an additional 2×105 iterations to appropriately
explore the posterior distribution. At the end of the algorithm a chain of
all accepted parameter values is stored (if a proposal is rejected the chain
will spend longer at the previously accepted value). A histogram of this
chain describes a posterior PDF for each parameter so that statistics such
as the mean, median and standard deviation can be calculated. The trace of
each chain was examined qualitatively to ensure that the algorithm had been
run for a sufficient number of iterations to converge on a result.
Basis functions
Our domain is split into five spatial regions separating west-central Europe
from north-east, south-east, south-west and north-west regions, shown in
Fig. S1. Within the west-central Europe area (the hatched region in Fig. S1),
a map of the fraction of different plant functional types in
each grid cell has been used to further break down the region (Fig. S6).
This is the same PFT map used in the JULES biospheric simulation (see Sect. 2.3.2).
A scaling factor is solved in the inversion, scaling GPP and TER
within the four outer regions and within maps of five or six PFTs in the
subdomain: broadleaf tree; needleleaf tree; C3 grasses;
C4 grasses; shrubland; and, in the case of TER, bare soil. Therefore there are 19 spatial
basis functions in total.
Definition of Jacobian matrix
Footprints from NAME, prior fluxes, boundary conditions and basis functions
are all combined into a matrix of partial derivatives, alternatively
described as a “Jacobian” or “sensitivity” matrix, that describes the
change in mole fraction with respect to a change in each of the input
parameters. This is the “model” in the inversion set-up, denoted
H in the description of the linear forward
model (Eq. 7), where ε is the mismatch between
modelled observations and what has actually been measured in the
atmosphere. H has dimensions m (number of data points) by
n (number of parameters).
y=Hx+ε
To create this linear model, we multiplied the footprints by the prior GPP
and TER fluxes separately and then multiplied these by the fractional map of
basis functions (described in Sect. 2.4.2) and summed over the domain. The
boundary conditions were broken down by four further basis functions for
each edge of the domain as explained in Sect. 2.2.2. The parameters vector,
x, consisted of a set of scaling factors that multiplied the
fluxes or boundary conditions. Multiplying the sensitivity matrix by the
prior estimate of x, a vector of ones, yields the prior modelled
mole fraction time series at a site. Therefore, during our inversion, we are
updating this vector of ones as a scaling factor, to scale up or down
emissions for each PFT and biospheric component to better agree with the
data. Whilst in theory we have posterior information about the gross GPP and
TER biospheric components separately, we combine this into a net ecosystem
exchange (NEE) flux estimate, as we believe this to be more robust
(Tolk et al., 2011). Therefore, throughout
this paper we discuss posterior NEE estimates; however, the results of the
separate sources can be found in the supplement in Figs. S7–S9.
Results
We have applied our CO2 inversion set-up to UK biospheric CO2 flux
estimation using output from two different models of biospheric flux as a
prior constraint in two inversions. We first describe differences between
the output from the two prior models and then present the UK flux estimates
found with this method, along with the spatial distribution of posterior fluxes.
Differences between DALEC and JULES
The CO2 fluxes from DALEC and JULES differ both temporally and
spatially. Figure 2a–c shows UK fluxes of GPP, TER and NEE from the two
models. Most notable differences are seen in TER where JULES has a large
diurnal range, whereas DALEC has a small diurnal range. Averaged to monthly
resolution, the fluxes are relatively similar although DALEC has a higher
TER flux from July to October. Diurnal ranges for GPP are more similar in
magnitude; however, JULES exhibits a stronger sink in spring with maximum
uptake in June. DALEC has maximum uptake in July and exhibits a stronger
sink in autumn. Combining these two fluxes, we can see that the profile of
NEE for both models is quite different. The daily maximum source from JULES
remains relatively constant throughout the year, whereas the daily maximum
source in DALEC follows a similar seasonal cycle to the daily maximum sink
(albeit with a smaller magnitude). Monthly net fluxes are similar between
both models for much of the year although JULES has stronger uptake between
March and June.
In order to understand some of these seasonal differences it is useful to
compare the processes taking place in each model. Section 2.3.1 and 2.3.2
provide detailed descriptions of each model and we give an overview of the
main differences here. DALEC explicitly simulates the soil and litter
stocks, growth and turnover processes. LAI is estimated by DALEC at a weekly
time step; DALEC was calibrated using MODIS LAI estimates at the correct
time and location of the analysis, explained in Sect. 2.3.1. In the JULES
system, soil and litter carbon stocks are fixed values for each grid cell,
calibrated from 1990 to 2000, and a fixed climatology of MODIS LAI and canopy
height is used. Therefore, DALEC has interannual variability in LAI and soil
carbon stocks and can adjust the parameters to find the most likely
estimates in combination with other data, whereas these parameters remain
constant in JULES. This is potentially advantageous for DALEC, although the
use of a climatology in JULES means that noise in the MODIS LAI estimates
will be averaged out. Since LAI and soil and litter carbon stocks are fixed
in JULES, variability in TER and GPP fluxes is governed by meteorology –
primarily temperature but also significant signals from photosynthetically
active radiation and precipitation via the soil moisture. Meteorology drives
the JULES model at a 2-hourly time step as opposed to a weekly time step in
DALEC. Therefore, in the 2-hourly DALEC product used here, the diurnal range
is not explicitly simulated and is the result of a downscaling process from
a weekly resolution. This downscaling is done based on light and temperature
curves as explained in Sect. 2.3.1. In DALEC, the autotrophic respiration is
parameterised as a fixed fraction of the GPP for a given site but varies
between sites, roughly ranging from 0.3 to 0.7. In JULES, the autotrophic
respiration is the sum of plant maintenance and growth respiration terms,
which are calculated separately as process-based functions of the GPP, the
maximum rate of carboxylation and leaf nitrogen content (Clark et al., 2011).
Typically, the autotrophic respiration in JULES is roughly 0.1–0.25 of the
GPP. Therefore, there are some large differences between the model
structures and parameterisations, particularly in how the respiration fluxes
are simulated. This could be leading to too small a diurnal range in DALEC
TER and too large a diurnal range in JULES TER.
Figures 3 and 4 show spatial maps of GPP, TER and NEE from both models
averaged over winter (December, January, February) and summer (June, July,
August) months. The pattern of TER is similar for both models; however, JULES
always has a stronger source over Northern Ireland and DALEC has a stronger
source in east England. In winter there are only small spatial variations in
DALEC GPP fluxes, whereas JULES has its largest uptake in south-west England
and Wales. In summer, the models are roughly in agreement in the size of the
sink in Wales and the majority of England; however, JULES has a stronger sink
in Scotland and Northern Ireland and DALEC has a stronger sink in central
and south-east England. The differences between the models in GPP and TER
lead to fairly different winter NEE flux maps. DALEC is a net source
everywhere in winter, with areas of strongest net source in southern
Scotland as well as east and central England. JULES is a small net winter sink in
Northern Ireland, Wales, and south and central England. Summer NEE fluxes
are similar between the models, although JULES has a stronger net sink in
Scotland and Northern Ireland.
Average prior flux maps for winter 2013 (December 2013, January–February 2014).
(a) TER from DALEC; (b) TER from JULES; (c) the
difference between DALEC and JULES TER; (d) GPP from DALEC;
(e) GPP from JULES; (f) the difference between DALEC and
JULES GPP; (g) NEE from DALEC; (h) NEE from JULES;
(i) the difference between DALEC and JULES NEE.
Prior average flux maps for summer 2014 (June–August 2014).
(a) TER from DALEC; (b) TER from JULES; (c) the
difference between DALEC and JULES TER; (d) GPP from DALEC;
(e) GPP from JULES; (f) the difference between DALEC and
JULES GPP; (g) NEE from DALEC; (h) NEE from JULES;
(i) the difference between DALEC and JULES NEE.
Posterior net UK biospheric CO2 flux 2013–2014
We have derived estimates for annual NEE from the UK using CO2 flux
output from the two different models of biospheric flux as prior information
(Fig. 5 – orange and blue bars for DALEC and JULES respectively):
13±8790 Tg CO2 yr-1 (DALEC prior) and
76±9091 Tg CO2 yr-1 (JULES prior) in 2013 and
2±6870 Tg CO2 yr-1 (DALEC prior)
and 51±7880 Tg CO2 yr-1 (JULES prior)
in 2014. These annual net flux estimates from both models agree within the
estimated uncertainties, and mean values are higher than their respective
priors in both cases. The uncertainties straddle the zero net flux line,
implying that the UK is roughly in balance between sources and sinks of
biospheric CO2. However, according to the inversion using JULES, a net
biospheric source is less likely than in the inversion using DALEC. When
added to the anthropogenic and ocean fluxes that remained fixed during the
inversion, we produce the following estimates for annual total net
CO2 release from the UK (Fig. 5 – yellow and green bars for DALEC and JULES
respectively): 448±8790 Tg CO2 yr-1 (DALEC
prior) and 386±9091 Tg CO2 yr-1 (JULES prior)
in 2013 and 418±6870 Tg CO2 yr-1 (DALEC prior)
and 369±7880 Tg CO2 yr-1 (JULES prior) in 2014.
While we are assuming that anthropogenic and ocean fluxes are perfectly
known, the uncertainties on these fluxes are comparatively small (Peylin et al., 2011). When the
anthropogenic source was varied by ±10 %, a conservatively large
estimate of these uncertainties, we found posterior biospheric flux estimates
using the DALEC prior that still suggest a balanced biosphere and posterior
flux estimates using the JULES prior that suggest a small net sink at the
lowest end of the possibilities explored here (see Fig. S10). All mean
annual posterior estimates, regardless of the anthropogenic source used,
suggest the prior net biospheric flux is underestimated; i.e. posterior
biospheric uptake of CO2 is smaller than predicted by the models.
However, this is less statistically significant with the 2013 inversion
using the DALEC prior.
The monthly posterior UK estimates using both models (Fig. 5) mostly agree
well with each other within the uncertainties; however, they are both notably
different from the prior estimates, especially in 2014. The posterior total
UK flux estimate, achieved by adding the posterior NEE fluxes to
anthropogenic and coastal ocean fluxes, shows that, according to the DALEC
inversion, the UK may not be a net sink of CO2 at any time of year
in 2013 and 2014. However, the JULES inversion suggests the UK is a net sink of
CO2 in June of both years.
Posterior monthly net UK CO2 flux (positive is emission to
atmosphere). Orange and blue monthly fluxes are posterior net biospheric (NEE)
fluxes for DALEC and JULES respectively. Prior biosphere fluxes from DALEC and
JULES are shown in dashed orange and blue lines respectively. The fixed
anthropogenic and ocean fluxes are denoted by the dark grey dashed line. Yellow
and green monthly fluxes are the sum of the posterior NEE fluxes and the fixed
anthropogenic and ocean fluxes. Shading represents 5th–95th percentile. The
bar charts represent annual net UK CO2 flux for 2013 (left) and
2014 (right). Hashed bars denote prior annual fluxes; solid bars denote posterior
annual fluxes. The bar colours correspond to the line colours: left-hand bars
for each model are NEE fluxes; right-hand bars for each model are total fluxes
(NEE + fixed sources). Uncertainty bars represent 5th–95th percentile.
DA – DALEC. JU – JULES.
Posterior seasonal cycle amplitudes are generally smaller than the prior
amplitudes, except in the DALEC inversion in 2014. Table 4 gives the
posterior maximum and minimum values of NEE, leading to seasonal cycle
amplitudes of 469 and 578 Tg CO2 yr-1 for 2013
and 633 and 737 Tg CO2 yr-1 for 2014,
for the DALEC and JULES inversions respectively. These values are 90 % and
76 % of the prior amplitudes in 2013 and 123 % and 85 % of the prior
amplitudes in 2014.
Posterior UK estimates for the maximum net biospheric source and sink
(values also shown in Fig. 5). The month in brackets indicates the month in
which the maximum source or sink occurred.
YearMaximum sink (Tg CO2 yr-1)Maximum source (Tg CO2 yr-1)DALEC2013-298±136140 (June)171±7694 (January)2014-360±8887 (June)273±6365 (November)JULES2013-456±9190 (June)122±7883 (December)2014-542±10097 (June)195±7065 (October)
The largest differences between the prior and posterior are seen in spring
and summer for both models. Posterior UK NEE estimates from the DALEC
inversion are in agreement with the prior for 11 months: during the first
half of 2013, in the majority of winter months (December, January, February)
and in June 2014. When the DALEC inversion posterior UK NEE estimates are
not in agreement with the prior, they are usually larger, with a maximum
difference in 2013 of 235±9192 Tg CO2 yr-1 in August
and a maximum difference in 2014 of 551±8480 Tg CO2 yr-1
in July, although in spring (March, April, May) 2014 they tend
to be smaller than the prior, with a maximum difference of
-194±6064 Tg CO2 yr-1 in April. Posterior UK NEE from the
JULES inversion agrees with the prior for 9 months during the 2-year
period, the majority of which is between November and February. Otherwise,
the posterior estimate from the JULES inversion is larger than the prior,
with a maximum difference in 2013 of 318±7170 Tg CO2 yr-1
in April and a maximum difference in 2014 of 407±7276 Tg CO2 yr-1 in July.
Looking at the spring and summer differences more closely, we find that the
JULES model has a systematically lower net spring flux than the posterior,
and the DALEC model is either in agreement with or higher than the posterior
estimate of the net spring flux. Generally, the models underestimate the net
summer flux compared to the posterior flux (to the greatest extent in 2014),
although the summer estimate from the JULES inversion in 2013 is not
statistically different from the prior. The average spring difference
between the posterior and the prior for the DALEC inversion is
-2±8889 Tg CO2 yr-1 in 2013 and
-133±6367 Tg CO2 yr-1 in 2014, whereas for the JULES inversion it is
219±87 Tg CO2 yr-1 in 2013 and 164±6567 Tg CO2 yr-1
in 2014. The average summer difference for the DALEC inversion is
135±108111 Tg CO2 yr-1 in 2013 and
263±8382 TgCO2 yr-1 in 2014, whereas for the JULES inversion
it is 94±107104 Tg CO2 yr-1 in 2013 and
312±85 Tg CO2 yr-1 in 2014. The prior sink in June as estimated by
the JULES model is nearly twice that of DALEC and posterior estimates tend
to agree with the DALEC prior in this month.
Figure S9c shows the daily minimum and maximum in the posterior net
biospheric estimates for 2014. It is worth bearing in mind at this point
that while the temporal resolution of the inversion is flexible, it can go
down to a minimum resolution of 1 day (as explained in Sect. 2.4.1).
Therefore, the diurnal profile of TER and GPP for each model is imposed;
however, it can be scaled up or down from day to day. Figure S11 shows that the
inversion typically scaled the fluxes within 4 or 5 temporal regions per
month, although for some parameters in some months scaling factors were
found up to roughly a daily resolution. For both inversions, the posterior
NEE flux shown in Fig. S9c has a similar profile. Compared to Fig. 2c the inversion tends to
a seasonal cycle in daily maximum uptake that resembles that of the JULES
model prior, with a turning point in maximum uptake occurring abruptly
between June and July, a steep gradient in spring and a shallow gradient in
autumn. On the other hand, the seasonal cycle in daily maximum source
resembles that of the DALEC model prior, which has a stronger seasonal
variation compared to that of the JULES model prior, albeit with a larger
amplitude. This would suggest that the underestimation in net spring flux
seen in the JULES prior is generally due to the model underestimating the
spring source rather than overestimating the spring sink. It also suggests
that the overestimation in net summer flux in the DALEC prior is possibly a
combination of the model overestimating the summer sink and underestimating
the summer source. The overestimation in the net summer flux in JULES is
more likely to be due to an underestimation of the summer source. However,
as diurnal fluxes vary on a scale nearly an order of magnitude larger than
that of the monthly fluxes, it is clear that any relatively small changes in
the maximum source or sink will have a relatively large effect on the daily
net flux. Therefore, the monthly net flux is the more robust result here and
we are not able to confidently draw conclusions from the sub-monthly results.
Posterior spatial distribution of biospheric fluxes
Figure 6 shows mean posterior net biospheric fluxes (NEE) for winter 2013
and summer 2014 from both the DALEC and JULES inversions. In winter 2013,
posterior NEE fluxes from the DALEC inversion are fairly heterogeneous and
are largest over south-west Scotland and east and central England. This
posterior spatial distribution is roughly similar to the prior. From the
inversion using JULES prior fluxes, the posterior net biospheric flux is
much smoother than it is for the inversion using DALEC. It is largest in
north-west England and almost zero in east England. The whole of
south and central England, Wales, and Northern Ireland have increased posterior
winter fluxes compared to the prior, turning these areas from a net sink in
the prior to a net source in the posterior.
Posterior net biospheric (NEE) flux maps averaged over winter 2013
(December 2013, January–February 2014) and summer 2014 (June–August 2014).
(a) Winter NEE flux from DALEC inversion. (b) Winter NEE flux
from JULES inversion. (c) Difference between winter NEE flux from
DALEC (DA) and JULES (JU) inversions. (d) Summer NEE flux from DALEC
inversion. (e) Summer NEE flux from JULES inversion. (f) Difference
between summer NEE flux from DALEC (DA) and JULES (JU) inversions.
In summer 2014, NEE fluxes from the two inversions display many
similarities, with areas of net source in east, central (extending further
south in the JULES inversion), and north-west England and areas of net sink
elsewhere. However, the net sink in the JULES inversion is larger than the
DALEC inversion in Scotland, south Wales, Northern Ireland and south-west
England. This differs from the prior flux maps, which have only very small
areas of small net uptake in central England in DALEC and in east England in
JULES. Both the DALEC and JULES posterior fluxes generally display reduced
uptake compared to the prior, except in north Wales.
Model–data comparison
Agreement between the data and the posterior simulated mole fractions at the
measurement sites used to constrain the inversion is greatly improved
compared to prior simulated mole fractions, with R2 values increasing
by a minimum of 0.24 and up to 0.5 (to give values ranging between 0.53
and 0.71) and root mean square error (RMSE) decreasing by at least 1.35 ppm and
up to 2.6 ppm (to give values ranging between 1.26 and 2.71 ppm).
Table 5 shows all statistics for the prior and posterior mole fractions compared
to the observations of atmospheric CO2 concentrations. Overall, the
fits are relatively similar between the DALEC and JULES inversions, implying
that the two inversions perform similarly well by these metrics. In terms
of R2, the best fit to the data is observed at Heathfield in the DALEC
inversion and Angus in the JULES inversion. In terms of RMSE, the best fit
to the data is observed at Angus in the DALEC inversion and Mace Head in the
JULES inversion. The smallest posterior mean bias is observed at Angus in
the DALEC inversion and Ridge Hill in the JULES inversion. Therefore, there
are some small spatial differences in how well each of the inversions is
able to fit the data but no clear indication of which areas of posterior
flux might be subject to the largest improvement in either inversion.
Figures S12 and S13 show the residual mole fractions in 2014 and indicate
that residuals are somewhat larger during the summer than the winter.
Prior and posterior fit to data statistics for the inversion period 2013–2014.
R2 and RMSE are calculated monthly and averaged over this period. Values
in brackets are the posterior fit statistics for the corresponding net flux
inversions. * Weybourne data (from February to December 2013) were used for
validation of the results only and were not included in the inversions.
To test our posterior results against data that have not been included in the
inversion, the posterior fluxes have been used to simulate mole fractions at
Weybourne Atmospheric Observatory (see Fig. 1 for location in relation to
the other sites and Table 1 for site information). The statistics of fit to
the data are given in italics in Table 5 and show an improvement in R2
of 0.18 with the DALEC inversion and 0.13 with the JULES inversion, an
improvement in RMSE of 1.09 ppm with the DALEC inversion and 0.75 ppm with
the JULES inversion, and an improvement in the mean bias of 0.64 ppm in the
DALEC inversion and 0.56 in the JULES inversion. These results show that the
a posteriori fluxes improve the fit to the data at a measurement station not
included in the inversion. The results are very similar between the two
inversions at this site but suggest that the DALEC inversion may perform
slightly better, at least in this region of the UK. Figure S14 shows the
residual mole fractions at Weybourne for each of the inversions carried out in this work.
DiscussionInversion performance
Solving for both TER and GPP separately allows the JULES prior and
DALEC prior inversions to converge to a similar posterior solution. Using
two very different prior NEE flux estimates, we produce two similar
posterior NEE flux estimates that have a similar seasonal amplitude and
agree on the majority of monthly and all annual fluxes within the estimated
uncertainties. This indicates that our posterior estimates are driven by the
data rather than determined by the prior. However, when we carry out the
same inversion but scale NEE (Fig. S15) we find the two posterior flux
estimates do not converge on a common result. The posterior seasonal cycles
remain relatively unchanged compared to the prior and annual net biospheric
flux estimates tend to be similar to, or larger than, the prior. These
annual net biospheric flux estimates are therefore 3–39 times smaller
than the inversion that separates GPP and TER, meaning the posterior
estimates from the two types of inversions do not overlap, even within
estimated uncertainties. Evaluating the statistics of how well the NEE
inversions fit the data (Table 5), we find they do not perform as well as
the separate GPP and TER inversion, both at the sites included in the
inversion and at the validation site, WAO. However, this is to be expected
to some degree, because separating the two sources gives the inversion more
degrees of freedom to fit the data.
As recommended by Tolk et al. (2011), we
are only hoping to achieve an improved estimate for the net fluxes here
rather than the gross GPP and TER fluxes themselves. The posterior gross
fluxes are included in the supplement (Figs. S7–S9), but due to the
correlation between the spatial and temporal distribution of GPP and TER
they have not been presented in the main text. This can be seen in summer
and winter flux maps (Figs. S7 and S8) and in the posterior annual flux
estimates in Fig. S9d, in particular where JULES TER and GPP show
similarly large differences from the prior. This could also be a result of
the imposed diurnal cycle, as it would appear the posterior TER flux in the
JULES inversion is tending to a higher daily minimum, matching that of the
DALEC prior, and may ultimately be trying to move towards a smaller diurnal
variation in TER. However, because the whole diurnal cycle must be scaled,
the daily maximum TER must also increase and may mean the GPP must increase,
causing increased uptake, to compensate for the increased source from TER.
Allowing flexibility on sub-daily timescales may lead to similar estimates
of GPP and TER between the two inversions with different priors. However,
questions remain over whether there is enough temporal information for this
to be the case.
The fact that common monthly and annual posterior net biospheric flux
estimates are reached when the prior biospheric fluxes are spatially and
temporally different would suggest that the choice of prior is not
necessarily a major factor in guiding the inversion result for our network,
when GPP and TER are scaled separately. In this respect, it is also
particularly encouraging that the seasonal cycles in the posterior diurnal
range are similar for both inversions (Fig. S9c).
Differences between prior and posterior NEE estimates
The posterior seasonal cycle in both inversions differs significantly from
the prior. This implies that the biospheric models used to obtain prior GPP
and TER fluxes are either over- or underestimating the strength of some
processes, or they are omitting some processes altogether. The largest
differences between the posterior solution and the prior model output are
seen in spring and summer. In Sect. 3.2 we have shown that spring
differences arise from an overestimation of the net spring uptake of
CO2 in the JULES model and an underestimation
of the net spring uptake in the DALEC model in 2014. However, in summer (particularly in 2014), the posterior
net UK fluxes are higher than both priors in July and August.
One process that occurs during the months July and August is crop harvest.
Harvest is not directly resolved in either of the models of the biosphere
used in this work, thereby providing a possible explanation for the
differences between the posterior and prior in these months. Harvest
typically occurs between July and September and arable agricultural land
covered 26 % of the UK in 2013 and 2014 (DEFRA, 2014, 2015), so
there is potential for unaccounted activity in this area to cause large
changes to net CO2 fluxes. The areas of net source in summer (shown in
Fig. 6) do also coincide with areas of large-scale agriculture (e.g. east
and central England). Crop harvest potentially changes the biosphere in the
following ways: firstly, crops mature en masse, leading to an abrupt loss of
productivity. Secondly, during harvest there is an abrupt removal of biomass
and input of harvest residues on the field. This increases litter input that
is readily available for decomposition, increasing heterotrophic
respiration. Thirdly, when the field is ploughed the soil is disturbed,
which can increase heterotrophic respiration. Finally, when the crop is no
longer covering the soil surface this layer can become drier and the energy
balance is altered. In Smallman et al. (2014), the reduction
in atmospheric CO2 concentration due to crop uptake is reported
for 2006 to 2008 and an abrupt increase in atmospheric CO2 can be seen
between June (peak source) and August, where CO2 uptake from crops is
halted as a result of harvest. Harvest may explain the abrupt shift from net
sink to net zero or net source observed between July and August in DALEC in 2013
and June and July in both models in 2014. The earlier time in 2014 does
coincide with a year of early harvest (DEFRA, 2015) although this
may well be fortuitous. Later in the summer, there may be some plant
regrowth in ploughed fields leading to increased GPP. This would be
consistent with the shallower gradient observed in net biospheric fluxes
between September and October 2013 in the DALEC posterior estimate, between
August and September 2014 in the JULES posterior estimate, and the decrease
in net flux observed between July and September 2014 in the DALEC posterior estimate.
If agricultural activity is the source of the July, August and September
difference between prior and posterior UK NEE estimates, then it could
amount to emissions of 4 %–10 % of currently reported annual
anthropogenic emissions in 2013 and 17 %–19 % in 2014. However, other
explanations for this difference could be large uncertainties in the
seasonal disaggregation of anthropogenic fluxes, uncertainties in the
transport model, or a combination of over- and underestimation of other biospheric processes.
Implications for UK CO2 emissions estimates
The results of UK biospheric CO2 fluxes using our set-up suggest the UK
biosphere is roughly in balance, whereas prior estimates from models of the
biosphere estimate a net sink. Even when we assume an uncertainty on our
anthropogenic fluxes of 10 % (a conservative estimate), inversions using
both models still give mean posterior estimates that are larger than their
respective priors (see Fig. S10). Therefore, when using models of the
biosphere to contribute to inventory estimates of CO2 emissions, care
must be taken to attribute sufficient uncertainties to model estimates,
otherwise the amount of CO2 taken up by the biosphere on an annual
basis may be overestimated. Methods such as the one described in this paper
could provide an important constraint on the UK's biospheric CO2 fluxes
as carbon sequestration processes, such as reforestation, and other land use
change activities are increasingly used as policy solutions to contribute to carbon targets.
Conclusion
We have developed a framework for estimating net biospheric CO2 fluxes
in the UK that takes advantage of recent innovation in atmospheric inverse
modelling and a relatively dense regional network of measurement sites. Two
inversions are carried out using prior flux estimates from two different
models of the biosphere, DALEC and JULES. Fluxes of GPP and TER are scaled
separately in the inversions. Despite significant differences in prior
biospheric fluxes, we find consistent monthly and annual posterior flux
estimates, suggesting that in this study the choice of model to provide
biospheric CO2 flux priors in the inversion is not a major factor in
guiding the inversion result with our framework and network. However, given
the hypothesised importance of missing process representation from both
models, e.g. agriculture, an improved model may result in an improved
analysis, reducing uncertainties and biases highlighted in this study.
Similarly to Tolk et al. (2011), we find
that the NEE is more robustly derived if GPP and TER are solved separately
and then combined a posteriori. Our results suggest that inversions that
scale only NEE could be underestimating net CO2 fluxes, as we find
posterior estimates 3–39 times smaller than those obtained using an
inversion where GPP and TER are separated.
We find that the UK biosphere is roughly in balance, with annual net fluxes
(averaged over the study period) of 8±79 and
64±85 Tg CO2 yr-1 according to the DALEC and JULES inversions
respectively. These mean annual fluxes are systematically higher than their
respective priors, implying that net biospheric fluxes are underestimated in
the models of the biosphere used in this study. The posterior seasonal
cycles from both inversions differ significantly from the prior seasonal
cycles and generally have a reduced amplitude of 90 % and 76 % of the
prior amplitude in 2013 according to the DALEC and JULES inversions
respectively as well as 85 % of the prior amplitude in 2014 according to the
JULES inversion; however, the posterior seasonal cycle amplitude from the
DALEC inversion in 2014 was increased by 122 %. Our results suggest an
overestimated net spring flux in the JULES model and an overestimation of
the net summer flux in both models of the biosphere. We propose that the
difference seen between the prior and posterior flux estimates in summer and
early autumn could be a result of the disturbance caused by crop harvest,
leading to an abrupt reduction in plant CO2 uptake and increase in
respiration sources, as it is not taken into account in either model.
However, this hypothesis is just one of a combination of uncertain factors
that could lead to the differences seen, so further work would be needed to
investigate the importance of crop harvest in UK CO2 emissions.
The method developed and described here represents a first step towards
looking at the UK biospheric CO2 budget with a hierarchical Bayesian
trans-dimensional MCMC inverse modelling framework. Further work is required
to robustly constrain biospheric CO2 fluxes through comparison with
other model set-ups.
Code availability
Hierarchical Bayesian trans-dimensional MCMC code is available
on request from Matthew Rigby (matt.rigby@bristol.ac.uk).
The supplement related to this article is available online at: https://doi.org/10.5194/acp-19-4345-2019-supplement.
Author contributions
EDW carried out the research. EDW, MR and AJM designed the
research. MFL and ALG developed the model code. SO, KS, ARS, MR, GLF and
ACM provided data. TLS, ECP, PL and MW provided model output. EDW, MR, MFL,
TLS, ECP, ACM, ALG, SO, KS, ARS, PL and PIP wrote the text.
Competing interests
The authors declare that they have no conflict of interest.
Special issue statement
This article is part of the special issue “The
10th International Carbon Dioxide Conference (ICDC10) and the 19th WMO/IAEA
Meeting on Carbon Dioxide, other Greenhouse Gases and Related Measurement
Techniques (GGMT-2017) (AMT/ACP/BG/CP/ESD inter-journal SI)”. It is a result
of the 10th International Carbon Dioxide Conference, Interlaken, Switzerland,
21–25 August 2017.
Acknowledgements
Emily D. White acknowledges the support of a NERC GW4+ Doctoral Training
Partnership studentship from the Natural Environment Research Council (NE/L002434/1)
and NERC grant NE/M014851/1. Observations from BSD and HFD were supported under
NERC grant NE/K002236/1. DECC network data are maintained by grant TRN1028/06/2015
from the UK Department of Business, Energy and Industrial Strategy. We are
grateful to Gerard Spain, Duncan Brown, Stephen Humphrey and Andy MacDonald,
Carole Helfter and Neil Mullinger for their work maintaining the measurements
at the Mace Head, Tacolneston and Bilsdale measurement sites. Anita L. Ganesan was
funded under a UK Natural Environment Research Council (NERC) Independent Research
Fellowship (NE/L010992/1). T. Luke Smallman and Mathew Williams were supported
by NERC GHG programme GREENHOUSE, grant NE/K002619/1, and this study was funded
as part of NERC's support of the National Centre for Earth Observation. Paul
Palmer gratefully acknowledges funding from NERC under grant reference NE/K002449/1
and gratefully acknowledges his Royal Society Wolfson Research Merit Award.
Review statement
This paper was edited by Andreas Hofzumahaus and reviewed by three anonymous referees.
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