We present a method to derive atmospheric-observation-based estimates of carbon dioxide (

There are significant uncertainties in the magnitude and spatiotemporal
distribution of global carbon dioxide (

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

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

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

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.

Here we outline a framework for evaluating the net biospheric

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

The main components of a regional atmospheric inverse modelling framework
are the atmospheric

This study focuses on the years 2013 and 2014. During this period,
atmospheric

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

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

Measurement site information. The location of sites is also shown in
Fig. 1.

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

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

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

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.

Prior UK fluxes in 2014.

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

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

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 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

DALEC estimates carbon fluxes at a weekly time step and 25 km

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,

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

Estimates of fluxes due to anthropogenic activity within the UK were
obtained from the National Atmospheric Emissions Inventory (NAEI,

Ocean flux estimates are from Takahashi et al. (2009).
They are based on a climatology of surface ocean

Like many atmospheric inverse methods, our framework is based on traditional
Bayesian statistics, given by Eq. (3):

Alongside the additional hyper-parameters

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.

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

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

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;

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

We have applied our

The

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).

Prior average flux maps for summer 2014 (June–August 2014).

We have derived estimates for annual NEE from the UK using

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

Posterior monthly net UK

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

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.

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

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

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.

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).

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.

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

Prior and posterior fit to data statistics for the inversion period 2013–2014.

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

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).

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

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

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.

The results of UK biospheric

We have developed a framework for estimating net biospheric

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

We find that the UK biosphere is roughly in balance, with annual net fluxes
(averaged over the study period) of

The method developed and described here represents a first step towards
looking at the UK biospheric

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:

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.

The authors declare that they have no conflict of interest.

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.

Emily D. White acknowledges the support of a NERC GW4

This paper was edited by Andreas Hofzumahaus and reviewed by three anonymous referees.