Three-hourly net ecosystem exchange (NEE) is estimated at
spatial scales of 0.25

The atmospheric mole fractions of greenhouse gases (GHGs) like CO

The continuous expansion of GHG in situ measurement capabilities enabled
atmospheric tracer inversion systems to better infer the sources and sinks
of CO

The observational site network across Europe has been markedly homogenised
since the Integrated Carbon Observation System (ICOS) was established in
2015, allowing for a better estimation of the regional budgets of CO

The regional inversion framework encounters various sources of uncertainties, such as (1) the uncertainty of a priori knowledge (necessary in the Bayesian framework inversions to regularise the solution of the ill-posed inverse problem) and (2) the representation error resulting from the inaccuracies in simulating the atmospheric transport. The structure of prior uncertainty (e.g. uncertainties in the prior biosphere flux estimates) is of particular importance as it determines the way in which the flux corrections calculated from the data information should be spread in space and time (Chevallier et al., 2012; Kountouris et al., 2015) Defining proper error covariance matrices in both flux and measurement space is therefore essential to obtain an optimal estimate of the true fluxes. Non-optimised flux components used as prescribed fluxes in the inverse frameworks should be provided with the highest achievable confidence, as any uncertainty in these components will directly modify the estimated biosphere–atmosphere fluxes.

Here, we present NEE estimates from a pre-operational regional inversion system set-up over Europe covering 14 years since 2006. An ensemble is created by varying (a) a priori biogenic fluxes, (b) a priori ocean fluxes, and (c) the number of available atmospheric observation sites in order to estimate their impact on a posteriori optimised biogenic fluxes. We furthermore discuss the interannual variability (IAV) over this period, with a special focus on the changes in NEE in 2018 and 2019, specifically in light of the water availability and temperature variations that occurred in the wake of anomalously warm and dry conditions over the continent. These changes are analysed using the seasonal and annual NEE fluxes aggregated over different subregions in Europe.

The inversion set-up, observational dataset, and prior fluxes used are described in Sect. 2, including details on ensemble member configuration. A statistical analysis of uncertainty and spreads over the ensembles of inversions is presented and discussed in Sect. 3.1. Section 3.2 presents the NEE estimated in the pre-operational inverse system based on several analysed cases. Finally, discussions and conclusions are summarised in Sect. 4.

The CarboScope Regional inversion system (CSR) is used to infer NEE from
observed atmospheric CO

The inversion searches for the optimal flux vector at 3-hourly temporal
resolution through minimising the cost function

Atmospheric transport is simulated by the Stochastic Time-Inverted
Lagrangian Transport (STILT) model (Lin et al.,
2003), which is utilised to calculate surface influences at the stations
(i.e. “footprints”) at a spatial resolution of 0.25

Since CO

The core of our observational dataset consists of data from 44 sites
collected in the ICOS Carbon Portal under the 2018 drought initiative
(

Station network distribution over Europe. Different graphical symbols denote the type of station classifications; coloured regions indicate Central Europe (green), Northern Europe (blue), Western Europe (purple), Southern Europe (orange), Eastern Europe (yellow), and South-eastern Europe (light red).

The representation error is assumed to be specific for different station
types, which are categorised as five classes according to the ability for
regional transport models to reasonably simulate the atmospheric
concentration, given the variable complexity of representing the local
circulation, over each station (Rödenbeck, 2005). Weekly
representation errors are presented in Table 1, defining the measurement
error covariance matrix in the cost function. The observations are mostly
provided at an hourly frequency, especially in recent years. We also include
measurements from flask sampling (mostly weekly) when available from the
corresponding sites. To better represent the well-mixed boundary layer in
the STILT model, we limit our analyses to measurements of 6 h daytime
for all stations, i.e. 11:00 to 16:00 LT, except for mountain
sites. For the latter, night-time hours (23:00 to 04:00 LT) are
chosen, as mountain sites experience free-tropospheric conditions, depending
on the mountain height. Particularly before establishing ICOS in 2015, the
variability of station data coverage across the period of interest was
rather high, underlining the sparsity of available data (Fig. 2). Since
then, the site network over Europe has been markedly expanded as new
stations have been installed. It should be noted that the variability in data
coverage is expected to result in an inconsistency of annual flux
variations. Therefore, we combined stations into three subsets: (a) the full set
of stations, referred to as “all sites”, (b) a subset of 15 stations that
have consistent coverage from 2006 to 2019, to which we will refer as “core
sites”, and (c) a third subset of 16 stations that do not have gaps longer
than 1 month during 2015–2019, subsequently referred to as “recent sites”.
The far-field contributions provided to the regional domain were calculated
in the two-step inversion approach (Rödenbeck et al.,
2009) using a global observational record from 75 sites
(

Representation error of station locations.

Dataset density measured from 2006 until 2019 over Europe. Yellow
to red colour scale denotes monthly-averaged dry mole fractions of CO

Terrestrial ecosystem flux models are utilised to provide prior knowledge of
biogenic fluxes (NEE, defined as net ecosystem exchange). To
appropriately represent the diurnal cycle in our modelling framework, NEE is
obtained from the biosphere models at an hourly temporal resolution. Three
biosphere models were used as priors in the inversion runs. The first is the
Vegetation Photosynthesis and Respiration Model, VPRM
(Mahadevan et al., 2008). VPRM is a diagnostic model driven by
shortwave radiation and temperature at 2 m from the ECMWF's high-resolution operational forecast product (IFS HRES). To calculate NEE and
respiration fluxes, it uses MODIS (Moderate Resolution Imaging
Spectroradiometer) indices derived from surface reflectance, namely the Enhanced Vegetation Index (EVI) and land surface water index (LSWI) together with
type-specific vegetation parameters optimised against the eddy covariance
(EC) data. Parameter values for VPRM previously used by
Kountouris et al. (2018b) were updated using the most
recent EC data and are available at

Following Kountouris et al. (2018b), we assume that the spatial correlation of the prior uncertainty follows a hyperbolic decay function, similar to the inversion case nBVH (no Bias VPRM as prior with a hyperbolic decaying correlation of the spatial uncertainty structure) described in that study. In this case, the annually aggregated uncertainty matches the assumed prior uncertainty without the need for an additional bias term in the biosphere flux model. The spatial correlation length scales are 66.4 km in the zonal direction and 33.2 km in the meridional direction. One notable difference in the current work is the improved implementation of the directional dependence, with a twofold increase in decay distance in the meridional direction. Temporarily, prior uncertainties are assumed to be correlated over 30 d, as found in Kountouris et al. (2015).

Ocean CO

We conduct three ensembles of inversion runs listed in Table 2 utilising
different set-ups of prior products (biosphere and ocean ensembles) as well
as selected sets of observational data (station set ensemble). The inversion
runs are labelled with unique codes for reference. B0 is defined as the base
case of our analysis. It is configured using default settings of the
inversion runs, with biogenic fluxes from VPRM and climatological ocean fluxes,
and using all available atmospheric data as input. In the biosphere ensemble
(consisting of B0, B1, and B2), FLUXCOM and SiBCASA replace the VPRM model in
both B1 and B2, respectively, allowing for a distinction between the effect of
using different prior flux models on posterior NEE. This ensemble of
inversions was performed for the period 2006–2018, as the availability of
SiBCASA fluxes was limited to this period of time. In the ocean ensemble, we
replace the climatological ocean fluxes used in B0 with the

Set-ups of the inversions.

The annual NEE estimates among the biosphere ensemble (Fig. 3) show good
agreement across the three biosphere models but also across S1 and O1
inversions, yielding similar budgets of CO

NEE fluxes estimated using B0, B1, B2, S1, and O1 inversions for
the 2006–2018 period over the full domain of Europe

It is noteworthy that there is a striking similarity in interannual variations between
the a posteriori fluxes and both VPRM and SiBCASA prior fluxes for the years
2009–2013. This agreement does not necessarily mean that posterior
interannual variability (IAV) is driven by biosphere models. This can be
deduced from B1 (FLUXCOM) estimates from which the IAV differs in both the
prior and posterior fluxes and where FLUXCOM NEE has weak interannual
variations. Instead, VPRM and SiBCASA are likely to import this signal from
the meteorological data used to force these models. However, the VPRM model
overestimates the mean CO

The statistical uncertainty and spreads over the ensembles are evaluated and affect our data (Fig. 3). It is noticed that the spreads over the posterior fluxes and prior fluxes are comparable with the corresponding uncertainties over the full domain (All Europe), Central Europe, and Northern Europe. Note that calculating the spread over a small size of samples might not reflect the true standard deviation. There is a clear reduction in uncertainty and spread in posterior fluxes either over the full domain (All Europe) or in subregions like Central and Northern Europe. Unlike prior uncertainty, posterior uncertainty slightly differs from year to year following the number of atmospheric sites available (Fig. 2). This gets even clearer when looking at the marked reduction in the posterior uncertainty in Central Europe as well as in regions with high station density, resulting in a stronger observational constraint. In contrast to Central Europe, a smaller reduction in posterior spread is found in Northern Europe as well as in other regions where there are few or no stations (e.g. Eastern Europe, Fig. S1 in the Supplement). In this case, NEE estimates are not well constrained by atmospheric data. Instead, a posteriori flux is driven by the inversion using biosphere models and their uncertainty, particularly for the distant areas that cannot be constrained by observations through the spatial correlation. Table 3 denotes the reduction in the biosphere ensemble spread in the a posteriori spread relative to the a priori spread over the full domain, Central and Northern Europe (95.1 %, 96.0 %, and 74.8 %, respectively). It indicates less reduction in Northern Europe due to the sparseness of observational sites. The large reduction in spread in Central Europe reflects a notable dependency of NEE estimates on the atmospheric measurements, substantially where the observation network is dense.

Reduction in the biosphere ensemble NEE spread over Europe.

To analyse the seasonal variations, the seasonal cycle from B0, B1, B2, S1, and O1 inversions is averaged over 13 years for the full domain of Europe together with the corresponding biogenic prior fluxes for VPRM, FLUXCOM, and SiBCASA (Fig. 4). Results show good agreement amid a posteriori results of all inversions, while prior biosphere models show large differences, a pattern similar to the one seen over the annual fluxes in Fig. 3. Nevertheless, posterior NEE fluxes estimated in the S1 inversion show differences during May–August when compared with the estimates of other runs, reflecting a larger sensitivity of IAV to summer fluxes when applying a different set of stations. In addition, the difference in posterior fluxes seen in Fig. 3 over the annually aggregated estimates computed from the B1 inversion over the period 2014–2018 largely results from the estimates during May and June when comparing them to the rest of biosphere ensemble elements (Fig. 4).

Seasonal cycle of NEE calculated as the average of monthly fluxes over 13 years estimated using the ensembles of inversions (solid lines) B0, B1, B2, S1, and O1 as well as the biogenic prior fluxes (dotted lines) obtained from VPRM, FLUXCOM, and SiBCASA.

Figure 5 illustrates the statistical uncertainty and the spread through the
overall ensembles of inversions (listed in Table 2) calculated annually over
three regions. As was discussed in the time series of NEE (Fig. 3), a
reduction in posterior NEE uncertainty with respect to the assumed prior
uncertainty is clear (dark grey bars in Fig. 5). A larger reduction is
realised in Central Europe, emphasising a strong atmospheric signal
constraint in the inversion. The spread among ensemble members (Fig. 5,
yellow bars) represents the standard deviation of the respective inversion
results. The ensemble spread over the a priori biosphere models agrees with
the assumed prior uncertainty, with a relatively high value (about 0.44 PgC yr

Spread uncertainties calculated from three inversion ensembles of biosphere, ocean, and station set (yellow bars). Grey bars refer to the statistical uncertainties, and blue bars denote the standard deviations of IAV.

In terms of the spread of the biosphere ensemble, the standard deviation of
posterior fluxes declines from 0.666 to 0.032 PgC yr

The largest impact on NEE estimates in the ensembles is observed when the
spread over the station set ensemble is analysed. In this regard, a robust
analysis can be based on a subset from Central Europe, as the subsets of
stations in this region clearly contrast in the two ensemble members
(core sites and recent sites). The spread of the station set ensemble was
found to be 0.11 PgC yr

The spatially distributed spread of all ensembles is depicted in Fig. 6. In
this instance, the standard deviation was calculated for each grid cell
rather than aggregating fluxes over regions first and then computing the
spread (Fig. 5). The spatial spread here illustrates the deviations in the
biosphere ensemble (“Biosphere spread”), the biosphere models (“Prior biosphere spread”), the station set ensemble (“Stationset spread”), and the ocean ensemble (“Ocean spread”). The maximum spread of 0.191

Spatial spread of biosphere, prior, station set, and ocean
ensembles. Standard deviation (SD) in the legend is normalised over maximum
spread 1.91

Figure 7 indicates the spatial distributions of prior and posterior NEE averaged over the full 13-year period, estimated from B0, B1, and B2 inversions as well as the corresponding innovation of fluxes (the difference between posterior and prior fluxes). Positive corrections have been made to the biosphere flux models that are regarded to be negatively biased (VPRM and FLUXCOM, as was unequivocally confirmed by the annual time series of NEE in Fig. 3). In contrast, SiBCASA results are closer to the mean of posterior fluxes, with a small domain-wide negative correction, except for local positive innovations seen over Northern Germany and the Western Mediterranean coast.

Posterior, prior, and innovation of fluxes (posterior – prior) averaged over the 2006–2018 period calculated from the biosphere ensemble of inversions (B0, B1, and B2). Green circles refer to observing sites.

In this section, we present CO

Summer NEE anomalies between 2006 and 2019 (

Anomalies of NEE fluxes during spring, summer, fall, and winter estimated from two inversion runs differing in biosphere models (FLUXCOM in red colour and VPRM in blue colour) using the atmospheric data of core sites. Solid lines indicate the a posteriori anomalies, while dashed lines refer to the corresponding a priori (biosphere models) anomalies.

The agreement between posterior fluxes using FLUXCOM and prior fluxes of VPRM in the spring season confirms two important conjectures: (1) posterior IAV are largely derived by atmospheric data regardless of the biosphere model used; (2) the VPRM model can capture year-to-year variations during spring, reflecting its capability to represent dynamic biospheric activity during the growing season. It is clear that FLUXCOM exhibits remarkably weaker annual variations during spring and fall in comparison with the VPRM and the a posteriori fluxes. In winter, the VPRM model agrees well with FLUXCOM in the interannual variations, showing less IAV compared to the NEE estimates. We attribute this to the lower signal of temperature assimilated in the biosphere models from the meteorological data as well as less information of radiation reflectance obtained from the remote-sensing data due to dominant cloudy scenes in winter, provided that the VPRM and FLUXCOM models use forcing data from meteorology and remote sensing. In addition, misrepresentation in the anthropogenic emissions prescribed in the inversion may contribute to the posterior IAV, in particular during winter due to the fact that the biosphere signal is generally weak.

To assess the temporal changes in NEE in response to such climate
variations, we compare the seasonal anomalies of NEE (prior and posterior)
to the anomalies of 2 m air temperature and Standardised Precipitation–Evapotranspiration Index (SPEI) (Beguería et al., 2014) during
spring, summer, fall, and winter as well as the annual mean (Fig. 9). Here
we show estimated NEE integrated over the full domain. Monthly
near-real-time data of SPEI (SPEI01) are obtained from

Panel

The findings of standardised anomalies in Fig. 9a show that the decrease in
CO

The excess of annually averaged temperature was predominant in 2018 and
2019, reaching around 0.40 and 0.47

During winter, water availability does not seem to be a limiting factor of
NEE as we notice from low correlations between posterior NEE and SPEI.
Instead, temperature negatively correlates with posterior NEE indicating
that the increase in temperature coincides with enhanced uptake of CO

Seasonal contribution to IAV calculated relative to 14 years for
posterior NEE fluxes (post), VPRM NEE fluxes (prior), SPEI, and

Using an identical set of observation sites for the last 5 years, the S2 inversion demonstrates the differences between NEE estimates in 2018 and
2019 as seen in Fig. 11. Results emphasise the aftermath of drought
episodes, showing a smaller uptake of CO

Differences in NEE estimates for 2018–2019 in seasonal and annual mean calculated from the S2 inversion set-up.

The 2019 anomalies of prior fluxes (first row), posterior NEE estimated from the S1 inversion (second row), 2 m air temperature (third row), and SPEI (fourth row) relative to 2006–2019 over Europe. Columns denote mean estimates of spring, summer, fall, winter, and annual NEE estimates, from left to right.

The annual budgets of NEE in 2019 and 2018 are summarised in Fig. 13 for six
subregions estimated using the B0 and S2 inversions. The choice to use the B0 inversion is to estimate annual flux budgets of CO

Posterior NEE flux budgets over six European regions in 2018 and 2019 using the B0 and S2 inversions (dark colours) compared to their priors from the VPRM model (light colours). Uncertainties associated with B0 and VPRM fluxes are referred to in the error bars.

These results, again, highlight the sensitivity of the inversion to data coverage but also the stronger impact of warmer summers on NEE, where S2 estimates suggest larger flux budgets in 2019 compared to 2018 over Western and Southern Europe. Overall, B0 and S2 results suggest a suppression of GPP, predominantly in Central and Northern Europe.

The smaller spread in the a posteriori fluxes found through the ensembles of
inversions is evident over All Europe reflecting the good performance of the
inversion system. In the biosphere ensemble, flux estimates are not very
sensitive to a priori terrestrial ecosystem fluxes. We deduce this from the
small spread over the a posteriori fluxes (Fig. 3), occurring despite major
differences in a priori fluxes. Likewise, different ocean flux models have
the smallest effect on estimating NEE, in particular inland, where
the ocean–land exchange is dissipated. However, the spread in the station set
ensemble is strongest, at 0.11 PgC yr

Our results denote a comparable reduction in posterior uncertainty and the spread relative to their a priori (Fig. 5). It is noteworthy that the indirect effect of statistical posterior uncertainty on the corresponding spread over the ensembles of inversions emerges from the common dependency on observational data, which predominantly appear in the well-constrained areas in Germany, France, Benelux, and the UK. Over such regions, the posterior uncertainty and spreads are greatly reduced and the inversions tend to converge regardless of which prior flux model is used. It is essential to consider the prior uncertainty assumption as well as the prior error structure in the spatial and temporal aspects. This will determine to which extent the posterior fluxes are dependent on the uncertainty biogenic fluxes, specifically in the regional inversions where the degrees of freedom can drastically increase following the finer spatial and temporal resolution of biosphere flux models and atmospheric transport models.

The linkage between NEE and climate variation has been examined via SPEI and
temperature as proxy data of climate variation. The anomalies of SPEI and
temperature are analysed along with NEE anomalies during the recent years
2018 and 2019 in the context of the period 2006–2017. The recent drought
events decreased the efficiency of GPP, in particular during spring and
summer, where soil moisture markedly declined during the summer of 2018 and
2019 accompanied with an exceptional rise in temperature (Ma et al.,
2020). But GPP during spring 2019 showed a higher efficiency (larger uptake
of CO

In terms of estimated winter fluxes, the medium anticorrelation between
temperature and NEE (also shown by the anomalies in Fig. 9a) may imply that
an increase in CO

Besides the previous explanation of

Overall, the NEE response to SWC and temperature varies depending on the temporal and spatial aspects of the region of interest and is connected to the hydrological cycle and physical dynamics of soils and the ambient atmosphere.

In this paper, the NEE flux budgets of 2018 and 2019 are estimated in a
pre-operational method to keep track of the changes in net terrestrial
fluxes of CO

NEE estimates and the respective prior fluxes as well as codes used in this
study can be made available upon request to the corresponding author.
Atmospheric dry mole fraction measurements of CO

The supplement related to this article is available online at:

SM and CG designed the study. SM conducted the CSR inversion simulations, analysed the results, and wrote the paper. CR designed and maintains the CSR source code. FTK prepared and provided the emission datasets from the EDGAR_v4.3 inventory. SW conducted and provided the simulations of the FLUXCOM model. KUT and MG contributed to the revision of the paper. All authors revised the paper and edited the text.

At least one of the (co-)authors is a member of the editorial board of

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The authors acknowledge the computational support of Deutsches
Klimarechenzentrum (DKRZ) where the CSR inversion system is implemented and the
providers of atmospheric dry mole fraction measurements of CO

This research has been supported by Horizon 2020 (VERIFY (grant no. 776810)).The article processing charges for this open-access publication were covered by the Max Planck Society.

This paper was edited by Mathias Palm and reviewed by two anonymous referees.