Inversions

Atmospheric CO 2 inversions estimate spatial distribution of surface CO 2 fluxes using a top-down approach, in which surface fluxes are estimated from atmospheric CO 2 concentration measurements across the globe. An atmospheric transport model that represents the global atmospheric circulation is required, as well as prior-information about the fluxes. Flux estimates over land include the carbon exchange in ecosystems, LUC related fluxes and forest fire CO 2 emissions as well as fossil-fuel emissions. To estimate NBP, the latter are subtracted from the flux estimates.

We use monthly CO 2 fluxes of two versions of the atmospheric inversion of the MACCII from the LSCE29,30. Version 11.2 covers the period from 1979 until 2011 and is used here from January 1982 onwards. It has a 2.5 × 3.75 (latitude, longitude) spatial resolution. Version 13.1 has a slightly higher latitudinal resolution (1.9) and covers year 2012 as well (Supplementary Table 1). Apart from the archive length, the main difference between v11.2 and v13.1 is the number of vertical layers in the underlying atmospheric transport model, the LMD General Circulation Model (LMDZ)29, that was doubled in the latter (39 versus 19), thus allowing a better representation of the variability of CO 2 in the planetary boundary layer, where the assimilated measurements are located.

Since MACC inversions are based on a large but variable number of stations during the study period (134 in total), with fewer observations in the beginning of the time series, part of the variability observed on the estimated fluxes may be affected by the changes in the number of sites41. Thus, we use the Jena s81 (v3.6) inversion that is based on fewer stations and is provided at 4 × 5 spatial resolution (Supplementary Table 1), but uses a consistent set of sites for the 1982–2012 period. Jena inversion computes NBP on each grid cell using the atmospheric transport model TM3, as described in ref. 31.

To subtract fossil fuel emissions, MACCII inversions use the EDGAR3.2 FastTrack 2000 emission database42 with scaling factor to account for trends: MACC uses the annual global totals of the Carbon Dioxide Information Analysis Center and prescribes an increase of 1.4% per year after 2001. Jena inversion uses EDGAR 4.2, with FastTrack 2010 for 2009 and 2010, extrapolation based on British Petrol global totals for 2011 and 2012, and 2% year increase afterwards.

Uncertainties of annual NBP at the continental scale are given, for each model, in Supplementary Table 1. Uncertainties of the annual fluxes account for errors in the prior fluxes, network configuration (number of sites, Supplementary Fig. 1) and in the transport model. The uncertainty of the annual anomalies is expected to be lower than that of the absolute fluxes, since these errors are positively correlated from 1 year to the next32. We use two inversions computed with the same model but variable number of sites, and a second with a fixed number of observations, and use the spread between inversions as an indicator of the uncertainty in the anomalies.

In order to test the available signals from the smaller number of sites in Europe used by the Jena s81 inversion, we performed three synthetic-data runs (1982–2010) by transporting net ecosystem exchange (NEE) fields as simulated by the Biome-BGC DGVM in the atmosphere using the same transport model as in the Jena inversion (v3.7), though on coarser 10 × 8 spatial resolution. To create pseudo data, modelled atmospheric CO 2 is sampled at the same locations and times as the real data for three different station sets: as in Jena s81 (14 sites) and s90 (25 sites) as well as mostly the same sites used for MACCII inversion (Supplementary Table 2). The CO 2 concentrations sampled in this way were inverted back using the Jena scheme (setting ocean and fossil fuel priors to zero). As the same transport model is used for synthetic data and inversion, results are not contaminated by model errors. By comparing with the original fluxes (Supplementary Fig. 9), the sensitivity of the inversion skill to the site network can then be evaluated. Despite the presence of discrepancies, the run with fewer stations (Jena s81) is able to capture the variability patterns of the CO 2 fluxes and differences in the magnitude of the fluxes are on average 0.04–0.05 PgC per year for each of the three runs.

Dynamic global vegetation models

DGVMs simulate the main processes of vegetation dynamics and decomposition associated with energy, water and carbon balances at the ecosystem scale and provide a bottom-up approach to evaluate NBP variability, as well as the corresponding GPP and respiration components.

The TRENDY project43 compiles outputs from a group of DGVMs to evaluate trends and drivers in land–atmosphere carbon exchange20. We use 11 DGVMs (Supplementary Table 2) from simulation S3, in which all models are forced by the same values of changing atmospheric CO 2 concentrations from ice core data and observations, historical climate observations from the CRU-NCEP v4 data set and LUC from the History Database of the Global Environment (HYDE) database of human-induced land-cover changes44.

Supplementary Table 2 provides a summary of the characteristics of the 11 DGVMs used in simulation S3, which is performed over the period 1860–2012. All models include deforestation, afforestation and regrowth, but differ in the way they represent disturbances (fire), nutrient limitation and do not realistically simulate land-management practices or crop seasonality, which strongly interplays with climate in determining NBP of European ecosystems. Nevertheless, DGVMs provide an independent data set to evaluate the variability of the land carbon sink. NBP from DGVMs was selected for two periods: the common period with the inversions and satellite data (1982–2012) for the main analysis, and the common period with the NAO and EA indices (1950–2012), except for JSBACH whose record ends in 2005. To partition NBP, continental and regional GPP and respiration (computed as the sum of autotrophic and heterotrophic respiration components) anomalies from the DGVMs were also evaluated between 1982 and 2012.

NDVI

Biweekly NDVI fields over 1982–2012 from the GIMMS NDVI data set, provided at 8 km spatial resolution35. NDVI values were integrated over each year on a pixel basis from the biweekly fields. NDVI anomalies were then computed as the departure from the average annual integral values, and used as a proxy for GPP anomalies28.

Monthly NBP values from inversions and DGVMs were first deseasonalized (mean seasonal-cycle removed) on a pixel basis to compute monthly anomaly and integrated over the year for annual NBP anomaly fields, for the European continent and for the regional boxes (Supplementary Fig. 3). A positive (negative) sign of NBP anomalies correspond to either an enhanced (weaker) sink or a smaller (increased) source. To evaluate the main pattern of NBP variability, a PCA was performed on NBP fields for inversions and DGVMs. Since results from PCA depend on the resolution of the data set, all fields were resampled to a common 1° spatial resolution. The first principal component of NBP variability (PC 1 ), the corresponding empirical orthogonal function (EOF 1 ) and explained variance were selected for each inversion and model. EOF 1 presented in all cases dipolar pattern. The consistency of these patterns was compared by locating the corresponding centres of action for each data set (Supplementary Fig. 4).

All climate variables used for this analysis were extracted from ERA-Interim reanalysis45: vertical integral of eastward transport water vapour (VT, in g km−1 s−1) and heat (HT, in MW km−1), fraction of cloud cover (%), SLP (in mb), 500-mb geopotential height (z500, in geopotential metres, g.p.m.), average air temperature at 2 m (T, in °C), volumetric soil-water content (SW, in % of volume) in the top layer46 and average snow depth (SD, in cm). The data comprise monthly average fields from 1982 to 2012, at 0.75 spatial resolution.

As complementary information about soil-water conditions, monthly values of the self-calibrated Palmer Drought Severity Index (PDSI)47, provided by the NOAA/OAR/ESRL PSD, Boulder, CO, USA at 2.5 spatial resolution was used. Since PDSI presented regional dependence (negative for Iberian Peninsula and central Europe and positive for western Russia and Scandinavia), we estimated drought conditions as the PDSI departure from the regional average (Supplementary Table 6).

Atmospheric circulation

We focus our analysis on the impacts of winter state Dec-Feb (DJF) of two teleconnections, using the monthly indices from NOAA’s Climate Prediction Centre, which are calculated by rotated PCA of monthly means of 500-mb geopotential height anomalies from NCEP/DOE II (ref. 48) as described in (ref. 49). This procedure allows the calculation of orthogonal (that is, non-correlated) indices for each month. The first mode corresponds to the NAO pattern, the leading mode of SLP variability in the North Atlantic and the main climate teleconnection affecting European weather. The second mode corresponds to EA circulation pattern. These modes affect more significantly European weather during winter2,50. For visualization of the spatial patterns associated with the two teleconnections used in this work, we performed a PCA on standardized monthly means of 500-mb geopotential height from NCEP/DOEII Reanalysis over the North-Atlantic region between 20 to 80 N and 90 W to 50 E for the winter months (DJF) as in ref. 49.

The phases of an index are defined as those exceeding the lower (negative) or upper (positive) terciles, and identified in superscript (for example, NAO+ for a positive phase of winter NAO). To evaluate the combined impacts of both teleconnections, we identify four subsets of years corresponding to the four possible NAO–EA phase combinations, together with a neutral composite (Supplementary Table 3).

Regional fluxes

Since data sets are provided at very different spatial resolutions (Supplementary Tables 1 and 2), and because inversions perform better on larger scales, we consider regionally integrated NBP from inversions and DGVMs for the European continent defined in the TransCom inter-comparison project51 (Supplementary Fig. 1). We additionally define four large regions encompassing most of Europe: Iberian Peninsula extending from −11 ° to 3.5 ° E and 34 ° to 44 ° N; continental central Europe encompassing the region between −5 ° to 25 ° E and 44 ° to 53 ° N, but excluding Great Britain; western Russia and eastern Europe extending from 29 ° to 60 ° E and 46 ° to 62 ° N; Scandinavia covering the region between 4.5 ° to 29 ° E and 56 ° to 71 ° N (Supplementary Fig. 1).

To evaluate the skill of inversions in capturing regional fluxes, we used the same synthetic runs from Jena inversion to evaluate: (i) the ability of the inversion to reproduce fluxes in large regions over Europe; (ii) the influence of the observational network. Despite the very coarse resolution, results (Supplementary Fig. 10) indicate that inversions do have moderate skill in distinguishing sub-regions within Europe. As expected from the better observational constrain, the skill increases with increasing number of stations. Nevertheless, even the s81 run (with few sites) is able to capture part of the regional differences, especially in eastern, central and western Europe. In south-western Europe (corresponding to the Iberian Peninsula), the inversion is not able to reproduce the fluxes, as expected from the very low observational constraint (only two sites in the complete MACCII set, located in the Pyrenees).

NBP response to NAO–EA

All data fields were selected for the study region (Supplementary Fig. 1). Continental and regional NBP anomalies were calculated for each inversion and DGVM and evaluated for each of the four NAO–EA combinations (Fig. 2). In the case of MACC v11.2 inversion and JSBACH, the data sets do not encompass the whole period, therefore, the composites were calculated with fewer years. To partition annual NBP anomalies, continental and regional GPP and total respiration (autotrophic plus heterotrophic respiration components) were calculated at monthly scale, and compared with the corresponding NDVI anomalies (Supplementary Fig. 7).

For each composite, a one-sided analysis of variance (ANOVA) was performed to test the significance of the average anomaly value on the continental and regional scales (Supplementary Table 4), separately for inversions and DGVMs. Absolute NBP anomalies for each composite are easier to associate with NBP variations from year to year. However, it is worth assessing whether the inversions (or DGVMs) agree on the relative response, that is, the difference in NBP anomalies between two NAO–EA combinations. Therefore, a two-sided ANOVA was carried out to test the difference between NBP anomaly estimates for pairs of the four combinations (Supplementary Table 5), on the continental scale. Supplementary Tables 4 and 5 also include results of the ANOVA analyses for the neutral composite. To assess whether relationships hold for longer periods, the same analysis was extended for the period 1950–2012 using DGVMs (Supplementary Fig. 5).

Since the synthetic runs of Jena inversion present some dependence of absolute fluxes in the observational network, it is worth assessing how the number of sites may influence the results of NBP anomalies in response to NAO–EA variations. As the observational network has increased with time, Jena inversion is provided for different periods using an increasing number (always constant for each data set) of sites. Here we compare the other two inversions from Jena v3.6 that still encompass at least 20 years and use the same model but more sites: s85 (1985–2012, 19 sites), s90 (1990–2012, 25 sites). We also performed a run with the newer version of Jena inversion (v3.7) using the MACCII sites, at the same resolution as Jena s81 v3.6. The corresponding anomalies for each NAO–EA combination are presented in Supplementary Fig. 11 and show that, despite results depending on the size of the observational network, the response of continental NBP to the phases of NAO and EA for the data sets with more observations is consistent with the anomalies estimated by the two MACCII inversions and Jena s81 v3.6. In most cases, the inversion run using the MACCII sites is closer to the anomalies estimated by MACCII, highlighting the dependence of the anomalies on the observational constrains, but also the importance of other sources of uncertainty, for example, differences in the transport models.