How does the terrestrial carbon exchange respond to interannual climatic variations? A quantiﬁcation based on atmospheric CO 2 data

. The response of the terrestrial Net Ecosystem Exchange (NEE) of CO 2 to climate variations and trends may crucially determine the future climate trajectory. Here we directly quantify this response on interannual time scales, by building a linear regression of interannual NEE anomalies against observed air temperature anomalies into an atmospheric inverse calculation based on long-term atmospheric CO 2 observations. This allows us to estimate the sensitivity of NEE to interannual variations in temperature (seen as climate proxy) resolved in space and with season. As this sensitivity comprises both direct temperature 5 effects and effects of other climate variables co-varying with temperature, we interpret it as “interannual climate sensitivity”. We ﬁnd distinct seasonal patterns of this sensitivity in the northern extratropics, that are consistent with the expected seasonal responses of photosynthesis, respiration, and ﬁre. Within uncertainties, these sensitivity patterns are consistent with independent inferrences from eddy covariance data. On large spatial scales, northern extratropical as well as tropical interannual NEE variations inferred from the NEE-T regression are very similar to the estimates of an atmospheric inversion with explicit in-10 terannual degrees of freedom. The results of this study can be used to benchmark ecosystem process models, to gap-ﬁll or extrapolate observational records, or to separate interannual variations from longer-term trends.


Introduction
About a quarter of the carbon dioxide (CO 2 ) emitted to the atmosphere by human fossil fuel burning and cement manufacturing is currently taken up by the terrestrial biosphere (Le Quéré et al., 2016), thereby slowing down the rise of atmospheric CO 2 levels and thus mitigating climate change.The magnitude of this terrestrial Net Ecosystem Exchange (NEE) of CO 2 , however, is subject to substantial variability and trends, to a large part as a response to variations and trends in climate.Due to this feedback loop, the response of NEE on climate may crucially determine the future climate trajectory (Friedlingstein et al., 2001), yet present-day coupled climate-carbon cycle models strongly disagree on its strength (Friedlingstein et al., 2014).
To reduce these uncertainties, observations of present-day year-to-year variations have been used as a constraint on the unobservable longer-term changes (Cox et al., 2013;Mystakidis et al., 2017), using the finding that these models show a close link between the climate-carbon cycle responses at year-to-year and centennial time scales.It cannot be known, however, transport model to simulate the atmospheric CO 2 field that would arise from a given flux field, the inversion algorithm finds the flux field that leads to the closest match between observed and simulated CO 2 mole fractions, according to a quadratic cost function.The cost function additionally brings in a-priori information to regularize the estimation, in particular spatial and temporal smoothness constraints on the flux field.The a-priori settings do not involve any information from biosphere process models.Fossil fuel fluxes are fixed to accounting-based values.In the particular run used here, ocean fluxes are fixed to estimates based on an interpolation of surface-ocean pCO 2 data (Jena CarboScope run oc_v1.5).A more detailed technical specification, including references and highlighting changes with respect to earlier Jena CarboScope versions, is given in Appendix A.
For reference in Sect.2.2 below, we mention here that this standard inversion calculation represents the total surface-toatmosphere CO 2 flux f as a decomposition into adjustable long-term mean terrestrial NEE (f adj NEE,LT ), adjustable large-scale seasonal NEE anomalies (f adj NEE,Seas ), adjustable interannual and shorter-term NEE anomalies (f adj NEE,IAV ), prescribed ocean fluxes (f fix Ocean ), and prescribed fossil fuel emissions (f fix Foss ).All these terms represent spatio-temporal fields.This standard inversion will be used as a reference to compare the results of the NEE-T inversion introduced below (Sect.2.2) at large spatial scales.Further, we used its estimated NEE variations in preparatory tests to confirm that NEE-T correlations actually exist, and to determine the degrees of freedom needed to accomodate their spatio-temporal heterogeneity.

The NEE-T inversion
Compared to the standard inversion (run s85oc_v4.1s),the NEE-T inversion (base run s85ocNEET_v4.1s)uses the same transport model and the same prescribed data-based CO 2 fluxes of the ocean (f fix Ocean ) and fossil fuel emissions (f fix Foss ).It also possesses the same adjustable degrees of freedom representing the long-term mean CO 2 fluxes (term f adj NEE,LT ) and the largescale seasonality (f adj NEE,Seas ).The NEE-T inversion differs only by replacing the explicitly time-dependent interannual NEE variations (f adj NEE,IAV ) with a linear NEE-T regression term plus residual terms, T represents the monthly spatio-temporal field of air temperature, taken from GISS (Hansen et al., 2010;GISTEMP Team, 2017), interpolated to the spatial grid and daily time steps of the inversion (Appendix A).Its long-term mean, mean seasonal cycle, and decadal variations including linear trend (T LT+Seas+Deca+Trend ) have been subtracted to only retain interannual (including non-seasonal month-to-month) anomalies.The scalar w is a temporal weighting being 1 within the analysis period 1985-2016 and zero outside; this ensures that the regression is specifically referring to this period.This interannual temperature anomaly field is multiplied by unknown (i.e., adjustable by the inversion) scaling factors γ NEE-T = ∆NEE / ∆T.These scaling factors are identical in each year of the inversion, but are allowed to vary smoothly both seasonally (correlation lengths of about 3 weeks) and spatially (correlation lengths of about 1200 km, as for the term f adj NEE,LT ).The need for seasonal and spatial resolution of γ NEE-T has been inferred from analysis of the standard inversion results (Sect.2.1).The a-priori spatial and temporal correlations are imposed on γ NEE-T to prevent a localization of inverse adjustments in the vicinity of the atmosperic stations.In contrast to the standard inversion, however, where the a-priori correlations lead to a smooth NEE field, the result of the NEE-T inversion still retains structure on the pixel and monthly scale from the temperature field.
Eq. ( 2) also contains adjustable residual terms to accomodate modes of variability from the atmospheric CO 2 signals that cannot be explicitly represented by the regression term and might therefore be at risk of being aliased into spurious adjustments to γ NEE-T .An adjustable linear trend (f adj NEE,Trend ) is needed because trends have explicitly been removed from T. For every pixel, f adj NEE,Trend is proportional to the time difference ∆t since the beginning of the calculation period, multiplied by an unknown trend parameter to be adjusted by the inversion (with zero prior).The trend parameters are correlated with each other in space with the same correlation length scale as the mean and interannual variability components of the standard inversion (i.e., as f adj NEE,LT and f adj NEE,IAV in Eq. ( 1)).Further, as the NEE field from the standard inversion contains a strong increase in seasonal cycle amplitude in northern extratropical latitudes (earlier described in Graven et al. (2013); Welp et al. (2016)) which is expected to not (solely) arise from changes in the temperature seasonal cycle, we decoupled this mode of variability from the regression by adding it as an explicitly adjustable term f adj NEE,SCTrend .For each degree of freedom (Fourier mode) in the mean seasonality term f adj NEE,Seas in Eq. ( 1)), f adj NEE,Trend contains the same mode multiplied by ∆t and having its own adjustable strength parameter.Any further modes of variability (including NEE variations related to variations in other environmental drivers uncorrelated to T variations, non-linear responses, memory effects and internal ecosystem dynamics, errors in the employed T field, errors of the a-priori fixed ocean and fossil fuel terms, as well as effects of transport model errors) are not explicitly accounted for and stay in the data residual of the inversion.
In contrast to the standard inversion using 23 stations with temporally homogeneous records, the NEE-T inversion uses atmospheric data from 89 stations (Table 1) partially with shorter records but spatially covering the globe more evenly (including stations in northern Siberia or tropical America).While the standard inversion with explicitly time-dependent degrees of freedom can develop spurious NEE variations when stations pop in or out with time, the major interannual variability from the NEE-T inversion is coming from the regression term using its degrees of freedom repeatedly each year, such that any data point influences all years of the calculation period simultaneously.Therefore, the NEE-T inversion is not prone to spurious variations from a temporally changing station network.

Sensitivity cases
The algorithm uses several inputs carrying uncertainties, and contains several parameters that are not well determined from a-priori available information.Therefore, we also ran an ensemble of sensitivity cases.In each such sensitivity case, one of the uncertain elements of the algorithm is changed within ranges that may be considered as plausible as the base case: (1) longer spatial a-priori correlations for γ NEE-T , (2) longer temporal a-priori correlations for γ NEE-T , (3) reduced a-priori uncertainties Biogeosciences Discuss., https://doi.org/10.5194/bg-2018-34Manuscript under review for journal Biogeosciences Discussion started: 22 January 2018 c Author(s) 2018.CC BY 4.0 License.
for γ NEE-T , (4) using ocean CO 2 fluxes from the PlankTOM5 ocean biogeochemical process model instead of the fluxes based on pCO 2 measurements, (5) taking the gridded monthly land temperature field from Berkeley Earth (www.BerkeleyEarth.org,accessed 2017-11-29) instead of the GISS data set, and (6) using ERA-Interim meteorological fields (Dee et al., 2011) to drive the atmospheric transport model rather than NCEP meteorological fields.
Eight additional sensitivity cases have been run to demonstrate coherent information in the atmospheric data.The set of 89 stations used in the base case was divided into 8 mutually exclusive parts (Table 1).In each of the sensitivity cases, one of these parts was omitted, leaving sets of 73 to 82 remaining stations.By this construction, all these 8 runs still have global data coverage, but every station is absent in one of the runs.If the results would depend on any particular station without being backed up by other stations, then the run omitting this station would show substantial difference from the base run.
The range of results from this ensemble of sensitivity cases will be shown as uncertainty range around the base case.

Comparison to eddy covariance data
For comparison of the estimated sensitivities γ NEE-T against independent information, we also calculate NEE-T relationships from eddy covariance (EC) measurements.We use NEE and co-measured air temperature records from the FLUXNET2015 data set (https://fluxnet.fluxdata.org).EC sites (Table 2) have been chosen based on having long records (at least 12 years); 2 sites with 11 years were included too to have more ecosystem types represented.Crop sites have not been included because their flux variability is expected to strongly depend on crop rotation.
We start from the half-hourly or hourly data sets (variables NEE_CUT_REF and TA_F_MDS, respectively).Records classified as "measured" (QC flag = 0) or "good quality gapfill" (QC flag = 1) in both variables are averaged over each month.
Months with data coverage of 90% or less are discarded from the statistical analysis.
For each EC site and each month of the year, all available monthly CO 2 flux values from the different years were regressed against the corresponding monthly air temperature values, using ordinary least squares regression.This yields sensitivities as regression slopes g EC NEE-T = ∆NEE EC / ∆T EC .We also calculated the confidence interval of the slope for the confidence level 90%, reflecting the uncertainty of g EC NEE-T given the scatter of the monthly values around a linear relationship.The sensitivities γ NEE-T from the inversion and g EC NEE-T from the explicit linear regression are not fully comparable mathematically because (i) the time period (and to some extent the frequency filtering) are different, and (ii) the explicit linear regression of the total NEE is not only influenced by the year-to-year variations but also by the ratio of NEE trend and temperature trend while γ NEE-T has deliberately been made insensitive to the trend (Sect.2.2).Therefore, we also calculated sensitivities g Inv NEE-T from the total monthly-mean non-fossil CO 2 flux (i.e., including regression and residual terms) and the employed temperature field of the inversions, in the same way and subsampled at the same months as for the EC data.A perfect match between g EC NEE-T and g Inv NEE-T cannot be expected nevertheless because (iii) sensitivities from the inversion even at its smallest resolved scale -the pixel scale-represent a mixture of ecosystem types in unknown proportions, while the EC data represent a specific ecosystem type, (iv) NEE from the inversion includes the effects of disturbances such as fire, which are absent from the EC data, and (v) there may be local trends in the ecosystem behaviour observed by the EC data due to aging or slow species shifts, which average out on the larger spatial scales seen by the atmospheric inversion.This prepresentation summarizes the essential variations of γ NEE-T , as it is found to be relatively uniform across longitude within the individual continents (not shown).
In essentially all northern extratropical land areas (north of about 35 • N), we estimate negative γ NEE-T in spring (and, to a lesser extent, autumn), consistent with photosynthesis being temperature limited such that higher-than-normal temperatures lead to more negative NEE (i.e., larger-than-normal CO 2 uptake) and vice versa.In summer, when photosynthesis is not limited by temperature any more, we find positive γ NEE-T values.Such positive γ NEE-T is consistent with enhanced respiration in warmer summers, but also with the fact that warmer-than-normal periods are often also dryer leading to reduced photosynthetic uptake or enhanced fire activity.In winter, NEE is not found to respond much to interannual climate variations.The interpretation of the seasonality of γ NEE-T is confirmed by its latitude dependence: Consistent with the later spring and shorter summer in the higher northern latitudes, the period of negative γ NEE-T starts later there, and the period of positive γ NEE-T is shorter.
In the Tropics, we find stronger and less systematic variations in γ NEE-T .However, as indicated by the missing stippling, we also find larger disagreement between our sensitivity cases designed to embrace plausible ranges for the essential inputs and parameters in the algorithm (Sect.2.3).This reveals that the seasonal variations in γ NEE-T are of limited robustness here.
Nevertheless, a clear feature in the tropics is the dominance of positive γ NEE-T values.
In extratropical South America and Africa, the seasonal pattern has similarities with the northern extratropical pattern shifted by 6 months.The pattern in Australia is difficult to interpret, but also not very robust.Larger errors in the southern extratropics may concievably arise because the much smaller land area involves a much smaller number of degrees of freedom available to satisfy the data constraints (remember that the oceanic flux cannot be adjusted in this inversion, while the pCO 2 -based ocean prior flux is actually less well constrained in the southern extratropics due to the much smaller density of pCO 2 data).

How much interannual variability of NEE can be reproduced by the seasonally resolved linear regression to T?
The assumed linear relationship between NEE anomalies and air temperature anomalies around their respective seasonal cycles represents a strong abstraction of the complex underlying physiological and ecosystem processes.Nevertheless, the interannual variations of global total NEE estimated by the NEE-T inversion is very similar to that estimated by the standard inversion (Fig. 2, top left).The agreement is confirmed by high correlation (Fig. 2, top right).For interpretation, we note that variations Almost the same level of agreement is also found for a split of the global NEE into a northern extratropical and a tropical plus southern extratropical contribution (Fig. 2, middle and bottom).Due to the faster atmospheric mixing within the extratropical hemispheres compared to the mixing across latitudes, these two NEE contributions are expected to be relatively well constrained by atmospheric data independently of each other.The linear approximation of the NEE-T inversion is able to distinguish extratropical and tropical behaviour.
For a further split into smaller regions, in particular along longitude, interannual NEE variations from standard and NEE-T inversions stay similar, but deviations get larger (not shown).This could indicate that the limits of the linear NEE-T relationship start to kick in at these scales.However, the NEE variations cannot be expected to be well constrained from the atmospheric data at the regional scale any more.Thus, the discrepancy can also be caused by the standard inversion, while the NEE-T inversion could be the more realistic one by profiting from the pixel-scale information added through the temperature field, as discussed in Sect.4.1.

Are the estimated patterns of γ NEE-T compatible with ecosystem-scale eddy covariance data?
Fig. 3 compares "interannual climate sensitivities" (ordinate) calculated by the NEE-T inversion with those calculated independently from eddy covariance (EC) data for each month of the year (abscissa).Each panel represents an EC site, roughly arranged by ecosystem types and latitudes.The colour line with the surrounding gray band give the sensitivities γ NEE-T from the various NEE-T inversion runs as in Fig. 2 taken at the respective pixels enclosing the EC sites.The black dots are the sensitivities g EC NEE-T calculated by explicit linear regression of monthly EC flux records against the co-measured monthly air temperature (Sect.2.4).
To allow a fairer comparison between inversion results and EC data, additional color dots give sensitivities g Inv NEE-T calculated from the NEE-T inversion results in the same way and subsampled at the same months as for the EC data (Sect.2.4).At most EC sites, the sensitivities calculated by the inversion itself (γ NEE-T , orange lines) or by explicit regression afterwards (g Inv NEE-T , orange dots) mostly agree within the confidence interval of the regression.This shows that the comparison of inversion and EC sensitivities is meaningful despite their differences in meaning and calculation (in particular, the trend influence (issue (ii) in Sect.2.4) on g Inv NEE-T turns out to be relatively small because the explicit regressions are only done over the limited time period spanned by the EC records).
Despite their completely independent sources of information and their remaining incompatibilities (Sect.2.4), the sensitivities from the EC data and the atmospheric NEE-T inversion have a similar order of magnitude as well as similar seasonal patterns for a majority of EC sites (Fig. 3).For most sites/months, the sensitivities agree within their confidence intervals.The level of agreement roughly depends on ecosystem type and latitude: -Generally good consistency is found in high northern latitudes (line 1) and at evergreen needleleaf forest (ENF) sites in temperate northern latitudes (line 2 and rightmost part of line 3).
-At mixed forest (MF) and decidious broadleaf forest (DBF) sites in temperate northern latitudes (left part of line 3 and line 4), consistency is mostly good as well, though some months in spring or summer have more negative g Inv NEE-T sensitivities from EC data (e.g., DE-Hai, DK-Sor, BE-Bra).However, the behaviour of DBF ecosystems is not an important contribution to larger-scale NEE variability because DBF ecosystems only cover 11% to 25% of the area around the sites shown.
-Generally good consistency within the confidence interval is also found at sites of various other ecosystem types in temperate northern latitudes (line 5).
-At the tropical and southern extratropical sites (last line), the comparison does not yield conclusive information, because the confidence intervals of the regression are much larger than the seasonal variations of both inversion and EC results.
We can only state that the g Inv NEE-T and g EC NEE-T sensitivities do not contradict each other statistically.Some qualitative consistency is found at the Australian EBF site, even though the dominant vegetation round the site is shrubland (about 45%).
Though this comparison partly remains inconclusive (as the confidence intervals at tropical and southern hemispheric sites are large, as g Inv NEE-T and g EC NEE-T are not actually fully comparable (Sect.2.4), and as by far not all areas and dominating ecosystem types are represented), it does support the results of the NEE-T inversion at least in the northern extratropics.

NEE variations in the northern extratropics
Given that we found robust seasonal patterns of γ NEE-T which can be interpreted in terms of the fundamental physiological processes (Sect.3.1), that these patterns are compatible with inferrences from independent ecosystem-scale eddy covariance (EC) measurements (Sect.3.3), and that the corresponding interannual NEE variations are compatible with the atmospheric constraint on the most reliable large scales (Sect.3.2), we conclude that the linear dependence of NEE anomalies on air temperature anomalies (as climate proxy) represents a meaningful approximative empirical description of the northern extratropical biosphere.The compatibility of the NEE-T relationships inferred from large-scale atmospheric constraints and ecosystem-scale EC constraints of dominating vegetation types suggests that the regional or continental NEE variations are to a substantial degree due to local variations linked to local climate anomalies; otherwise the NEE-T inversion could not have worked.Given that, we expect the NEE-T inversion to provide more realistic interannual NEE variations on regional scales than the standard Note that, as EC data measure fluxes on small spatial scales (a few 100 meters), the EC flux variations themselves cannot directly be compared to the inversion results representing NEE over (sub)continental scales and integrating over many ecosystem types and climate regimes.The NEE-T regression is an example that derived relationships are able to brigde this scale gap.

NEE variations in the tropics
In contrast to the northern extratropics, we did not find conclusive seasonal patterns of γ NEE-T in the tropics (Sect.3.1).However, despite the substantial uncertainty range of γ NEE-T (Fig. 1), the sensitivity cases reproduce almost identical interannual NEE variations in the tropics (see the narrow gray band round the NEE-T estimate in Fig. 2, bottom left).This underlines that pan-topical NEE variations are actually well constrained from the atmospheric data, while the seasonal differences in γ NEE-T arise to compensate for the set-up differences among the sensitivity cases.We assume that all the seasonally different γ NEE-T estimates correspond to a similar effective sensitivity (having a positive value) on slightly longer time scales.This notion is supported by the finding that the NEE-T inversion possesses predictive skill on the time scale of El Niño / Southern Oscillation (Rödenbeck et al., 2018).
The positive effective γ NEE-T in the tropics (Sect.3.1) is consistent with the strong positive correlation of atmospheric CO 2 growth with large-scale tropical annual temperature (Wang et al., 2013).This is unlikely to arise from a direct temperature effect, however, because ecosystem-scale process studies (e.g., Meir et al., 2008;Bonal et al., 2008;Alden et al., 2016) point to water availability, rather than temperature, as the dominant control.This is also confirmed impressively by the large confidence intervals of the NEE-T regression of the EC data from the only tropical site available here (GF-Guy, leftmost on last line of Fig. 3).A strong correlation to temperature can still arise statistically due to the strong link of temperature and precipitation anomalies over larger spatial scales (Berg et al., 2014).Moreover, vapour pressure deficit (VPD) controlling photosynthesis responds to temperature variations particularly strongly in the warm tropical climate due to the non-linearity of the VPD(T) dependence (Monteith and Unsworth, 1990).Further, T is spatially coherent over much larger areas in the tropics while variability in water availability is local and averges out over larger spatial scales (Jung et al., 2017).

Could the results be improved by using a multivariate regression against further climatic variables?
We tested the algorithm also with precipitation (P) or solar radiation as explanatory variables, individually or in multivariate combinations (not shown).While, for example, an NEE-P inversion had almost as good an explanatory power as the NEE-T inversion, a multivariate NEE-T-P inversion did not explain much more NEE variations than the univariate NEE-T inversion did already.This confirms the strong background correlations of air temperature with the other climate variables on interannual time scales.It also means that a multivariate regression would -despite a mathematically unique partitioning into contributions of the individual explanatory variables-likely not yield an uniquely interpretable attribution of NEE variability to different causes.Given that, a univariate NEE-T inversion seems advantageous because T likely has data sets best constrained by observations.As a regression is confined to variability present in the explanatory variables, using less well observed or even modelled variables (as would be the case for precipitation or cloud cover) involves the risk of contamination.

Conclusions and outlook
The response of Net Ecosystem Exchange (NEE) to climate anomalies has been estimated by linear regression against anomalies in air temperature (T) within an atmospheric inversion based on a set of long-term atmospheric CO 2 observations.The resulting spatially and seasonally resolved regression coefficients γ NEE-T are interpreted as a "interannual climate sensitivity", comprising the direct temperature response as well as responses to covarying anomalies in other environmental conditions (e.g., moisture, radiation) (Sect.4.3).
-The inferred "interannual climate sensitivity" γ NEE-T shows distinct and interpretable patterns along latitude and season.
In particular, we find negative γ NEE-T during spring and autumn (consistent with a temperature-limited photosynthesis) and positive γ NEE-T during summer (consistent with a water-limited photosynthesis) in all northern extratropical ecosystems (Sect.3.1).
-Despite the complexity of the underlying plant and ecosystem processes, the spatially and seasonally resolved linear regression of NEE against temperature anomalies (taken as climate proxy), fitted to atmospheric CO 2 data, can reproduce a large fraction of NEE's interannual variations, at least in the northern extratropics.This conclusion is based on the agreement of the inferred NEE variations with a time-explicit atmospheric inversion at well-constraint large spatial scales (Sect.3.2), and the consistency of γ NEE-T with independent calculations from eddy covariance data at small spatial scales (Sect.3.3).Among the reasons for this potentially surprising finding is that the regression is only applied to the interannual anomalies of NEE around its mean seasonal cycle (rather than to the full range of seasonal temperature variations), and that the different behaviours in different seasons have been accounted for.
The results of the NEE-T inversion presented here can be applied to benchmark process models of the land biosphere or Earth system models, as γ NEE-T can also be calculated from the model output (using detrended NEE over the period 1985-2016 for consistency).As its adjustable degrees of freedom are identically applied every year, the regression offers a way to bridge temporal gaps in the atmospheric CO 2 records; it transfers information from the recent data-rich years into the more data-sparse past.Similarly, the NEE-T regression allows to forcast the CO 2 flux for some years, if forcasted air temperatures (and extrapolations of fossil fuel emissions and the ocean exchange) are available.As a further application, the regression may help to uncover smaller decadal trends in the atmospheric CO 2 signal by separating them from the larger interannual responses of NEE.Extending the calculation to the full period of atmospheric CO 2 measurements (since the late 1950ies, see Atmospheric tracer transport is simulated by the TM3 model (Heimann and Körner, 2003) (resolution ≈ 4 • × 5 • × 19 layers) driven by meteorological fields from the NCEP reanalysis (Kalnay et al., 1996).NCEP is used since v4.1 again (rather than ERA-Interim) as only NCEP is currently available before 1980.
Fig.1presents the seasonal and spatial patterns of the "interannual climate sensitivity" as Hovmöller Diagrams, showing longitudinally averaged γ NEE-T in dependence on latitude and month-of-year.The longitudinal average is taken separately over North and South America (left panel), Europe and Africa (middle panel), and Asia and Australia (right panel), respectively.
Biogeosciences Discuss., https://doi.org/10.5194/bg-2018-34Manuscript under review for journal Biogeosciences Discussion started: 22 January 2018 c Author(s) 2018.CC BY 4.0 License.in the global total CO 2 flux are very well constrained from atmospheric CO 2 observations at time scales longer than the atmospheric mixing time (about 4 years)(Ballantyne et al., 2012).Variations on the year-to-year scale are tightly constrained already(Peylin et al., 2013).We thus use the global CO 2 flux from the standard inversion having explicit interannual degrees of freedom as a benchmark.Since the ocean flux is identical in both standard and NEE-T inversion runs, the high level of agreement in Fig.2(top) means that the spatially and seasonally resolved linear NEE-T regression provides already a good approximation to global interannual NEE variations.

Figure 1 .
Figure 1."Interannual climate sensitivity" γ NEE-T in (gC/m −2 /yr)/K shown as Hovmöller diagrams: Longitudinal averages of γ NEE-T are plotted as color over latitude (vertical) and month of the year (horizontal).The stippling indicates robustness: crosses mark values with absolute deviations ≤ 40 (gC/m −2 /yr)/K (1 color level) of all sensitivity cases from the base case.

Figure 2 .
Figure 2. Left: Interannual anomalies of NEE integrated over all land (top), northern extratropical land (middle), and tropical plus southern land (bottom), as estimated by the standard inversion (Sect.2.1, black) and different runs of the NEE-T inversion (Sect.2.2, colour).The gray band comprises the results of the sensitivity cases.Right: Taylor diagrams quantifying the agreement between the NEE-T inversions and the standard inversion.Due to the construction of the Taylor diagram(Taylor, 2001), the horizontal position of a point gives the relative fraction of the reference signal present in the test time series, while the vertical distance of this point from the horizontal axis gives the relative amplitude (temporal standard deviation) of any additional signal components uncorrelated to the reference signal.