As a starting point, we use the existing Bayesian atmospheric CO2 inversion implemented in the Jena CarboScope, run s85oc_v4.1s update ofsee http://www.BGC-Jena.mpg.de/CarboScope/. It estimates spatially and temporally explicit CO2 fluxes between the Earth's surface and the atmosphere based on atmospheric CO2 measurements from 23 stations (marked with * in Table ) each of which spans the entire analysis period (chosen here to be 1985–2016 when more data are available; see for runs over 1957–2016). Using an atmospheric tracer transport model to simulate the atmospheric CO2 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 CO2 mole fractions. In addition, the estimation is regularized by a priori constraints meant to suppress excessive spatial and high-frequency variability in 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 s85oc_v4.1s used here, ocean fluxes are fixed to estimates based on an interpolation of surface–ocean pCO2 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 .

For reference in Sect.  below, we mention here that this standard inversion calculation represents the total surface-to-atmosphere CO2 flux f as a decomposition, f=fNEE,LTadj+fNEE,Seasadj+fNEE,IAVadj+fOceanfix+fFossfix, into adjustable long-term mean terrestrial NEE (fNEE,LTadj), adjustable large-scale seasonal NEE anomalies (fNEE,Seasadj), adjustable inter-annual and shorter-term NEE anomalies (fNEE,IAVadj), the prescribed ocean fluxes (fOceanfix), and the prescribed fossil fuel emissions (fFossfix). 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. ) 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 accommodate their spatio-temporal heterogeneity.

Compared to the standard inversion (run s85oc_v4.1s), the NEE–T inversion (base run s04XocNEET_v4.1s) uses the same transport model and the same prescribed data-based CO2 fluxes of the ocean (fOceanfix) and fossil fuel emissions (fFossfix). It also possesses the same adjustable degrees of freedom representing the long-term mean CO2 fluxes (term fNEE,LTadj) and its large-scale seasonality (fNEE,Seasadj).

The NEE–T inversion differs only by replacing the explicitly time-dependent inter-annual NEE variations (fNEE,IAVadj) with a linear NEE–T regression term plus residual terms: fNEE,IAVadj→γNEE-Tadjw(T-TLT+Seas+Deca+Trend)+(1-w)fNEE,IAVadj+fNEE,Trendadj+fNEE,SCTrendadj. T represents the monthly spatio-temporal field of air temperature taken from GISS and interpolated to the spatial grid and daily time steps of the inversion (Appendix ). Its long-term mean, mean seasonal cycle, and decadal variations including linear trend (TLT+Seas+Deca+Trend) have been subtracted to only retain inter-annual (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 specifically refers to this period. The inter-annual temperature anomaly field is multiplied by unknown (i.e. adjustable by the inversion) scaling factors γNEE-T (the NEE–T regression coefficients). These scaling factors are identical in each year of the inversion, but are allowed to vary smoothly both seasonally (with a correlation length of about 3 weeks such that γNEE-T contains 13 independent degrees of freedom in time, repeated every year) and spatially (with correlation lengths of about 1600 km in the longitude direction and 800 km in the latitude direction, imposing a spatial smoothing on γNEE-T over the same spatial scales as the smoothing imposed on the inter-annual flux anomalies fNEE,IAVadj in the standard inversion). The need for seasonal and spatial resolution of γNEE-T has been inferred from an analysis of the standard inversion results (Sect. ). The a priori spatial and temporal correlations are imposed on γNEE-T to prevent a localization of inverse adjustments in the vicinity of the atmospheric stations. In contrast to the standard inversion, however, where the a priori correlations lead to a smooth NEE field, the NEE result of the NEE–T inversion still retains structure on the pixel and monthly scale from the temperature field. By having only 13 degrees of freedom in the time dimension, the introduction of the regression term also regularizes the inversion further compared with the explicit inter-annual term of the standard inversion, which has 796 degrees of freedom in the time dimension.

Equation () also contains adjustable residual terms (2nd line) to accommodate modes of variability from the atmospheric CO2 signals that cannot be explicitly represented by the regression term and might therefore be at risk of being aliased into spurious adjustments to γNEE-T.

Outside the non-zero period 1985–2016 of the regression term, inter-annual NEE variations are represented by a standard inter-annual term fNEE,IAVadj with weights (1-w) opposite to those of the regression term.

In contrast to the standard inversion using 23 stations with temporally homogeneous records over 1985–2016, the NEE–T inversion uses atmospheric data from 89 stations (Table ) partially with shorter records but spatially covering the globe more evenly (including stations in northern Siberia and 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 inter-annual variability from the NEE–T inversion comes from the regression term using its degrees of freedom (γNEE-T) 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.

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 (2.4 times in the longitude direction and 1.6 times in the latitude direction) for γNEE-T, (2) 4 weeks (rather than 3 weeks) of temporal a priori correlation length scale for γNEE-T, (3) halved a priori uncertainty range for γNEE-T, (4) using ocean CO2 fluxes from the PlankTOM5 ocean biogeochemical process model instead of the fluxes based on pCO2 measurements, (5) taking the gridded monthly land temperature field from Berkeley Earth (www.BerkeleyEarth.org, last access: 29 November 2017) instead of the GISS data set, and (6) using ERA-Interim meteorological fields 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 eight mutually exclusive parts (Table ). In each of the sensitivity cases, one of these parts was omitted, leaving sets of 73 to 82 remaining stations. With this construction, all eight runs still have global data coverage, but every station is absent in one of the runs. If the results depended on any particular station without being backed up by other stations, then the run omitting this station would show a substantial difference from the base run.

The range of results from this ensemble of sensitivity cases will be shown as an uncertainty range around the base case.

For comparison of the estimated sensitivities γNEE-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, last access: 25 October 2017). EC sites (Table ) have been chosen based on having long records (at least 12 years; two sites with 11 years were also included to have more ecosystem types represented). Crop sites have not been included because their flux variability may 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 gap-fill” (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 CO2 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 gNEE-TEC=ΔNEEEC / ΔTEC. We also calculated the confidence interval of the slope for the confidence level 90%, reflecting the uncertainty of gNEE-TEC given the scatter of the monthly values around a linear relationship.

The sensitivities γNEE-T from the inversion and gNEE-TEC 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 γNEE-T has deliberately been made insensitive to the trend (Sect. ). Therefore, we also calculated sensitivities gNEE-TInv from the total monthly mean non-fossil CO2 flux (i.e. including regression and residual terms of Eq. ) 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 gNEE-TEC and gNEE-TInv 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 ageing or slow species shifts, which average out on the larger spatial scales seen by the atmospheric inversion.

As a starting point, we present the results of the NEE–T inversion in terms of γNEE-T, which is the local regression coefficient between inter-annual variations in NEE and temperature, resolved seasonally (Sect. ). As γNEE-T not only reflects direct temperature responses but also responses to other environmental variables that co-vary with temperature (such as water availability, incoming solar radiation), we refer to it as inter-annual climate sensitivity.

Figure  presents the seasonal and spatial patterns of the inter-annual climate sensitivity as Hovmöller diagrams showing longitudinally averaged γNEE-T with dependence on latitude and month of the 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). This representation summarizes the essential variations of γNEE-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 γNEE-T in spring (and to a lesser extent autumn), which is consistent with photosynthesis being temperature limited such that higher-than-normal temperatures lead to more negative NEE (i.e. larger-than-normal CO2 uptake) and vice versa. Warmer conditions tend to coincide with higher incoming solar radiation in May and/or June in the northern extratropics (according to a correlation analysis of CRUNCEPv7 data, not shown), which would tend to amplify the direct temperature effect. In summer when photosynthesis is no longer limited by temperature, we find positive γNEE-T values. Such positive γNEE-T is consistent with enhanced respiration in warmer summers, but also with the fact that warmer-than-normal periods are often also drier, leading to reduced photosynthetic uptake or enhanced fire activity. In winter, NEE is not found to respond much to inter-annual climate variations. The interpretation of the seasonality of γNEE-T is confirmed by its latitude dependence: consistent with the later spring and shorter summer in the higher northern latitudes, the period of negative γNEE-T starts later there, and the period of positive γNEE-T is shorter.

In the tropics, we find stronger and less systematic variations in γNEE-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. ). This reveals that the seasonal variations in γNEE-T are of limited robustness here. Nevertheless, a clear feature in the tropics is the dominance of positive γNEE-T values.

In southern extratropical 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 conceivably 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 pCO2-based ocean prior flux is actually less well constrained in the southern extratropics due to the much smaller density of pCO2 data).

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 inter-annual variations of global total NEE estimated by the NEE–T inversion are very similar to those estimated by the standard inversion (Fig. 2a). The agreement is confirmed by high correlation (Fig. 2d). For interpretation, we note that variations in the global total CO2 flux are very well constrained from atmospheric CO2 observations at timescales longer than the atmospheric mixing time (about 4 years) . Variations on the year-to-year scale are already tightly constrained . We thus use the global CO2 flux from the standard inversion with explicit inter-annual degrees of freedom as a benchmark. Since the ocean flux is identical in both the standard and NEE–T inversion runs, the high level of agreement in Fig.  (panels a and d) means that the spatially and seasonally resolved linear NEE–T regression already provides a good approximation of global inter-annual NEE 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. 2b, c and e, f). 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, inter-annual 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 can no longer be expected to be well constrained from the atmospheric data at the regional scale. 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. .

Figure  compares inter-annual 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 orange line with the surrounding grey band gives the sensitivities γNEE-T from the various NEE–T inversion runs as in Fig.  taken at the respective pixels enclosing the EC sites. The black dots are the sensitivities gNEE-TEC calculated by the explicit linear regression of monthly EC flux records against the co-measured monthly air temperature (Sect. ).

To allow for a fairer comparison between inversion results and EC data, additional colour dots give sensitivities gNEE-TInv calculated from the NEE–T inversion results in the same way and subsampled at the same months as for the EC data (Sect. ). At most EC sites, the sensitivities calculated by the inversion itself (γNEE-T, orange lines) or by explicit regression afterwards (gNEE-TInv, 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. ) on gNEE-TInv 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. ), the sensitivities from the EC data and the atmospheric NEE–T inversion have a similar order of magnitude and similar seasonal patterns for a majority of EC sites (Fig. ). For most sites and 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 of panels in Fig. ) and at evergreen needleleaf forest (ENF) sites in temperate northern latitudes (line 2 and rightmost part of line 3).

Given that we found robust seasonal patterns of γNEE-T which can be interpreted in terms of the fundamental physiological processes (Sect. ), that these patterns are compatible with inferences from independent ecosystem-scale eddy covariance (EC) measurements (Sect. ), and that the corresponding inter-annual NEE variations are compatible with the atmospheric constraint on the most reliable large scales (Sect. ), 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 the 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 inter-annual NEE variations on regional scales than the standard inversion, which smoothly interpolates NEE on scales smaller than station-to-station differences (compare to the last paragraph of Sect. ).

Note that as EC data measure fluxes on small spatial scales (a few hundreds of metres), 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. In contrast to the fluxes, however, derived relationships (such as the NEE–T relationships considered here) may well be able to bridge this scale gap.

Besides the inter-annual variations, the NEE–T inversion also reproduces the small negative trend in NEE through its residual term fNEE,Trendadj in Eq. () (Fig. ). Likewise, it reproduces the northern extratropical increase in seasonal cycle amplitude through its residual term fNEE,SCTrendadj (not shown).

In contrast to the northern extratropics, we did not find conclusive seasonal patterns of γNEE-T in the tropics (Sect. ). However, despite the substantial uncertainty range of γNEE-T (Fig. ), the sensitivity cases reproduce almost identical inter-annual NEE variations in the tropics (see the narrow grey band around the NEE–T estimate in Fig. 2c). This underlines the fact that pan-tropical NEE variations are actually well constrained from the atmospheric data, while the seasonal differences in γNEE-T arise to compensate for the set-up differences among the sensitivity cases. As shown below (Sect. ), all the seasonally different γNEE-T estimates correspond to a similar effective sensitivity (having a positive value) on yearly timescales. Due to this, the NEE–T inversion is found to possess predictive skill on the timescale of the El Niño–Southern Oscillation .

The positive effective γNEE-T in the tropics (Sect. ) is consistent with the strong positive correlation of atmospheric CO2 growth with large-scale tropical annual temperature . This is unlikely to arise from a direct temperature effect, however, because process studies e.g. point to water availability rather than temperature as the dominant control on the ecosystem scale. This is also confirmed 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. ). A strong correlation with temperature can still arise statistically due to the strong link of temperature and precipitation anomalies over larger spatial scales . Moreover, the vapour pressure deficit (VPD) controlling photosynthesis responds particularly strongly to temperature variations in the warm tropical climate due to the non-linearity of the VPD(T) dependence . Further, T is spatially coherent over much larger areas in the tropics, while variability in water availability is local and averages out over larger spatial scales . Nevertheless, a direct temperature effect in the tropics was found by , at least for a component flux of NEE (wood production) in 12-year plot data.

Data-based empirical relationships between inter-annual NEE variations and air temperature variations have been proposed in the literature as benchmarks to evaluate biogeochemical process models. For example, calculated an effective global climate sensitivity of 5.1±0.9 PgC yr-1 K-1 over 1960–2010 by regressing the annual CO2 growth rate observed at the station Mauna Loa (Hawaii) (taken as a proxy for the global total CO2 flux) against 30∘ N–30∘ S (both land and ocean) averaged air temperature (after detrending both time series by subtracting an 11-year running mean). In a similar way (using the average atmospheric growth rate from a varying set of background sites, a slightly different time series treatment, and 24∘ N–24∘ S land temperature), obtained a value of 3.5±0.6 PgC yr-1 K-1 over 1959–2011. regressed the mean Mauna Loa and South Pole CO2 growth rates against 23∘ N–23∘ S vegetated land temperature over moving 20-year windows and reported effective global climate sensitivities between 3.4±0.4 PgC yr-1 K-1 (during 1960–1979) and 5.4±0.4 PgC yr-1 K-1 (during 1992–2011).

The inversion results presented here allow us to extend these benchmarks in two ways. As a first extension, we can evaluate to what extent the inter-annual variations in local or averaged atmospheric CO2 growth rates are indeed equivalent to the inter-annual variations in the global total CO2 flux (as implicitly assumed in the above-mentioned studies) and to what extent the global total CO2 flux is indeed representative of global terrestrial NEE or, even more specifically, tropical NEE. This can be evaluated here because all these time series (spatially explicit CO2 fluxes with all their contributions, as well as the corresponding atmospheric CO2 variations at the measurement stations) are available within the inversion calculation. To ensure a mutually consistent treatment of these time series, we used running yearly averages (January through December, February through next January, etc.) of the flux time series and running yearly differences (next January minus January, next February minus February, etc., multiplied by 2.12 PgCppm-1; ) of the atmospheric CO2 time series. All these inter-annual time series were then regressed over 1985–2016 against annual tropical land temperature (25∘ N–25∘ S) derived from the same temperature field without decadal variations as used in the NEE–T inversion. The resulting effective climate sensitivities are shown in Fig. . The sensitivities of the total CO2 flux (solid bars in the middle) calculated from the standard inversion (black) or from the NEE–T inversion (orange) are similar to each other and fall in between the values by and . Part of the discrepancies between these results can be attributed to the different time periods and the different time series treatments (in particular, to the extent to which decadal variability has been removed). Figure , however, reveals another reason for the discrepancies: the sensitivity of the Mauna Loa growth rate (middle hashed blue bar) is larger than that of the global flux (solid bars). This cannot be due to a deficiency in the inversions to fit Mauna Loa's variability because the modelled Mauna Loa sensitivities (hashed bars next to the middle blue bar) agree well with the observed ones. Thus, a sensitivity calculated from the Mauna Loa growth rate as in somewhat overestimates the sensitivity of the global flux. The Mauna Loa sensitivity is still much closer to that of the global CO2 flux than sensitivities calculated from most other stations: southern extratropical stations like the South Pole or the mean of Mauna Loa and the South Pole as in lead to a substantial underestimation (it is unclear why the sensitivity reported by for the recent 1992–2011 period is nevertheless even higher than our Mauna Loa value), while northern extratropical stations like Point Barrow lead to an even stronger overestimation than Mauna Loa. This suggests that using a varying mixture of stations as in can induce further errors, in particular when possible changes in sensitivity are considered. We note that the atmospheric inversions benefit from using multiple station records because the transport model links the atmospheric CO2 signals to their different areas of origin rather than the instantaneous link of the atmospheric signals to the global flux as in the direct use of station records.

Care is also needed in the interpretation of the estimated effective sensitivities: the sensitivity of the total CO2 flux (solid bars) underestimates that of global NEE only (horizontally hashed bars) because the ocean flux is substantially anti-correlated with NEE on the inter-annual timescale. The sensitivity of tropical-only NEE (vertically hashed bars) is smaller than that of global NEE, though the reduction is less than according to the ratio of land area, confirming the dominance of tropical NEE variations.

As a second extension of process model benchmarking, the data-based estimates of the spatially and seasonally resolved γNEE-T from the NEE–T inversion can directly be employed as target values by regressing the NEE simulated by the terrestrial biosphere or Earth system model against the model temperature for individual small regions and seasons across the years 1985–2016 and comparing these model-derived local and season-specific sensitivities to the data-based values presented here (using the ensemble of sensitivity cases as a measure of uncertainty in γNEE-T). Importantly, before regressing, the model NEE and temperature fields need to be deseasonalized, detrended, and filtered in the same way as done for the observed temperature in the NEE–T inversion (Sect. ) because the numerical γNEE-T values are somewhat specific to the chosen filtering, in particular to the exact way to remove decadal variations (as is also the case for the effective global climate sensitivity targets by , and ). For the northern extratropics, where γNEE-T is quite robustly constrained and shows distinct spatial and seasonal patterns (Sect. ), this offers a much more detailed benchmark of the process representation in the models than the existing single-valued effective climate sensitivity of the global CO2 growth rate. For the tropics, unfortunately γNEE-T is not constrained well enough to do that, but due to the fact that pan-tropical NEE variations are nevertheless quite robust (Sect. ), the effective climate sensitivity of tropical NEE from Fig.  (4.2 PgCyr-1K-1 with a range across the sensitivity cases of 3.8…4.4 PgCyr-1K-1) may be used as a specifically tropical target instead.

We also tested the algorithm 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 inter-annual timescales. It also means that a multivariate regression would – despite a mathematically unique partitioning into contributions of the individual explanatory variables – likely not yield a 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 the 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.