The use of δ13C observations alongside CO2 observations constitute a useful change to the traditional CO2-only CTDAS application, as it provide an additional constraint on carbon surface fluxes and isotope exchange processes in plants. The rationale behind this is that the 13CO2 and 12CO2 contents in the atmosphere are affected through the same CO2 pathways from land and ocean surfaces. There are, however, specific processes that change the 13CO2 exchange fluxes slightly differently from 12CO2 fluxes. We can write a global mass balance for atmospheric δ13C (δa) so that the different isotopic processes are explicitly defined and dependent on total CO2 fluxes for the derivation of Eq. 1 see. We can then identify the (1) emission forcing terms, (2) net exchange isotope forcing terms, and (3) gross-flux isodisequilibrium forcing terms: Caddtδa=Fffδff-δa+Ffireδfire-δa[emission forcing terms]+Nbϵph+Noϵao[net exchange isotope terms]+Fbaδb-δbeq[terrestrial isodisequilibrium forcing terms]+Foaδaeq-δa[ocean isodisequilibrium forcing term], where Ca is the total carbon content (unit mol or mass) in the atmosphere (in the form of CO2). The subscripts ba and oa denote the direction of the one-way gross fluxes (unit mol or mass per unit time). For example, Fba refers to the respiratory release of CO2 from terrestrial biosphere to atmosphere. The isotopic ratios of 13C/12C are expressed as δxx (‰), where the subscripts refer to the signature in biosphere vegetation and soils (b), in biomass burning flux (fire), or in the fossil fuel emission flux (ff). The signature δaeq depicts the isotopic ratio of CO2 that is in equilibrium with the ocean surface and δbeq depicts the ratio in the terrestrial biosphere that would be in isotopic equilibrium with the current atmosphere, which is more depleted in 13CO2 than when the biomass was formed years ago. Nb and No refer to net exchange fluxes (gross release minus gross uptake) of CO2, and Fff and Ffire are the fossil fuel and biomass burning CO2 emissions, respectively.

The terrestrial (photosynthetic) isotopic discrimination in Eq. () is expressed as ϵph=δbeq-δa≈-Δph (‰), and can be derived from a CO2 gradient-weighted average of different isotope fractionation effects during the transfer of CO2 molecules from the canopy air until their reaction with the enzyme Ribulose-1,5-bisphosphate (Rubisco) in the chloroplasts of the plant leaf. There are two main fractioning effects along this pathway: the plant fractionates with Δs=4.4 ‰ when CO2 diffuses from leaf boundary through leaf stomata, and with Δf=28 ‰ during carboxylation. Smaller fractionation effects occur during diffusion between canopy air and leaf boundary (Δb=2.9 ‰), and during dissolution of CO2 in mesophyll water (Δdiss=1.1 ‰) and transport to chloroplasts (Δaq=0.7 ‰). The parameterization of Δph for C3 plants has been described by and takes the following form as in : Δph=Δbca-csca+Δscs-cica+Δdiss+Δaqci-ccca+Δfccca, where ca, s, i, c represent CO2 partial pressures in canopy air space, leaf boundary layer, stomatal cavity, and in the chloroplasts, respectively. The overall discrimination Δph value reflects mostly the fractionation step with the highest resistivity . For example, during a drought when the leaf's stomatal conductance is lowered in an attempt to prevent evaporative water loss, the diffusive Δs is the most limiting factor resulting in a lower overall Δph. The opposite happens under more favorable environmental conditions when stomatal aperture is higher and carboxylation is the limiting factor, resulting in a higher overall Δph.

The overall discrimination leaves the atmosphere relatively enriched and plants relatively depleted in 13C. C3 plants are depleted in 13C by approximately -20 ‰ relative to the atmosphere and C4 by approximately -4 ‰ as they can assimilate 13CO2 more efficiently with Rubisco. C4 photosynthesis is essentially a more complex form of carbon fixation than C3 photosynthesis as it shields Rubisco in the bundle sheath cells from wastefully binding with oxygen rather than carbon dioxide.

In addition to discrimination effects during photosynthetic uptake, we also need to account for isotopic enrichment of the atmosphere through respiratory release of carbon with a heavier isotopic signature after spending from one year to several decades or more in the plant and soil organic matter. This respiratory part will still enrich the atmosphere with 13CO2 even if net CO2 uptake equals zero , and we refer to it as the terrestrial isodisequilibrium flux in Eq. ().

Discrimination associated with the dissolution of CO2 in ocean water is much smaller and spatiotemporally homogeneous (ϵao=-2 ‰) than in the terrestrial biosphere. The difference between ocean and land discrimination provide an additional constraint on the net fluxes and has already been demonstrated in previous studies e.g.,. We also have to account for isotopic disequilibrium that exists between the atmosphere and oceans. This isodisequilibrium flux is associated with the outgassing of CO2 from the ocean waters, and has globally an enriching tendency on the δa signatures.

Besides the land and ocean discrimination and disequilibrium forcing terms we have two additional terms in Eq. (). Firstly, there are CO2 emissions due to combustion of fossil fuels, which have a distinct isotopic signature depending on the organic fuel type, but globally its signature is approximately δff=-30 ‰. Secondly, there are CO2 emissions due to biomass burning, where δfire bears the signature of the 13CO2 and 12CO2 fluxes of Ffire, which is typically the signature of burnt leaf foliage, woody tissue, and the aboveground litter .

We followed the method presented by for designing the joint CO2 and δa data assimilation system. The architecture is similar to the CarbonTracker Data Assimilation Shell (CTDAS) v1.0 discussed in detail by . Just like the traditional CO2-only inversions, we aim to close the CO2 budget through fluxes from fossil fuel combustion, biomass burning, and net exchange fluxes from the terrestrial biosphere and oceans. In addition, we also intend to simultaneously close the 13CO2 (13Ca) budget using the same set of CO2 fluxes. Isotopic signatures themselves are not conserved quantities, therefore we calculate conserved mole fractions of CO2 and 13CO2 in our transport model, which we can sample at designated locations and times to calculate δa. The combined set of balance equations (unit mol per unit time) takes the following form: ddtCa=Fff+Ffire+λbNb+λoNo,ddt13Ca=13Fff+13Ffire+13Nb+13No. After some manipulation of Eqs. () and (), by following , we obtain the following: ddt13Ca=FffRff+FfireRfire+λbNbλdiscrϵph/1000+1Ra+λoNoϵao/1000+1Ra+Db+Do. The 13Ca balance equation is now a close analog of Eq. (), because 13Ca is a function of discrimination, Nb and No, and isodisequilibrium fluxes. The R values depict the isotopic ratio of 13CO2/CO2 in the atmosphere (Ra), in fossil fuel (Rff), and biomass burning emissions (Rfire), and their values are approximately 0.011. The isodisequilibrium fluxes from land and ocean surfaces are here simply shown as Db and Do, respectively. The term λdiscrϵph/1000+1 represents the optimized ratio between the isotopic signature in the photosynthetic flux and atmosphere (Rph/Ra), and ranges between 0.980 and 0.996 depending on the prior ϵph and discrimination scaler λdiscr. The term ϵao/1000+1 represents the ocean flux ratio and is held constant at 0.998 assuming ϵao=-2‰, and is not optimized. The parameters λb and λo represent the linear scaling factors for each week and ecosystem region (ecoregion) to adjust the net carbon exchange over land and ocean surfaces, respectively. For land, the scaling factor is associated with one scalar per ecoregion based on the land use classification following (Fig. ). The terrestrial biosphere is further divided into 11 larger geographical areas also known as TransCom regions . Like in the early CarbonTracker releases, each of the 11 TransCom land regions contains a maximum of 19 ecoregion types (Fig. ) and the ocean is divided into 30 large basins encompassing large-scale ocean circulation features. This gives a maximum of 239 (= 11 ⋅ 19 + 30) different scaling factors each week . The new parameter is λdiscr, which is used to scale a maximum of 209 terrestrial discrimination parameters per week. They are associated with the same 1∘ × 1∘ ecoregions as the terrestrial fluxes. Note that the maximum number of scalable land parameters is in reality ∼130, and not 209, because not each land region contains all 19 ecoregion types.

The terrestrial net exchange term in Eq. () (λbNbλdiscrϵph/1000+1Ra) includes two multiplicative scaling factors, making the required solution nonlinear. This poses a potential problem where variations in net exchange and discrimination are canceling each other out to such a degree that it leads to low signal-to-noise ratios, especially for discrimination. This is further investigated in Sect. . The fossil fuel combustion, biomass burning, and terrestrial and ocean isodisequilibrium fluxes all remain fixed a priori estimates. We describe in Sect.  the tuning of the latter disequilibrium fluxes to close the long-term mean balance of δ13C in our system.

The scaling factors λb, λo, and λdiscr are the unknowns that are combined in state vector x (with dimension s), for which we will try to find an optimal solution by minimizing a quadratic cost function. In this function, there is a balance between information drawn from the observation vector y (with dimension m) with a covariance R (m × m) and prior knowledge from the state vector xp (s) with a covariance P (s × s): J=y-HxTR-1y-Hx+x-xpTP-1x-xp.

The observation operator H (m) represents the atmospheric transport model that propagates the surface fluxes from Eqs. () and () and samples accordingly the mole fractions of CO2 and 13CO2 at the same location and moment as the observations y.

The solution for x that minimizes J is x=xp+K⋅y-Hxp, where K represents the Kalman gain matrix . Equation () can be expressed in terms of λ (posterior scaling factor), λp (prior scaling factor), and separate measurements of CO2 (c) and δ13C (δ) with dimensions (j) and (k), respectively: λbio1..λbio209λoce210..λoce239λdiscr240..λdiscr448=λpbio1..λpbio209λpoce210..λpoce239λpdiscr240..λpdiscr448+K⋅c1c2c3c4..cjδ1δ2δ3δ4..δk-Hλpbio1..λpbio209λpoce210..λpoce239λpdiscr240..λpdiscr448. In state vectors x and xp, the scaling factors for terrestrial discrimination are appended after the flux scaling factors. Similarly in the observation vectors y and H(xp), the δ13C observations are appended after the CO2 observations. The K matrix determines how much a scaling factor needs to change given a set of CO2 and δ13C measurements. The matrices R and P modulate whether observations or bottom-up estimates are given more weight to the solution.

The P matrix contains 448 × 448 elements in total and is shown in Fig. . The first 209 × 209 element block contains the land flux uncertainties per ecoregion and their spatial correlations. The second 30 × 30 element block contains the ocean flux uncertainties per ocean basin. We gave the land scalars and the ocean scalars a maximum uncertainty of 80 and 100 % along the diagonal, respectively, as in earlier CarbonTracker releases. The third 209 × 209 element block contains the terrestrial discrimination scalars with a maximum uncertainty of 20 % along the diagonal with an identical spatial correlation structure as applied to the terrestrial flux uncertainty scalars. This implies that we can scale ϵph by a factor of 1.0 ± 0.2, and thus for a typical C3 plant (ϵph=-20‰) the mean and uncertainty lies around -20 ± 4 ‰. Furthermore, there is covariation between ecoregions of nearby TransCom regions, e.g., between North America boreal and temperate regions and between Europe and Eurasian regions. We did not allow covariances between net exchange and discrimination in order to give the parameters enough freedom in the solution.

The covariance structure of R is similar to CO2-only CTDAS, but is extended with additional uncertainties in δ13C observations. These expected uncertainties quantify our ability to simulate observations given the uncertainty in atmospheric transport modeling and measurement errors. Section  gives an overview of the used uncertainties for each observation category.

With this inversion framework in place CTDAS-C13 progresses in a similar manner as the traditional CO2-only CTDAS. For each week, the set of unknowns in the state vector are updated in a cycle that contains two steps. First there is a forecast step, which is driven by our fluxes and current background state vector xp to forecast an ensemble of CO2 and 13CO2 mole fractions 5 weeks ahead in time. This is followed by an analysis step to determine the new state of the system with Eq. () such that it is consistent with the observations for the current week of the cycle. The analyzed state is propagated to the next cycle using the same model as Eq. 1 of the Supplement, and with this new state a new cycle begins with another forecast step to forecast a new ensemble of the background state 5 weeks ahead in time, now with an additional set of observations from a new week. The ensemble for each tracer is created from 150 ensemble members to provide a Gaussian probability density function of the state vector.

The simulation of atmospheric transport is provided by the two-way nested global transport model TM5 release 3 . This application simulates the atmospheric transport of CO2 and 13CO2 at a global 6∘ × 4∘ resolution, with no nesting. It is driven by 3 hourly meteorological output from ECMWF ERA-Interim reanalysis . All the CO2 and 13CO2 flux fields provided to the model are in units of molCO2m-2s-1 and mol13CO2m-2s-1, respectively. Atmospheric concentrations of CO2 and 13CO2 are calculated as mole fractions in molmol-1. Signatures of δ13C are computed to the relative per mil value using the following conversion formulation in order to facilitate comparison with observations: δ13C=RRref-1⋅1000, where Rref is the VPDB reference ratio adopted for 13CO2/ (12CO2 + 13CO2), which is 0.011112 . R is the ratio of simulated mole fractions 13CO2/CO2.

We performed four inversion experiments as summarized in Table . The simulation period covered the years 2000 through 2011, but our analyses focused on the period 2001–2011, i.e., we omitted the spin-up year. As a benchmark, we performed a traditional inversion to estimate the net carbon exchange fluxes of the ocean and land using only CO2 observations, which we call TRAD-CO2. For the second inversion, we added δ13C observations alongside CO2 to constrain only the exchange fluxes; therefore, we call this experiment TRAD-CO2C13. The experiment in which we estimated discrimination and fluxes simultaneously is called NEW-CO2C13. This inversion is nonlinear because the discrimination scaling parameter is in the same multiplication term as the net flux scaling parameter. The fourth experiment was a linear inversion experiment where we estimated only the land discrimination parameter using δ13C data. We call this experiment NEW-2STEP because discrimination was solved in a second step after optimization of the net exchange fluxes. This means that ocean and land fluxes were derived from the optimized state vector and its covariance from the TRAD-CO2 inversion.

We first evaluate the global CO2 and δ13C budgets simulated by our combination of fluxes as described in Sect.  to assess where we expect the largest changes in the optimization. As shown in Fig. a, the prior net exchange flux estimates and unscaled disequilibrium fluxes were not large enough to close the gap with the observed tracers, CO2, and δ13C. The sum of the flux arrows overestimated the annual CO2 growth rate along the x axis and overestimated δ13C depletion along the y axis. In a traditional TRAD-CO2 inversion, the estimated ocean and land fluxes closed the CO2 budget along the x axis. The leverage in the net exchange fluxes was, however, not large enough to close the δ13C budget along the y axis as well. In an inversion that includes δ13C observations, the gap in δ13C would adjust the CO2 flux magnitudes and ocean/land partitioning to unrealistic magnitudes in an effort to overcome the large offset between the simulated and observed δ13C growth rate. Instead we chose to use scaled disequilibrium fluxes in our inversions in order to estimate land and ocean CO2 flux magnitudes that remain close to the results of other traditional carbon cycle budgeting studies . We chose the disequilibrium fluxes to adjust because (1) the exact magnitudes of these terms are still unknown due to uncertainties in the carbon pool turnover, gross carbon fluxes, and isotopic discrimination, and (2) these terms do not affect the CO2 mass balance. It assured a closed mean δ13C budget of our inversions without creating unrealistic carbon sinks over land and oceans (Fig. b). Most importantly, closing the climatological (11 year) budget allowed us to focus our study on interannual changes in the net fluxes and photosynthetic discrimination.

We obtained the best fit with δ13C data when the land and ocean disequilibrium flux were scaled by a factor of 1.2 without changing either their spatial patterns or time trends. This is consistent with recent double deconvolution studies where the global δ13C balance was closed with a factor of 1.3 in land and ocean disequilibrium . Our value was determined after assessing an ensemble of different sets of scaling numbers (ranging from 1.1 to 1.5) in a forward TM5 simulation, which was driven by the optimized net land and ocean flux estimates from the TRAD-CO2 experiment. This assured a closed multi-year δ13C budget together with a closed multi-year CO2 budget. As selection criteria, we used (1) the 11 year mean root mean square difference (RMSD) of a large selection of δ13C sites and (2) the average bias between simulated and observed values. In the non-scaled disequilibrium simulation we obtained a RMSD of 0.165 ‰ and a bias of -0.110 ‰ averaged over all sites. The optimal result was obtained with a scaling factor of 1.2, which reduced the RMSD to 0.079 ‰ and the mean bias to -0.010 ‰. Note that these scaling factors cannot be applied to other inversion studies because the disequilibrium scaling factors are tuned for this particular system and time period.

To demonstrate our procedure in terms of individual data sets, we refer to Fig. . After scaling the disequilibrium fluxes and using optimized net carbon exchange from the TRAD-CO2 inversion, time series of δ13C at 32 of the 46 Northern Hemisphere sites showed no remaining significant trend (sites where p value > 0.05) in the summer residuals, and the residuals from the trend lines were within or close to the MDM specified for our dual-species inversions. Some of the sites with remaining trends are located at great distances from large continental carbon sources and sinks, and exert little influence on the posterior λdiscr parameter (e.g., CHR, GMI). Some of the other sites were assigned a large MDM (e.g., BAL, NWR, TAP) giving them less weight in the estimation of the posterior λdiscr parameter. The collection of sites with remaining trends do not seem to have a systematic geographic pattern and are likely reflecting a change in local oceanic or biospheric isotope exchange, such as must be the case for the Bermuda West (BMW, non-significant positive trend) and Bermuda East (BME, significant downward trend) site.

With the long-term trend of δ13C appropriately captured, we proceeded to optimize NEE and Δph with our new framework (NEW-CO2C13). We show that this inversion further reduced δ13C residuals (Fig. a), without compromising (nor strongly improving) the fit to CO2 (Fig. b) that we attained from the TRAD-CO2 inversion. In Fig. a the ratio of δ13C RMSD of NEW-CO2C13 to δ13C RMSD of the TRAD-CO2 inversions was at most sites smaller or equal to 0.95 (indicating a significantly higher accuracy of NEW-CO2C13 in form of bias and noise reduction): δ13CRMSD(NEW-CO2C13)δ13CRMSD(TRAD-CO2)<0.95.

In Fig. b, the ratio of CO2 RMSD of NEW-CO2C13 to CO2 RMSD of TRAD-CO2 was at most locations between 0.95 and 1.05. This suggests that the two atmospheric constraints applied are complementary, and there is no indication that the TRAD-CO2 results from CarbonTracker were inconsistent with δ13C measurements. This is an important prerequisite for a credible estimate of discrimination in our system. Furthermore, Fig. a shows a notable latitudinal divide in the reduction of δ13C RMSD, indicating the utility of NEW-CO2C13 in the Northern Hemisphere due to the large availability of measurements and scalable discrimination parameters.

At sites like Alert (Nunavut, Canada) the NEW-CO2C13 inversion provided a better fit to the measured data than the TRAD-CO2 inversion (Fig. ). The 11 year averaged δ13C residuals were close to zero for both inversions, as the disequilibrium flux was tuned specifically to prevent large residuals in a-priori simulated δ13C as described in Sect. . The 1σ SD of the δ13C residuals at Alert were smaller in the NEW-CO2C13 inversion in comparison to TRAD-CO2 due to the additional optimization of Δph alongside net exchange fluxes. The CO2 residuals for Alert in Fig.  were for both inversions almost identical.

Simultaneously optimizing both λdiscr and λbio is inherently nonlinear and thus possibly problematic for our assimilation system; therefore, we tested the validity of our approach in the NEW-CO2C13 inversion. We hypothesized that a region's net carbon uptake and discrimination would change in a similar fashion in the nonlinear inversion, as it would for a linear inversion. The linear inversion experiment consisted of two consecutive steps: (1) the optimization of the net exchange fluxes using only CO2 observations (TRAD-CO2) followed by (2) the estimation of the land discrimination parameter using only δ13C observations (NEW-2STEP). In the nonlinear NEW-CO2C13 inversion the optimization of fluxes and discrimination was done simultaneously. For net carbon uptake by vegetation, we refer to net ecosystem exchange or NEE defined as positive when CO2 is taken up from the atmosphere. For plant isotope discrimination we refer to Δph in per mil, which is defined as positive.

As shown in Fig. , the 11 year mean NEE for the 11 land TransCom regions are very similar in the nonlinear NEW-CO2C13 and linear TRAD-CO2 inversions. Deviations are in the order of tens of teragrams, and within 1σ SD of the flux interannual variability (IAV). Figure  also shows the impact of C4 photosynthesis on the mean TransCom aggregated Δph values. In the boreal regions, where there is very little C4 plant growth, the discrimination is at its maximum (approximately 20 ‰, 5 ‰ above the global average), but in regions where there is C4 plant growth (e.g., due to agriculture in the United States or savannas in Africa) the mean Δph values are lower (approximately 12–15 ‰). These regional patterns of Δph imposed by SiBCASA (see also Fig. ) are maintained by the NEW-CO2C13 inversion framework. Because we aimed to retrieve robust temporal patterns of IAV, the most relevant indicators for the robustness of our nonlinear inversion approach are given by the correlation coefficients (r) between the two types of inversions. We calculated r for NEE and Δph between the linear and nonlinear inversions. As the seasonal cycles in uptake and discrimination are largely dictated by the prior estimates, we removed them using a 3 month boxcar mean smooth curve fitting to obtain the anomalies relative to the seasonal trend. The NEE in NEW-CO2C13 is very similar to the NEE in TRAD-CO2, as indicated by the high r values (> 0.96 for N = 52 ⋅ 11 weeks) for all TransCom regions. The r values are lower for Δph, but still exceed 0.75 in the Northern Hemisphere. The correlation is particularly high over North America boreal, North America temperate, and European regions. Smaller correlations are obtained in tropical and temperate South America and tropical Asia. This is expected, however, as these regions typically suffer from a lack of observational constraints.

The linear NEW-2STEP inversion estimated the same large increase in discrimination IAV as in the nonlinear NEW-CO2C13 inversion for the Northern Hemisphere in comparison to the first-guess estimate of SiBCASA (8-fold increase in SD, see Table ). In addition, we also found in both inversions a strong positive correlation between Δph and NEE on annual time scales (r=0.79) with a significant slope (p=0.001, 95 % confidence interval of a two-sided distribution with 9 degrees of freedom). In years when annual mean NEE is low (less carbon uptake), the Δph is low too (less discrimination), implying that stomata have partially closed, and vice versa. This correlation did not emerge in the TRAD-CO2 estimate based on atmospheric CO2 observations alone, and it also did not emerge if δ13C observations were additionally used in the TRAD-CO2C13 estimate, to estimate NEE but not Δph. The SiBCASA terrestrial biosphere model that provides the first-guess NEE and Δph of our data assimilation framework based on commonly used drought response parameterizations, simulated neither the large IAV in NEE and Δph nor their strong correlation. It is evident from the NEW-2STEP inversion that changes in Δph and the correlation with NEE were driven by δ13C observations, and were not a symptom of the systems inability to separately estimate NEE and Δph variations. This suggests that the estimated IAV of Δph in the nonlinear inversion is truly a signal retrieved from δ13C that would otherwise be aliased erroneously into the carbon fluxes or not retrieved at all.

A closer inspection reveals that the reported correlation between the Northern Hemisphere's NEE and Δph in Table  could indicate a moisture-driven response on the ecosystem level. We identified several moments of severe to extreme drought as characterized by the Standardized Precipitation and Evaporation Index (SPEI; , ) below -1.0 that covered an extensive area of more than a million square kilometers in the United States. These droughts are described in literature as the droughts (or heat waves) of summer 2002 and 2011 . The annual averaged maps of SPEI for 2001–2011 are shown in the top panel of Fig.  calculated for the Northern American temperate TransCom domain. Independent of the SPEI drought index, we estimated changes in Δph and NEE over the same American domain with the NEW-CO2C13 inversion using atmospheric CO2 and δ13C data (Fig.  middle and lower panels). A correlation between Δph and SPEI could only be established by applying an area weighting function to the SPEI index to give years that experienced large and severe droughts, the strongest association with reductions in Δph. We used the following function for the Weighted Drought Index (WDI): WDI=∑i=1SPEI[i]⋅Grid-cell-area[i]Total-area.

In words, we sum over the product of the SPEI index and the grid cell surface area where SPEI is below -1.0 and subsequently we divide it by the total area of the TransCom domain. Hence, the WDI is an expression of the drought in terms of the surface area that is affected. A larger drought surface area will result in a more negative WDI. Using this function, we see that the lower values for Δph correspond strongly with years of low SPEI over large serried areas, indicating a temporal correlation of r=+0.75 between the SPEI variable and Δph (see correlation in Fig.  with a significant slope: p=0.008, 95 % confidence interval of a two-sided distribution with 9 degrees of freedom). The two largest anomalies (>1σ of 11 year IAV) in annual mean Δph correspond with low SPEI in 2002 and in 2011. A third notable drought as recorded in SPEI happened in 2006; although carbon uptake was reduced, it did not amount to a significant signal in Δph. Similar correlations do exist over other parts of the Northern Hemisphere in our inversion solution. For instance, severe droughts in western Europe (2003) and Russia (2010) lowered the discrimination by 1.0 ‰, and exceeded more than 1σ SD of its 11 year IAV (not shown).

In addition, in years when Δph is low, the annual mean NEE tends to be low too, possibly as a result of reduced GPP. This implies that leaf stomata have partially closed and are therefore affecting both Δph and carbon uptake from photosynthesis. The reduction of the optimized net carbon sink for North America is 100–400 TgCyr-1 during the drought years of 2002, 2006, and 2011 (in comparison to their surrounding years).

These correlations that are averaged over continent sized areas do, however, breakdown on smaller scales. On regional scales, we observed a partial misallocation of the model adjustments of NEE and Δph in comparison to SPEI. This is largely a consequence of our limited capacity to monitor CO2 and δ13C. For example, for North America temperate 2002, where the drought index was negative over the mountain states, the impact on the carbon cycle was strongest over the eastern forests of the United States. In these forest ecosystems, CO2 exchange is much stronger than over the mountains, and hence their impact on atmospheric δ13C as well.

Notice that the prior net carbon sink is underestimated in comparison to the optimization because SiBCASA assumes a near steady state between GPP and TER (Fig. ). SiBCASA was in fact able to simulate small carbon uptake anomalies during the reported droughts using its own environmental response parameterizations. However, it lacked a substantial amount of interannual variability in NEE and Δph and lacked a strong correlation of Δph with SPEI (Fig. ). This suggests a potential absence of an important coupling between the hydrology and carbon discrimination processes in the model.