We use outputs from historical simulations by ESMs with at least 30 realizations to investigate the ToE in the land carbon sink. The models selected include the CESM2-LE with 90 simulations and four models in CMIP6 : ACCESS-ESM1-5 with 38 simulations , CanESM5 with 40 simulations , IPSL-CM6A-LR with 33 simulations , and MPI-ESM1-2-LR with 41 simulations . All historical simulations are conducted under the CMIP6 historical forcing, including volcanic eruptions and changes in atmospheric composition due to human activities . The future scenario simulations are modeled under different Shared Socioeconomic Pathways (SSPs), based on varying levels of human-emitted CO₂ and mitigation efforts .

The historical simulations covers the period of 1851–2014 and the future scenario simulations cover the period from 2015 to 2100. The spatial resolution of CESM2-LE outputs is 0.9375° × 1.25°, and four CMIP6 models is 2.5° × 2.5° (pre-processed by from their native spatial resolution). We select the net biome production (NBP), gross primary production (GPP), and total ecosystem respiration (TER) from the above five ESMs. Note that the TER in CESM2-LE is calculated according to Eq. (), where TER is estimated as the difference between GPP, primary production (NPP), corresponding to autotrophic respiration, soil respiration (SR), and litter respiration (LR) (Eq. ). 1TER=GPP-NPP+SR+LR The TER in four CMIP6 models is calculated based on the sum of autotrophic (ra) and heterotrophic respiration (rh) (Eq. ). 2TER=ra+rh CESM2-LE outputs of NBP, GPP, NPP, SR, and LR are downloaded from https://www.earthsystemgrid.org/dataset/ucar.cgd.cesm2le.lnd.proc.monthly_ave.html (last access: 11 July 2024). For the other four CMIP6 models, NBP, GPP, ra and rh are downloaded (originally from https://esgf-node.llnl.gov/projects/cmip6/) then pretreated by . We further download the monthly mean sea level pressure (SLP) from the five models from their respective sources.

For the regional analysis, we use the regional carbon cycle assessment and processes (RECCAP-2) map (https://www.bgc-jena.mpg.de/geodb/projects/Data.php, last access: 19 October 2023) that categorizes the global land surface into 10 distinct domains, with resolution of 0.5° × 0.5°.

We also included the observations of atmospheric CO₂ growth rate (AGR) at Mauna Loa from 1960 to 2009, downloaded from https://gml.noaa.gov/webdata/ccgg/trends/co2/co2_gr_gl.txt (last access: 18 August 2025). We used monthly mean SLP from the ERA5 reanalysis dataset for the period 1959–2009, with resolution of 0.25° × 0.25°, downloaded from 10.24381/cds.f17050d7 .

NBP, GPP, and TER from CESM2-LE are provided in the unit of gCm-2s-1, from which an annual sum is calculated. NBP, GPP, and TER from four CMIP6 models are in unit of kgCm-2s-1 and converted to annual sums in gCm-2yr-1. TER is calculated according to Eq. () for CESM2-LE and according to Eq. () in the four CMIP6 models. In order to have consistent sign with GPP, TER here is multiplied by -1. In the historical simulations (1851–2014), NBP, GPP, and TER of the five model datasets are area-weighted and aggregated to domain mean with the spatial resolutions of 2.5° × 2.5°, 5° × 5°, 10° × 10°, 20° × 20°, 30° × 30°, 45° × 45°, 60° × 60°, and global mean. The global mean of NBP, GPP, and TER is also calculated for the four future scenarios, with period of 2016–2100 selected (in CMIP6 models the time series starts at July 2015, so we select from 2016 instead). Note that CESM2-LE only includes one future scenario (SSP3-7.0), and other models included all four future scenarios. SLP from all five ESMs is aggregated to the resolution of 10° × 10°. Data pre-processing, including unit conversion and spatial aggregation, was performed with the Climate Data Operators software CDO.

The RECCAP-2 map is area–weighted and aggregated to 2.5° × 2.5°, then categorize the NBP, GPP, and TER to 10 RECCAP-2 regions.

The pretreatment steps of atmospheric CO₂ growth rate (AGR) at Mauna Loa from 1960 to 2009 follows . We first remove five volcanic years (1963, 1982, 1983, 1991, and 1992), then fitted the long-term trend with locally weighted scatterplot smoothing LOWESS. SLP from ERA5 also have five volcanic years removed, then area–weighted and aggregated to the spatial resolution of 9° × 9°.

We perform four statistical analyses: (1) ToE in land carbon fluxes from historical simulations. We analyse the ToE of the anthropogenic perturbed signal in NBP, GPP, and TER in the historical simulations. Following , the signal (S) is the linear regression slope of the ensemble mean in the period of 1960–2009, and noise (N) is the standard deviation of all simulations in the period 1930–1959. We first compare the historical time series of NBP, GPP, and TER, and then calculate the ToE according to Eq. (). (2) Spatial effects on ToE. We examine how the ToE varies globally and across the 10 RECCAP-2 regions. In addition, we evaluate the influence of spatial resolution on ToE. We calculate pixel-based ToE values at multiple spatial scales (ranging from 5° × 5° to 60° × 60°) and compare these with the global scale. (3) ToE in future projections of the land carbon fluxes. We calculate the ToE for NBP, GPP, and TER, with the signal period in 2020–2070 and the noise period in 2020–2070 (with the ensemble mean removed). (4) Noise reduction through dynamical adjustment. Given the large year-to-year variability in NBP, we use ridge regression to remove the circulation-induced variability in global NBP. To assess the effectiveness of ToE reduction on a global scale through dynamical adjustment, we calculate the relative reduction (dS) according to Eq. ().

Note that only the calculated signal (regression slope) with significance value P<0.05 is selected. If the calculated signal (regression slope) is negative, we then take the absolute signal value to get a positive ToE. Here we select to show the ToEs less than 150 years. 4dS=100%⋅(VO-VR)/VO Note that VO represents the original value (ToE or N) and VR is the (ToE or N) estimated from the original time series (NBP or GPP) after removing the circulation-induced variability estimated by using the ridge regression model.

We also calculated the contribution of N and S to ToE changes in each RECCAP-2 region, relative to the global scale, for NBP, GPP, and TER. Equation () is the natural logarithmic form of Eq. (). We first calculate the logarithmic changes on the global and regional scales, and then calculate the differences between each region and the global mean (Eq. ). 5ln⁡(ToE)=ln⁡(2×N)+ln⁡(1/S)6ln⁡(ToEregion)-ln⁡(ToEglobal)=ln⁡(2×Nregion)-ln⁡(2×Nglobal)+ln⁡(1/Sregion)-ln⁡(1/Sglobal) The contribution of changes in N and S are: 7Ncontri=100%×ln⁡(2×Nregion)-ln⁡(2×Nglobal)ln⁡(ToEregion)-ln⁡(ToEglobal)8Scontri=100%×ln⁡(1/Sregion)-ln⁡(1/Sglobal)ln⁡(ToEregion)-ln⁡(ToEglobal) Note that for future scenarios, we substitute the region's value to each future scenario's value.

We first examine the NBP time series for the historical simulations from 1851 to 2014 (Fig. ). Before the 1960s, the ensemble mean (long-term trend) for each model remains relatively stable with slight variations. After the 1960s, the ensemble mean shows a noticeable increase. Despite this, the magnitude of NBP variability remains consistent or slightly increase throughout the historical period, for all models. In individual simulations, we observe that the year-to-year variations are considerably larger than the changes in the ensemble mean, enhancing or offsetting the long-term NBP trend (Fig. ).

We then examine the time series of GPP and TER in the historical simulations (Fig. ). Both GPP and TER show similar trends across models, though ACCESS-ESM1-5 shows a larger magnitude difference (Fig. ). The ensemble mean of GPP and TER are similar until the 1960s, after which GPP slightly surpassed TER (Fig. ). year-to-year variations are minor compared to the long-term trend in the ensemble mean, suggesting that photosynthesis and respiration are strongly influenced by anthropogenic perturbations. Because the trends in GPP and TER largely compensate when combined to calculate NBP, the resulting NBP exhibits smaller long-term trends but pronounced interannual variability.

We then examine how long it takes for the anthropogenic signal (ensemble mean of each model) to emerge from year-to-year variations of NBP in global scale and across 10 RECCAP-2 regions (Fig. b). Globally, CESM2-LE has the shortest detection time at 26 years, while CanESM5 takes the longest at 66 years (Fig. b). The detection time in ACCESS-ESM1-5 is not available, due to a flat trend of ensemble mean after 1960s.

We first check the ensemble mean of NBP in global scale and 10 RECCAP-2 regions (Fig. ). The trends of ensemble mean in NBP subjects to larger interannual variability in regional than in global scales, particularly in Southeast Asia and Africa. Comparing noise (N) and signal (S) (Fig.  and Eq. ), we found that the variation in detection time across models is mainly due to differences in year-to-year variability and signal trends.

In most of the 10 RECCAP-2 domains, ToE detection in NBP takes longer than at the global scale (Fig. b). We calculate the contribution of changes in N and S to regional ToE, compared with historical global scale NBP (Fig. ). In regions such as South Asia and Australasia, the longer regional ToE is mainly due to larger regional noise (Fig. ). While in other regions such as East Asia, the longer regional ToE is mainly attributable to smaller regional S (Fig. ). These effects delay the detection of anthropogenic signals, a phenomenon we refer to as “spatial delay”.

The spatial delay in NBP can be explained by the reduced noise from internal climate variability when fluxes are aggregated globally, while the signal trend may be either enhanced or diminished depending on the specific region considered (Figs. , ). This is a well-known pattern in detection and emergence studies in the climate literature . However, the spatial delay does not apply everywhere. In Russia, models like CanESM5, and IPSL-CM6A-LR show shorter detection time compared to the global scale (Figs. , ). This is mainly due to apparent smaller noise in Russia of the two models, compared with global scale and other regions (Figs. , ).

We then evaluate the ToE for GPP and TER (Fig. c, d), both show similar patterns in detection time, and the relative importance of noise and signal at regional scale (Figs. , , , ). Globally, it takes around 8 to 13 years to detect anthropogenic signal in GPP and 6 to 10 years for TER (Fig. c, d). As found for NBP, both GPP and TER show a spatial delay from global scale to regional scale (Fig. c, d). For GPP and TER, longer regional ToEs are mostly due to larger regional noise rather than weaker signal trends, except in West Asia, where it is mainly driven by an apparent weaker signal trend (Figs. , ). Australasia in GPP and TER both generally have the longest detection time, due to higher noise compared to lower signal levels (Figs. , ), indicating higher internal climate variability. In both GPP and TER, South America and Southeast Asia experience high levels of noise and signal, while West Asia has relatively low levels of noise and signal (Figs. , ).

Compared with the land carbon sink (NBP), photosynthesis (GPP) and ecosystem respiration (TER) individually show a much shorter detection time of the anthropogenic signal (Fig. ). This is likely due to the fact that GPP and TER trends are strongly influenced by anthropogenic perturbations, with the magnitude of the trend exceeding the magnitude of internal climate variability in a much shorter time. However, when calculating NBP, the long-term trends of GPP and TER offset each other, leaving NBP with weaker long-term trends relative to the year-to-year natural variations, thus making it harder to detect the anthropogenic signal in NBP.

To further analyse the spatial delay effect, we calculate the distribution of pixel based ToE for NBP, GPP, and TER under varying resolutions in the historical simulations. For NBP, as the resolution becomes coarser, the spread of the ToE distribution decreases substantially (Fig. ), though the median remains similar. This might be due to noise reduction by spatial aggregation through offsetting internal climate variability (Fig. ). A similar pattern is observed in GPP and TER, where aggregation reduces the spreads of ToE without substantially altering the medians (Figs.  and ).

We found global scale takes shorter time to detect long-term trends induced by anthropogenic effects than at regional scales, with ToEs increasing for smaller domains as reported by , though their study used fewer models and less than 10 simulations. A few regions, however, show shorter ToEs than the global scale. For example, in Russia, CanESM5 and IPSL-CM6A-LR simulate relatively small noise and stronger signal trends, leading to shorter ToEs. This maybe relate to the sparsely distributed ecosystems included in models, which are less sensitive to changes in climate drivers. We found that, for regional NBP, larger interannual variability in the signal trend also contributes to longer detection time, likely reflecting different regional climate drivers (e.g., fires, decadal internal variability, land use changes . Such large signal variability in regions like Southeast Asia and Africa therefore introduces substantial uncertainties in detecting the anthropogenic signal on decadal timescales.

The large interannual variations in NBP largely arise from variations in GPP and respiration. As regional ecosystems are more sensitive to precipitation than to temperature , much of this variability maybe influenced by precipitation . However, anthropogenic signals in precipitation are less robust and emerged later than those in temperature . Identifying these signals and their impacts on regional ecosystem activity could therefore enable a cleaner and earlier detection of anthropogenic influences on land carbon sinks.

We examine the time series of NBP under various future scenarios from 2016 to 2100 (Fig. ). NBP trends of ensemble mean show large deviations across models (Fig. ).

In CESM2-LE, the SSP3-7.0 scenario shows a steady increase in NBP until around 2040, followed by stable trend until 2100 (Fig. ). ACCESS-ESM1-5 and IPSL-CM6A-LR exhibit mixed NBP trends in all scenarios, with a relatively stable trend before 2050 and a gradual decline afterwards—ACCESS-ESM1-5 even shifted to a net carbon source (Fig. ). In CanESM5, all scenarios are mixed and together increasing until 2050 (Fig. ). After that, all scenarios diverged according to different emission scenarios (Fig. ). MPI-ESM1-2-LR also have all scenarios mixed before around 2050, then diverge clearly with a lower overall trend (Fig. ). Except CanESM5, the large year-to-year variability in NBP makes it challenging to distinguish long-term trends across scenarios.

We then examine the time series of GPP and TER under future scenarios (Figs.  and ). GPP continues to rise in all models until 2100, except for SSP1-2.6, in which GPP slightly decreases after ca. 2060 (Fig. ). TER follows a similar pattern, with an increasing trend in line with the different CO₂ emission scenarios (Fig. ). The increase in GPP is likely due to the enhanced CO₂ fertilization and warming in mid-to-high latitudes .

Distinguishing the ToE for NBP from different future scenarios is challenging, due to smaller anthropogenic signal and larger year-to-year variations across four future scenarios (Fig. ). Only CanESM5 shows a clear separation between scenarios, with ToE of 147 years for SSP1-2.6, 60 years for SSP2-4.5, 35 years for SSP3-7.0, and 19 years for SSP5-8.5. Other models take over 44 years to detect the anthropogenic signal among all scenarios (Fig. ). In contrast, GPP and TER trends are more distinct and separated according to different scenarios, resulting in much shorter ToE (Figs. , ). This might be due to an increase in the CO₂ emission level, or a stronger anthropogenic signal that outweighs the increased noise level, making the detection time more driven by impacts from anthropogenic perturbations rather than internal climate variability (Figs. , ).

The divergence of NBP across models is much larger in future scenarios than in historical simulations. While models are inherently different, these differences in the historical period may be amplified in future scenarios due to: (a) the increasing influence of CO₂ fertilization and land use change ; and (b) Rising temperature and more frequent extreme events . Both may intensify differences in climate-carbon feedbacks among models .

In future scenarios, it takes longer to detect the anthropogenic signal in NBP, when compared to historical simulations. This delay is mainly due to the small anthropogenic signal caused by the compensation effect of GPP and TER, whose differences are smaller than those in historical simulations (Figs. , –). This may result from a slowdown in the long-term GPP trend under warmer climate and increasing CO₂ concentrations in future scenarios. In addition, larger noise levels (Fig. ) that might driven by more frequent extreme events in a warming climate amplifies year-to-year variations in the land carbon sink. Reducing these year-to-year variations is crucial for reducing the ToE in NBP. In the next section, we apply dynamical adjustment to filter out the atmospheric circulation-induced variability in global NBP time series, and assess whether it can contribute to reduce ToE in both historical simulations and future scenarios.

We use the ridge regression to filter out atmospheric circulation-induced variability in year-to-year global NBP variability (Fig. ). By applying the ridge regression model that based on sea level pressure as covariates, the circulation-induced variability in the respective carbon flux is predicted. The predicted circulation-induced variability is assumed to contain direct influences (via thermodynamics or CO₂ fertilization) of climate change . Because circulation-induced variability is highly variable and often assumed to be largely internal variability, the residual can be expected to show a higher signal-to-noise ratio (e.g., ).

The noise of global NBP is substantially reduced after filtering out circulation-induced variability, so that ToE is reduced in both historical simulations and future scenarios (Fig. , Appendix A, Table ). In the historical simulations, the relative reduction in ToE ranges from 34 % (CESM2-LE) to 39 % (CanESM5), corresponding to 9 and 26 years, respectively (Fig. , Table ). For future scenarios, the reduction ranges from 29 % to 55 % (42 and 19 years reduction, respectively), except for ACCESS-ESM1-5, where reductions are mostly less pronounced (Table ). For GPP, the relative reduction in ToE is smaller (Fig.  and Table ). In the historical simulations, it ranges from 13 % (CanESM5) to 32 % (ACCESS-ESM1-5), corresponding to 1 and 4 years, respectively (Fig.  and Table ). For future scenarios, the relative reduction ranges from 19 % to 60 % (1 and 67 years reduction, respectively) (Fig.  and Table ). The large reduction of ToE indicates that NBP and GPP are both substantially affected by circulation-induced variability.

We then test the observations of Atmospheric CO₂ growth rate (AGR) from Mauna Loa for the period 1960–2009, matching the period of signal for the ESM analysis (Fig. ). The ToE of the observed AGR is 33 years, with noise of 0.87 gCyr-1 and signal of 0.05 gCyr-2 (Fig. ). After removing circulation-induced variations through dynamical adjustment, the ToE of the adjusted new AGR is reduced to 23 years, with noise of 0.70 gCyr-1 and signal of 0.06 gCyr-2 (Fig. ). This represents an overall reduction of about 30 %, contributed by 19 % reduction in noise and 20 % increase in signal. The results show that this approach can be applied in observations, enabling earlier detection of anthropogenic signals in global carbon cycle variability.