Terrestrial ecosystems play important roles in the C cycling of climate systems and provide various ecosystem services (e.g., water supply and wild habitats for biodiversity); however, these ecosystem functions are threatened by climate change . Previous model intercomparison studies (e.g., VEMAP , dynamic global vegetation models (DGVMs) , Coupled Carbon Cycle Climate Model Intercomparison Project (C4MIP) , and The fifth phase of the Coupled Model Intercomparison Project (CMIP5) ) have demonstrated a lack of coherence in future projections of terrestrial C cycling for different global land models because of differences in their representations of system processes. For climate change impact assessments, the cascade of uncertainty sources must be considered . Greenhouse gas concentrations, temperature, and precipitation are critical factors in determining the feedback of terrestrial ecosystems in response to atmospheric carbon dioxide (CO2) . These factors could become more important for terrestrial ecosystem C cycling under future higher CO2 concentrations and climate change conditions . The recent International Panel on Climate Change assessments (AR5) took anthropogenic CO2 emission uncertainties into account in a representative concentration pathway (RCP) scenario . Future projected changes in temperature and precipitation have large spatial and temporal uncertainties even for the same radiative forcing levels because of the different structures and parameters used in global climate models (GCMs) . These differences could affect the global C budget of terrestrial ecosystems. Global vegetation models (GVMs) such as (DGVMs and components of earth system models also have inherently large uncertainties because of differences in model structures and parameters e.g.,. Thus, various sources of uncertainty may cause divergence in projected C cycling.

For climate impact assessments and adaptations, different levels of uncertainty sources should be considered in order to manage climate change risks. Such information in impact assessments may benefit from experience gained in the climate-modeling community and vice versa . For example, recently, the likelihood of the occurrence of large Amazon dieback in this century has become lower in simulation studies because of the reduction of uncertainties in the projected precipitation in Amazon regions among GCMs . However, the improvement of vegetation processes in this region could result in the improvement of local vegetation–climate feedbacks, which might contribute to changes in temperature and precipitation in this region . At the global scale, in earth system models in the CMIP5 study, the sensitivities in global land climate–carbon feedback varied considerably . The reduction of C budget uncertainties in ecosystem models could serve to reduce climate change uncertainties, particularly regarding the climate sensitivity of earth system models. In addition, determining which uncertainty source is dominant in the projection is an important aspect of recognizing the limitations of ecosystem C cycling projections and climate impact assessments via GVM and GCM. However, to date, how each uncertainty source (CO2 concentration, GCM, and GVM) is important in regions and periods affected by climate change still remains to be clarified in climate impact research.

In ecosystem climate impact assessments, how the uncertainties of climate impacts matter is still a challenging issue, in part due to the lack of standardized impact evaluation protocols. The Inter-Sectoral Impact Model Intercomparison Project (ISI-MIP) is the first attempt to apply ensembles of both impact and climate models to obtain robust future assessments . In assessments of climate impacts on ecosystem functions, regionality is extremely important for the severity and timing of impacts owing to the different types of climate change in each region and the presence of different ecosystem types in different areas . For comprehensive climate impact assessments on ecosystems, it is necessary to possess spatiotemporal information for which uncertainty sources can be chosen or ignored, for which some processes contributed to uncertainty, and for which it is known how the contribution of each uncertainty source changed with time. Separation of the different sources of uncertainty in projections of ecosystem models in various aspects can be used to comprehend the uncertainties and risks in climate impacts on ecosystem conditions and C cycling.

In this study, we examined the C dynamics in six GVMs obtained from the ISI-MIP. In the ISI-MIP, these GVMs were simulated using five GCMs forced with four newly developed climate scenarios, i.e., RCP in the CMIP5 experiments . In this model intercomparison project, an orthogonal experimental design with RCP, GCM, and GVM was adopted. In total, 70 independent simulation sets were used in this study, which enabled us to evaluate the relative contributions to total uncertainty of the projection factors (emission scenarios, climate projections, and GVMs) in terrestrial C cycling. Our objective was to explore the comprehensive uncertainties in future global and regional terrestrial C projections by decomposing the uncertainty sources in terms of time, space, and processes.

For the historical period (1970–2000), the models simulated similar historical NPP, VegC, and SOC trends for different GCMs (Fig. ). However, at the end of the projection period, there were marked differences for all variables (Fig. ). In particular, NPP and SOC varied from a net sink to a net source in the highest baseline emission scenario (RCP8.5). In higher emission scenarios, the total uncertainties for all variables increased to a greater extent. The total uncertainties for each variable in this study were comparable with or greater than those for projected C cycling in a previous model intercomparison study even with a smaller number of GVMs.

Compared with previous model intercomparison studies of terrestrial C cycling, the ISI-MIP study has an important simulation protocol advantage, i.e., it is a partial factorial experiment with three independent treatments for CO2 emission scenarios (RCP), GCM, and GVM. Therefore, uncertainty can be decomposed into the sum of interclass variance (σRCP2, σGCM2, σGVM2, and their interactions) and within-class variance (σresid2). The ANOVA results revealed that each source made quite a different contribution to the total uncertainty, which varied with projection period (Fig. ). Whereas GCMs were the dominant sources of uncertainty for NPP early in the projection period (2000–2040), RCP dominated later in the projection period (2050–2100) (Fig. ). This trend of increasing RCP importance is similar to that of VegC (Fig. ). This may be attributed to the enlargement of CO2 concentration differences among RCPs for this period. The interaction terms as a source of uncertainty were significant (p<0.05 level, not described) and contributed considerably to total uncertainties (up to 20 %) in NPP. This result indicates that there were different sensitivities to the CO2 fertilization effect on vegetation processes among the GVMs that also contributed to projection uncertainties.

Uniqueness in the HYBRID4 model projection was observed in the ΔVegC residence time (Fig. ). This is partially due to HYBRID4 having strong stomatal responses to elevated vapor pressure deficits, and thus simulated negative ΔNPP between 2080 and 2100 even in higher CO2 conditions . In addition, GVM had a contribution of less than 20 % to global ΔNPP (Fig. ); however, there were large fractional uncertainties in the ΔVegC residence time (over 60 % at the end of the 21st century). The ΔVegC residence time represents the turnover rates of plant parts and the mortality rates of individuals, processes modeled using baseline rates, climate sensitivities (including fire), and competitively induced mortality. So ΔVegC residence time is affected indirectly through shifts in vegetation composition . The interaction terms in VegC residence time changes dominated at about 20 % during the entire simulation period, indicating that GVM has a different response to individual GCMs and RCPs. For example, the HYBRID4 model notably showed high sensitivity to GVMs (Fig. ). This term constitutes a non-negligible fraction compared with the main effects of each uncertainty source. pointed out that the humidity term in the vapor pressure deficit is a critical factor to differentiate the projected NPP among GVMs in the ISI-MIP. This is because the adoption of a response function to the vapor pressure deficit is critical for responses to warmer climate conditions . Furthermore, in this study, only HYBRID4 incorporated a fully coupled N cycle; therefore, besides CO2 fertilization effects, implementation of the N cycle in more models is required for more plausible modeling of effects of CO2 fertilization in terrestrial C projections .

Humidity data for GCMs were not adjusted to the bias-corrected air temperature and precipitation in the ISI-MIP study . This might be another potential source of uncertainty and bias for ecosystem projections and for evapotranspiration in global hydrological water models . Our results suggested that an essential factor to reduce uncertainties in the climate assessment of ecosystems is improved understanding of C dynamics after photosynthesis rather than reduction of uncertainties in the exchange of C between the atmosphere and vegetation. In fact, the representations of these processes are quite different among GVMs .

The uncertainties in SOC changes driven by GVM were significantly large and were dominant over the entire simulation period (Fig. ), possibly suggesting that SOC processes are not well constrained by the observational data or consistent between models, suggesting that the uncertainties derived from the GVMs overwhelmed those derived from the climate scenarios. In addition, a previous study showed that VegC dynamics did not correlate strongly with that for SOC , i.e., SOC processes contributed considerably to GVM-driven clustering in the SOC dendrogram. Another ISI-MIP study demonstrated that the sensitivity of global SOC decomposition to increasing global mean temperature varied significantly among GVMs . Moreover, differences in the initial SOC stock resulting from different spin-up procedures among GVMs critically contributed to the incoherence in SOC dynamics. In a CMIP5 study, demonstrated that microbial decomposition processes are a dominant factor determining the amount of global SOC stock rather than C input from photosynthetic products. Determination of the initial SOC stock is important for future soil carbon stock and land surface fluxes . In our results, there was no regional and ecosystem-type (climatic divisions) dependency on GVM contributions to uncertainty in SOC changes. Therefore, to reduce GVM uncertainties in SOC projection, improvement of spin-up procedures and microbial decomposition will be effective for reduction of SOC uncertainties at both local and global scale.

Considering the geographic distribution, we determined that the contributions of each uncertainty source to each grid variance were spatially heterogenous (Fig. ), although the total contributions of each uncertainty source in the grid-based assessment (Fig. ) were roughly in agreement with Fig.  for each period (2050 and 2099). These heterogeneities could be linked with climatic divisions (Fig. ). For example, in ΔSOC, GVMs are also a main contributor in most regions in both periods (2050 and 2099). However, the grid-based assessment revealed geographically distinct regions for each uncertainty source. Although GCM was not a large contributor to global SOC dynamics (Figs.  and ), GCM had a significant effect on uncertainty in arid (BW) to semi-arid (BS) regions (e.g., sub-Saharan Africa, the southwestern USA, South America (pampa), Central Asia, and Australia) for all variables. In a CMIP5 study, reported that changes in precipitation patterns in their regions showed the low degree of coincidence among GCMs. These results suggest that the projection of precipitation patterns among GCMs is critically important to evaluate the impact of climate change on ecosystem conditions and C stocks in these regions (as shown in the Supplement). Although the carbon stocks and changes in these regions are not large, it is important to predict local climate condition uncertainties in order to obtain local climate predictions of ecosystem changes during climate change. In NPP and VegC in the 2090s, GVM is the dominant source in semitropical to tropical climate zones (especially in Southeast Asia, Latin America, and central Africa), whereas GVM is not dominant for global ΔNPP during this period. This implies that modification of tropical rainforest C cycling is critical for reducing uncertainties in global NPP. In broad terms, the contribution of GVM as an uncertainty source in ΔNPP becomes smaller in cooler climatic regions (C–D); however, those of GVM to ΔVegC were larger in cooler climatic regions (Fig. ). This inconsistency can be explained by the large differences between GVMs in the vegetation turnover rate in northern ecosystems because of the different representations of vegetation dynamic processes (e.g., forest fires, N cycling, and senescence) . These results highlight that model improvement on the basis of plant functional type (corresponding to climate divisions) could be important for the effective reduction of uncertainty in climate impact assessments.

Our results do not mean that GCMs are not important for the uncertainties in VegC and SOC projection from the viewpoint of global C stocks. For example, under RCP8.5, the HYBRID4 model simulation showed that VegC diverged considerably among GCMs by 2100 (from 162 to 547 Pg C). Moreover, in , one DGVM forced with 10 different GCMs showed a difference of approximately 500 Pg C among projections of changes in global terrestrial C stock (VegC and SOC) by 2100. Furthermore, the numbers of GCMs and impact models used in this study likely affected the results. Hence, our results indicate a smaller contribution by GCM to total uncertainties than a lack of inter-GVM constraints owing to insufficient validation for the SOC and VegC processes from global observations. In the case of RCP2.6, the model projections were comparable for ΔNPP; however, the results for ΔVegC and ΔSOC differed significantly. This implies that internal ecosystem processes such as photosynthate partitioning and mortality were poorly constrained in the GVMs. Moreover, process uncertainties considerably affect SOC dynamics as a C source via litter inputs. More observation-based model intercomparison (e.g., MsTMIP, ) for each component is required for GVMs to reduce the overall uncertainty. For SOC dynamics, empirical estimations using observation-based heterotrophic respiration are available for validation of SOC decomposition processes. In addition to each model modification, in future, multiple land-use scenarios should be considered in projections to understand additional potential uncertainties (σlanduse2) in the global terrestrial C budget. Furthermore, the use of bias-corrected GCM forcing data will probably affect C dynamics as well as the projections in hydrological models ; however, there is still a lack of validation for the effect of various bias-correction methods on C cycling projections and their relative uncertainty.

In conclusion, by combining multiple GVMs, GCMs, and RCP scenarios, we determined the different contributions of each factor to total uncertainty, which is highly dependent on the variables (NPP, VegC, SOC, and VegC residence time), projection periods, and regions. The contribution of each source of uncertainty in these variables showed different patterns compared with the hydrological variables simulated by global hydrological models from another ISI-MIP study . At the global scale, by the middle of the 21st century, GCM is the dominant uncertainty source in most regions for NPP, VegC, and VegC residence time. However, GVM largely remains the major uncertainty in the impact models in most regions, particularly at the end of the 21st century.

Although RCP can differentiate NPP in temperate and cool climate regions, the uncertainties of VegC and VegC residence time are dominated by GVM. These results suggest that the fate of photosynthetic carbon over the long term is an important uncertainty process for GVM models in climate impact assessments. Thus, our findings indicate that model improvement on the basis of plant functional type (corresponding to the climate divisions) could be important for the effective reduction of uncertainty in climate impact assessments.

For global SOC projections, the uncertainty driven by GVM was greater than that of the climate scenarios, i.e., RCPs and GCMs. This SOC uncertainty might be attributable mainly to the variety of SOC processes among GVMs and a lack of constraints for spin-up procedures. The uncertainties associated with SOC projections are significantly high, and the global SOC stocks by 2099 shift from net CO2 sources to net sinks (from -195 to 471 Pg C). Because of the magnitude of the uncertainty range in projected global SOC stock, the reduction of SOC uncertainties in GVM could be important for the terrestrial C budget.

Particularly in arid to dry climate regions, GCM was the dominant uncertainty source for all compartments and fluxes of ecosystem models even at the end of the 21st century because NPP in these regions is strongly subjected to water-use limitation. The CO2 emission scenario (RCP) as an uncertainty source is important for the late projection period for both NPP and VegC. Moreover, the CO2 fertilization sensitivity of vegetation processes is quantitatively important for future C projection uncertainties.