CABLE is a global land surface model as described by Kowalczyk et al. (2006) and incorporates global carbon, nitrogen, and phosphorus cycles (Wang et al., 2010, 2011). This study does not activate phosphorus cycle in the model largely because phosphorus has minor impacts on C cycle (Zhang et al., 2011). Leaf photosynthesis, stomatal conductance, and heat and water transfer in CABLE are calculated using the two-leaf approach (Wang and Leuning, 1998).

Gross primary production (GPP) is calculated for both C3 and C4 plants (Farquhar et al., 1980; Kowalczyk et al., 2006). The Farquhar model is a biochemical model and modified in CABLE to calculate CO2 assimilation rate at canopy level as a minimum of three potential limitation processes of photosynthesis: light, enzyme, and C sink. Generally, all three of these photosynthetic limitations are positively related to maximal carboxylation rate (Vcmax) or maximal potential electron transport rate (Jmax) and intercellular CO2 concentration (Ci). Both Vcmax and Jmax are temperature dependent (Leuning, 2002) and are maximized at around 30 ∘C. Thus, in response to warming, the model usually predicts a positive response in GPP in cold and temperate regions but a negative response in GPP in hot regions. Ci depends on the stomata conductance and atmospheric [CO2]. GPP in CABLE positively responds to rising atmospheric [CO2]. CABLE photosynthesis is also controlled by soil moisture.

Autotrophic respiration (Ra) in CABLE is also temperature dependent and follows the modified Arrhenius formula (Ryan, 1991; Sitch et al., 2003). At the canopy scale, Ra is proportional to vegetation nitrogen content and a temperature-related coefficient. Ra will positively respond to warming climate. Heterotrophic respiration (RH) is proportional to litter and soil decomposition rate and C pool sizes. The decomposition rates in the model are controlled by soil temperature and water. The temperature response is based on a Q10 equation. Decomposition rates will positively respond to warming. The water response function is from the daily time step ecosystem model (DAYCENT) (Kelly et al., 2000) and the decomposition rate positively responds to wetter soil conditions.

CABLE has three vegetation compartments (leaf, wood, and root), three litter compartments (metabolic litter, structure litter, and coarse wood debris), and three soil compartments (fast soil pool, slow soil pool, and passive soil pool) (Wang et al., 2010).

We use the meteorological datasets from the National Centers for Environmental Prediction and Climatic Research Unit (CRUNCEP) to drive our model. The meteorological inputs from 1901 to 2100 include temperature, specific humidity, air pressure, downward solar radiation, downward long-wave radiation, rainfall, snowfall, and wind speed. The meteorological variables of CRUNCEP data from 1901 to 2005 are interpolated from 6-hourly into hourly (Qian et al., 2006) and re-gridded from 0.5∘ × 0.5∘ to 1.875∘ × 2.5∘ spatial resolution. From 2006 to 2100, the hourly meteorological variables are generated from the Community Earth System Model version 1.0 (CESM) (Li et al., 2016; Hurrell et al., 2013) for Representative Concentration Pathway (RCP) 8.5.

C storage for all three scenarios (climate warming, rising atmospheric [CO2], and both together) is initialized at pre-industrial steady states, which is achieved by a spin-up approach. The spin-up method cycles 10-year CRUNCEP data (1901–1910) to drive CABLE, with [CO2] constant at the 1901 level. A semi-analytic solution is used to accelerate spin-up simulation (Xia et al., 2012).

The description of three scenarios in this study is summarized in Table 1. Simulation one (S1) fixes the atmospheric [CO2] but uses changing climate forcing. Simulation two (S2) fixes climate forcing but increases atmospheric [CO2]. Simulation three (S3) uses both changing climate forcing and increasing atmospheric [CO2].

Mean C age is defined as the mean time elapsed since C atoms (current in the system) entered the system, which is important for understanding C transit time described below. Following Rasmussen et al. (2016), mean C age (a‾) can be formulated a‾(t)=∑i=1daitxi(t)∑i=1dxi(t). In Eq. (1), ai represents the mean age of C in the ith compartment, xi represents C pool size of the ith compartment, and d is the total number of C compartments.

Mixing fresh C input into old ecosystem C may reduce the mean ecosystem C age. Meanwhile, C remaining in the system will age with time. As shown by Rasmussen et al. (2016), dynamics of mean compartment C age can be described by the following differential equation: dai(t)dt=1+∑j=1dajt-aitbijkj(t)xj(t)-aitsi(t)xi(t). In Eq. (2), si(t) is the direct C input rate from net primary production (NPP) to the ith compartment in g C m-2 yr-1, bij is the proportion of decomposed carbon from the jth compartment to be transferred to the ith compartment. kj is the decomposition rate of the jth compartment; the unit is per year. Thus, change in compartment C age depends on C aging, network C transfers among pools with different ages, and C input. Note that this equation works only for linear models.

With a time step Δt, the C transferred from the jth compartment to the ith compartment (Fij) equals bijkj(t)xj(t)Δt and C input (Si) equals Si(t) = si(t)Δt, Eq. (2) can be rewritten in a finite-element form to represent C age dynamics: Δai(t)=Δt+∑j=1dajt-aitFij-aitSi(t)xi(t). In Eq. (3), the first term, Δt, indicates natural C aging. the second term,∑j=1dajt-aitFij-aitSi(t)xi(t), represents the mean age change of the ith compartment due to mixing with transferred C from other compartments or external C input (i.e. NPP).

After the C cycle spin-up, we obtain the steady-state C ages in each compartment by solving Eq. (2) with the Euler method. The changes of mean compartment C age are less than 0.1 % between two successive cycles.

C transit time is defined as the average time for a C atom to spend in the ecosystem until its exit, or the time from entering the ecosystem to leaving the ecosystem (or residence time; Luo et al., 2001). For a multiple-compartment system, the mean C transit time, τ‾ts, can be calculated using the following equation (Rasmussen et al., 2016): τ‾ts(t)=∑i=1daitxi(t)(∑j=1dbji)ki(t)∑i=1dxi(t)(∑j=1dbji)ki(t). When i=j, bji equals -1, indicating one unit of C exited from the ith compartment. When i≠j, bji represents the proportion of exited C of the ith compartment transferred to the jth compartment. ∑j=1dbji=0 when the exited C from the ith compartment is fully transferred to all the other compartments, such as litterfall transferring from plant to litter compartments, without C loss. ∑j=1dbji<0 when the exited C from the ith compartment is partly transferred to the other compartments, such as litter or soil C decomposition, with the rest lost to the atmosphere via respiration. The denominator is the total amount of C loss from the ecosystem. The numerator is the sum of products of respired C mass and C age.

Equation (4) can be reorganized as τ‾ts(t)=∑i=1daitfhr,i(t), when we define the fraction of the total C loss from the ith compartment (fhr,i), hr represents heterotrophic respiration as fhr,i(t)=xi(t)(∑j=1dbji)ki(t)∑i=1dxi(t)(∑j=1dbji)ki(t). Equation (5) indicates that ecosystem C transit time consists of products of two components: compartment C age (ai) and the fractional composition of respired C (fhr,i). Compartment C age as represented by Eq. (2) changes due to C mixing with C in other compartments or external input.

According to Eq. (5), the change in ecosystem C transit time τ‾R can be attributed to the change in compartment C age (change in C age structure) and the change in respired C composition as (see the Supplement for details) Δτ‾ts(t)=∑i=1daitΔfhr,it+∑i=1dfhr,itΔait+o(aitfhr,it). The first term in Eq. (6) refers to C transit time change due to change in respired C composition. If the fraction of respired C from fast-turnover pool decreases, the mean ecosystem C transit time may increase because more respired C comes from slow-turnover pools with older C ages. The second term refers to C transit time change due to change in compartment C age structure. Under elevated CO2, for example, young C enters a compartment more than it leaves. C in the compartment becomes younger (i.e. young C replenishment). Subsequently, mean ecosystem C transit time will decrease. The third term refers to residuals that cannot be explained by the previous two terms.

In this study, the C age dynamics and diagnostics represented by Eqs. (1)–(6) are implemented into CABLE global simulations. During our analysis of results, C age and transit time are averaged at different spatial scales, i.e. grid cell scale, latitudinal scale, and global scale. Pool sizes (xi), pool ages (ai), and pool-to-pool fluxes (Fij) in Eqs. (1)–(6) uses the grid cell mean, latitudinal mean, and global mean of each compartment to calculate three different scales of C age and transit time. Therefore, the arithmetic average of C age or transit time at each grid cell (e.g. Fig. 1a) does not equal the global average of C transit time (e.g. Fig. 3a).

The global ecosystem C transit time at steady state generally shows a latitudinal variation pattern (Fig. 1). The high values (greater than 70 years) are simulated not only in high-latitude regions, such as northern Russia, northern Europe, and northern Canada but also in high-altitude regions such as the Tibetan Plateau. Small values in C transit time (less than 30 years) are simulated in tropical rainforest, such as Amazon forest, Conga forest, and Indonesian forest. Ecosystem C transit times in some grasslands in middle-south Africa, south America, the southern Great Plains of the US, and central northern Australia (savanna) are sometimes even smaller than those in tropical forest. The spatial patterns of the mean ecosystem C age are quite similar to the patterns of C transit time. However, the magnitude is significantly higher than ecosystem C transit time. The mean ecosystem C age ranges from 118 to 7952 years, whereas ecosystem C transit time ranges only from 13 to 341 years.

The global latitudinal pattern of C transit time in 1982–2005 is consistent with the observation-based pattern of turnover time (Fig. 2). The latter is estimated at each grid cell globally using the stock-over-flux method to divide ecosystem C storage by GPP (Carvalhais et al., 2014). The magnitude of the estimate is mostly within the uncertainty range of the observation-based pattern. We compare estimated C transit time in 1982–2005 with the turnover time, partly to match modelled values with contemporary observations and partly due to the fact that terrestrial C cycle is still approximately at a quasi-steady state between 1982 and 2005. Over the 1980s and 1990s, the annual average of global net land carbon sink estimated from the Global Carbon Project (GCP) is about 0.8 GtC yr-1 with an uncertainty of 0.6 GtC yr-1. As a reference, the annual average of net land carbon sink in the most recent decade (2007–2016) is 2.3 GtC yr-1 with an uncertainty of 0.7 GtC yr-1 (Le Quéré et al., 2018). The net change of global land carbon in the 1980s and 1990s is not that significant, which indicates the land C cycle has not moved too far away from the steady state. Moreover, the simulated latitudinal pattern of C transit time almost overlaps with C turnover time, showing that C cycle is still near the steady state at present day. Annual C turnover time theoretically equals C transit time when the C cycle is close to steady state (Sierra et al., 2016).

In the 200-year simulation, mean global ecosystem C transit time increases by 11.8 years in response to climate warming (S1) and decreases by 5.6 years in response to rising atmospheric [CO2] (S2) (Fig. 3a). When climate warming and rising atmospheric [CO2] force together (S3), C transit time decreases by 1.6 years. The increase in C transit time in S1 is not significant in the 20th century but substantial in the 21st century. Oppositely, the decrease in C transit time in S2 is steady before 2060 but slows down afterward. Mean C transit time in S3 decreases but with a smaller magnitude than that for S2 in the 21st century.

Across all three scenarios, the majority (over 93.4 %) of changes in C transit time can be explained by two combined changes in compartment C age structure and respired C composition. Changes in the compartment C age structure and the respired C composition both significantly contribute to the total change in global C transit time. However, the contribution fraction varies among the three scenarios at different times. In the climate warming scenario (S1), respired C composition changes contribute about 70 % of the increase in C transit time in the 21st century (Fig. 3b). In the rising atmospheric [CO2] scenario (S2), respired C composition change and C age structure change contribute equally (Fig. 3c). When coupling climate warming and rising atmospheric [CO2] together in S3, respired C composition change significantly contributes only in the middle of the 200-year simulation (around the year 2000) and a little at the end of the 21st century. The contribution of C age structure change to the change in C transit time gradually increases.

The increase in C transit time in the climate warming scenario (S1) is the most significant from low-latitude regions in South America and Africa (Fig. 4a). Respired C composition change explains most of these regional changes (Fig. 4c). The decrease in C transit time in the rising atmospheric [CO2] scenario (S2) is evenly simulated all over the world (Fig. 4d). Respired C composition change also plays an important role in most regions except for North Africa with little vegetation coverage. The C transit time in the combined climate warming and rising atmospheric [CO2] scenario (S3) mostly decreases in the Northern Hemisphere but increases in some tropical grassland regions in South America and Africa (Fig. 4g). In those regions where C transit time decreases, compartment C age structure change due to fresh C replenishment explains most of the change in C transit time.

Note that the response under combined effects (S3) is not a sum of those from individual effects (S1 plus S2). The nonadditive response to climate warming and rising atmospheric [CO2] is probably due to their interactions, which have been commonly found in many ecological studies (Norby and Luo, 2004; Luo et al., 2008; Leuzinger et al., 2011; Campbell et al., 1997; Zhang et al., 2016).

Similar to the changes in C transit time, the global C turnover time increases with climate warming and decreases with rising atmospheric [CO2] (Fig. 5a). However, the magnitude substantially differs between these two methods (Figs. 3a, 5a). In response to climate warming (S1), global ecosystem C turnover time increases by only 2.4 years at the end of the simulation, which is only one-fifth of the increase in C transit time (11.8 years). In response to rising atmospheric [CO2] (S2), global C turnover time decreases by 3.7 years, whereas C transit time decreases by 5.6 years. In response to the coupled scenario (S3) in which climate warming and rising atmospheric [CO2] force together, global ecosystem C turnover time decreases by 4.5 years, while C transit time decreases by only 1.6 years.

In 1901, the global C turnover time is about 0.5 year longer than the C transit time (Figs. 3a, 5a). Theoretically, C turnover time equals transit time when land C cycle is at steady state. The offset at the initial state of simulations probably results from C seasonal cycles, which are not at steady state. The underestimates of the change in C turnover time relative to C transit time increase in the climate warming scenario (S1) by up to 9.4 years in the end of the 21st century, which is 79.6 % of the total increase in C transit time (Fig. 5b). In the rising atmospheric [CO2] scenario (S2), the deviation constantly grows to about 1.9 years, 27.7 % of the underestimated decrease in C turnover time. In the climate warming and rising atmospheric [CO2] scenario (S3), the change in C turnover time is overestimated by 2.9 years or 181.1 % relative to the change in C transit time in 2100 (Fig. 5b, c).

Latitudinal patterns in C transit time and C turnover time at the initial state in 1900 are nearly the same. Steady-state estimates are from 20 years in low latitudes and 100 years in high latitudes (Fig. 6a, d). However, significant deviation still exists in high latitudes (north of 60∘ N and south of 50∘ S) (Fig. 6g) because seasonal soil freeze–thaw processes in this region lead to a strong seasonal cycle of soil decomposition and violate the steady-state assumption of the C turnover time. The underestimates of C turnover time can be up to 10 years in high-latitude regions, which is about 8 % of C transit time. In other areas, deviation of turnover time is less than 0.5 years.

Changes in C turnover time and C transit time deviate in different regions in response to climate warming (S1) (Fig. 6b, c, e, f). In temperate and tropical regions, C transit time significantly increases, while C turnover time also increases but at a much smaller magnitude. In the tropics, C transit time increases by 13 years in 2100, up to 60 % of the initial value in 1900, whereas C turnover time increases by only 2 years. In the high-latitude region, C transit time slightly decreases (Fig. 6b and c) but C turnover time significantly decreases by several decades in the high latitudes (Fig. 6f). In some regions between 40 and 60∘ N, C transit time increases but turnover time decreases in response to climate warming. C turnover time overall changes less than C transit time in the S1 scenario. Warming-induced changes in C turnover time are underestimated by 5 % at the high latitudes of the Southern Hemisphere and up to 50 % at the low latitudes (Fig. 6h), which ranges from 2 to 29 years (Fig. 6i).

In response to rising atmospheric [CO2] (S2), both C turnover time and transit time decrease. The magnitude of changes for both of them is generally greater at the mid-latitudes than at either low or high latitudes (Fig. 6b, e). At most latitudes, C turnover time decreases less than C transit time, leading to a positive deviation (Fig. 6h, i). The deviation of the change is higher in low than high latitudes. In response to rising atmospheric [CO2], the underestimate of the decrease in C turnover time is at most 2 years in absolute deviation or 10 % in relative deviation (Fig. 6h, i).

In the climate warming and rising atmospheric [CO2] scenario (S3), C turnover time and C transit time decrease at most of the latitudinal regions except for some tropic areas (Fig. b, 6c, e, f). The decrease in C turnover time is more than that in C transit time (Fig. 6h, i). Especially in high latitudes, the difference in changes is much more significant. C turnover time is reduced by up to 3 decades (Fig. 6f) or 35 % (Fig. 6e), whereas C transit time shows nearly no relative changes. Deviation in these areas can be up to 27 years (Fig. 6i).

Changes in C transit time can be explained by its two components: the respired C composition and compartment C age structure. The first component is to account for different contributions of respired C from different pools to total ecosystem C loss. Previous studies have demonstrated that pathways of respiring C from multiple compartments are variably controlled by the global change factor (Luo et al., 2001). Results from this study provide more spatial details about where C transit time changes due to respired C composition change. For example, over 80 % of the increase in C transit time under warming is explained by respired C composition change in the South American grassland region (Fig. 4a). In contrast, change in respired C composition only accounts for approximately 10 % of the increase in C transit time under warming in the boreal and high-latitude regions of North America.

The second component is the C age structure, primarily from change in mean C age of the individual pool modified by the relative fraction of each pool. In the coupled climate warming with rising atmospheric [CO2] scenario (S3), C age structure change primarily contributes to the C transit time response in most global regions in 2100 (Fig. 4h). In this scenario, mean ecosystem C transit time decreases by 1.6 years. The decrease in C transit time results from increased young C uptake with rising atmospheric [CO2], which is more than the increased young C loss with warming. A previous study has also shown that models with multiple pools usually have a more heterogeneous C age structure and thus can store extremely old C than a single pool model (Manzoni et al., 2009).

C turnover time has been widely used to quantify the ecosystem C cycle partly because both ecosystem C storage and C flux can be easily measured (Sanderman et al., 2003; Chen et al., 2013; Carvalhais et al., 2014; McCulley et al., 2004; Raich and Schlesinger, 1992; Yan et al., 2017). The C turnover time has been theoretically shown to equal C transit time at steady state but they deviate under non-steady states (Sierra et al., 2016). This study illustrates how much deviation occurs between C transit time and C turnover time in response to three scenarios of climate change. Our results show that even at initial steady state, global ecosystem C turnover time is slightly greater than C transit time by 3 %. This is because the steady state reached by spin-up does not mean the terrestrial C cycle system is completely at equilibrium. Seasonal variations in ecosystem C uptake and turnover still lead to periodical oscillation of the terrestrial C cycle.

The deviation between C transit time and turnover time also indicates to what extent that turnover time can properly represent time characteristics in the C cycle. In the climate warming and rising atmospheric [CO2] scenario (S3), the deviation does not increase significantly until 2050. The modelled latitudinal pattern of present-day C transit time matches the C turnover time estimated from observations well (Carvalhais et al., 2014). This indicates that the stock-over-flux estimates are still useful at present day. However, the deviation between C transit time and turnover time remarkably increases after 2050 (Fig. 5b). Then it requires caution when we use the C turnover time for estimating C sequestration in multiple compartmental ecosystems.

In transient state, the changes in C transit time and C turnover time differ the most in the climate warming scenario (S1). Tropical and high-latitude regions contribute the most to the deviation (Fig. 6h, i). In tropical and subtropical regions, C transit time increases by about 60 % (Fig. 6b) while C turnover time increases by 20 % or less (Fig. 6e). The great difference between changes in C transit time and turnover time is due to their different assumptions. In response to climate warming, composition change in respired C contributes most to the change in C transit time in tropical regions. However, C turnover time assumes all ecosystem C as one homogenous pool, even if both plant and soil C can be extremely heterogeneous. This homogeneity assumption ignores the composition changes in respired C, which causes up to 80 % of change in C transit time.

In high-latitude regions, C transit time slightly decreases by up to 10 %, whereas C turnover time considerably decreases by over 30 % in response to climate warming. Warming significantly increases soil respiration due to permafrost thaw, whereas the change in permafrost ecosystem C pool size is relatively small. Thus, C turnover time significantly decreases. C transit time slowly responds to climate warming because the young C input added to permafrost ecosystems is relatively small compared to large C storage in this area and C age structure does not change much. These big deviations between C turnover time and C transit time in tropical and permafrost regions suggest that future C cycle analysis based on turnover time likely leads to strong deviations as it does not represent transient C dynamics in multi-pool ecosystems.

This study has illustrated how C transit time and turnover time deviate under climate warming and rising atmospheric [CO2] scenarios. Those deviations may become even bigger under other global change scenarios. For example, land use change and fire can drive ecosystems out of steady state to be at disequilibrium (Luo and Weng, 2011). Clear-cutting of forest or forest fire removes at least the aboveground wood C pools and thus greatly changes both the total C stock and NPP, leading to a large change in C turnover time (Wang et al., 1999; Zhou and Luo, 2008). Clear-cutting of forest or forest fire also changes age structure and composition of respired C from different pools within the ecosystem, resulting in change in C transit time. Such a disturbance usually drives the ecosystem to a stronger degree of disequilibrium than climate change does. The deviation between turnover time and transit time should be bigger under a severe disturbance than climate change since our results have indicated that C transit time and turnover time deviates more significantly when an ecosystem is further away from equilibrium (Fig. 5).

In contrast to the static vegetation distribution used in CABLE, natural vegetation distribution may change over time in the real world. C transit time and turnover time may further deviate under natural vegetation dynamics. However, whether forest will expand or die back in a future warming world is still quite unknown. Previous studies come to various conclusions due to their focus on different areas with different methods (Masek, 2001; Soja et al., 2007; Cox et al., 2004, 2013). Nevertheless, most bioclimatic models consistently suggest temperate and boreal biomes rapidly increase in area under warming (Kirilenko and Solomon, 1998). If the forest species, which stores more C in slow-turnover tissue, takes over the grass species, which stores more C in fast-turnover tissue, the expansion of forest may increase C transit time significantly. However, C turnover time, by lumping all different C compartments together, may underestimate such changes.

In the real world, the land C cycle is always at dynamic disequilibrium due to cyclic environmental conditions (e.g. diurnal, seasonal, and interannual variability), directional global change (e.g. climate warming, rising atmospheric CO2 concentration, altered precipitation, and nitrogen deposition), recursive disturbance–recovery cycles, shifted climatic and disturbance regimes, and vegetation changes (Luo and Weng, 2011). Thus, the estimated C turnover time is expected to differ from the C transit time at any time point and at any spatial location. The degree of deviation between C turnover time and transit time may vary.

In addition to various agents that cause an ecosystem to be at disequilibrium, deviation between estimated C transit time and turnover time also depends on model structure. Vertically resolved soil C models, for example, include vertical C mixing and depth-dependent C decomposition rates (Koven et al., 2013; Huang et al., 2018). Representation of vertically resolved processes likely increases soil heterogeneity. When warming induces deep soil thaw and increases deep soil decomposition, the fraction of respired C from the deep layer with old C increases. The C transit time together with a vertically resolved model may substantially increase, whereas C turnover time, which implicitly assumes the ecosystem to be one homogeneous pool, may not respond much.

Previous studies have argued that C transit time is conceptually sounder than C turnover time (Rasmussen et al., 2016; Sierra et al., 2016). In this study, we have shown that the C turnover time can substantially deviate from the transit time in response to climate change and other environmental changes. However, C turnover time can be easily calculated from C stock over flux, both of which can be easily measured. In contrast, C transit time cannot be easily estimated from field measurements. Equation (5) indicates that we need data from measurement of mean C ages (ai) and fractional composition of respired C (fhr,i) in individual C pools in order to calculate mean ecosystem C transit time (τ‾ts). Neither ai nor fhr,i have been widely measured in field. Thus, our research community faces a tremendous challenge to estimate a conceptually sound and scientifically important parameter.

In the past, radiocarbon 14C has been used to quantify mean C ages of various litter and soil pools (Gaudinski et al., 2000). Measured soil respiration in response to elevated CO2 treatment in Duke Forest has been decomposed to various fractional composition using a deconvolution method or inverse analysis (Luo et al., 2001). It appears that estimation of C transit time in real-world ecosystems requires measurement of isotope signatures in different litter and soil fractions together with measurement of respiration from soil surface and soil components. Those measurements, together with many other datasets, may need to be analysed to estimate mean C ages, fractional composition of respired C in individual C pools, and then mean ecosystem C transit time (τ‾ts) using some innovative methods, such as data assimilation.

Estimating C transit times in the real world can help constrain projections in land C sequestration because internal timescales of the carbon cycle are a major source of model uncertainty (Friend et al., 2014; He et al., 2016). Our study has shown that the change in C transit time can be separated into two components, C composition change and C age change. Assessment of the two components would provide additional constraints on model projections. Many of the ecosystem pools, such as leaf C, wood C, root C pool, litter C pools, and soil C, can be measured separately. They provide plenty of information to constrain ecosystem C composition change. Isotope data from each of those ecosystem components also can offer information to constrain the mean compartment age. Although discrete soil C pools may not be easy to separate, many datasets from field and laboratory measurements have been used to constrain multi-pool soil carbon models by using data assimilation techniques (Liang et al., 2018; Xu et al., 2006). To constrain C transit time through its two components with observation, modelled C cycle and land C sequestration can be significantly improved.