# Underrepresented controls of aridity in climate sensitivity of carbon cycle models

Sujan Koirala, Chris Jones, Bernhard Ahrens, Naixin Fan, Victor Brovkin, Christine Delire, Yuanchao Fan, Veronika Gayler, Emilie Joetzjer, Hanna Lee, et al.

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Sujan Koirala, Chris Jones, Bernhard Ahrens, Naixin Fan, Victor Brovkin, et al. Underrepresented controls of aridity in climate sensitivity of carbon cycle models. 2022, 10.21203/rs.3.rs-2013805/v1. hal-04302319

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# Underrepresented controls of aridity in climate sensitivity of carbon cycle models

**Sujan Koirala** (✉ sujan.koirala@bgc-jena.mpg.de)

Max Planck Institute for Biogeochemistry

**Chris Jones**

Met Office Hadley Centre https://orcid.org/0000-0002-7141-9285

**Bernhard Ahrens**

Max Planck Institute for Biogeochemistry https://orcid.org/0000-0001-7226-6682

**Naixin Fan**

Max Planck Institute for Biogeochemistry and Technische Universität Dresden, Institute of Photogrammetry and Remote Sensing

**Victor Brovkin**

Max Plank Institute for Meteorology https://orcid.org/0000-0001-6420-3198

**Christine Delire**

CNRM, Université de Toulouse, Météo-France, CNRS https://orcid.org/0000-0002-6114-3211

**Yuanchao Fan**

NORCE Norwegian Research Centre, Bjerknes Centre for Climate Research and Center for the Environment, Faculty of Arts & Sciences, Harvard University

**Veronika Gayler**

Max Plank Institute for Meteorology

**Emilie Joetzjer**

Centre National de Recherches Météorologiques, Université de Toulouse/Météo-France/CNRS

**Hanna Lee**

NORCE Norwegian Research Centre, Bjerknes Centre for Climate Research

**Stefano Materia**

Fondazione Centro Euro-Mediterraneo sui Cambiamenti Climatici (CMCC)

**Julia Nabel**

Max Planck Institute for Meteorology https://orcid.org/0000-0002-8122-5206

**Daniele Peano**

Fondazione Centro Euro-Mediterraneo sui Cambiamenti Climatici (CMCC),

**Pilippe Peylin**

CNRS

**David Wårlind**

Lund University

**Andrew Wiltshire**
**Sönke Zaehle**

Max Planck Institute for Biogeochemistry https://orcid.org/0000-0001-5602-7956

**Markus Reichstein**

Max Planck Institute for Biogeochemistry, Jena https://orcid.org/0000-0001-5736-1112

**Nuno Carvalhais**

Max Planck Institute for Biogeochemistry

## Article

**Keywords:**

**Posted Date:** September 1st, 2022

**DOI:** https://doi.org/10.21203/rs.3.rs-2013805/v1

**License:** © Ⓔ This work is licensed under a Creative Commons Attribution 4.0 International License.

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Underrepresented controls of aridity in
climate sensitivity of carbon cycle models

Sujan Koirala¹, Chris Jones², Bernhard Ahrens¹, Naixin Fan¹,³, Victor Brovkin⁴, Christine Delire⁵, Yuanchao Fan⁶, ⁷, Veronika Gayler⁴, Emilie Joetzjer⁵, Hanna Lee⁶, Stefano Materia⁸, Julia E.M.S. Nabel¹, ⁴, Daniele Peano⁸, Philippe Peylin⁹, David Wårlind¹⁰, Andy Wiltshire², Sönke Zaehle¹, Markus Reichstein¹, Nuno Carvalhais¹,¹¹

¹Max Planck Institute for Biogeochemistry, Jena, Germany.

²Met Office Hadley Centre, Exeter, EX1 3PB, UK

³Technische Universität Dresden, Institute of Photogrammetry and Remote Sensing, Helmholtzstr. 10, 01069, Dresden, Germany

⁴Max Planck Institute for Meteorology, Hamburg, Germany.

⁵Centre National de Recherches Météorologiques, Université de Toulouse/Météo-France/CNRS, Toulouse, France

⁶NORCE Norwegian Research Centre, Bjerknes Centre for Climate Research, Bergen, Norway

⁷Center for the Environment, Faculty of Arts & Sciences, Harvard University, Cambridge, MA, USA

⁸Fondazione Centro Euro-Mediterraneo sui Cambiamenti Climatici (CMCC), Bologna, Italy

⁹Laboratoire des Sciences du Climat et de l'Environnement, CEA-CNRS-UVSQ CE Orme des Merisiers, Gif sur Yvette, France

¹⁰Department of Physical Geography and Ecosystem Science, Lund University, Lund, Sweden

¹¹Departamento de Ciências e Engenharia do Ambiente, DCEA, Faculdade de Ciências e Tecnologia, FCT, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal

Corresponding Author: Sujan Koirala (skoirala@bgc-jena.mpg.de)
Terrestrial ecosystems respond to changes in environmental conditions, mainly via key climatic controls of precipitation and temperature on vegetation activities and decomposition processes ¹. Yet, the relationship between climate and the overall spatiotemporal dynamics and uncertainties of the global carbon cycle, i.e., gross primary productivity (GPP), effective ecosystem carbon turnover times (τ), and consequently the total ecosystem carbon stock (C<sub>total</sub>), are unclear ²⁻⁵. Using a global observation-based synthesis, we first show that the apparent partial spatial climate sensitivities of GPP and τ are associated with relative availability of precipitation and temperature, and are therefore modulated by aridity. The apparent sensitivity of GPP to temperature increases from arid to humid climatic regions. In contrast, its sensitivity to precipitation is invariant throughout different climatic regions. Simultaneously, the τ-precipitation response is strongly non-linear resulting in ~2 times longer τ in arid regions compared to humid regions for a given temperature. Compared with these observed patterns, the offline carbon cycle simulations of seven European Earth System Models (ESMs), that participated in CMIP6, perform relatively better for climate sensitivities of GPP than those of τ. This leads to a large spread and bias in C<sub>total</sub> in both warm and cold semi-arid and arid regions where only a few models capture the observed τ-precipitation relationship. The emergence of the hydrological controls, modulated by aridity, on global carbon cycle implies that the changes in precipitation may moderate the temperature-driven climate feedback of the global carbon cycle under climate change.

## Introduction

The exchange of carbon between the biosphere and atmosphere represents a key mechanism controlling the effect of global changes on the carbon cycle ⁶, as well as on the water and energy cycles ⁷. The land ecosystems, at the centre of biosphere-atmosphere interaction, store carbon by integrating the differences in carbon captured through gross primary productivity (GPP), and carbon released through decomposition processes. Due to the complex dependencies of the photosynthesis and decomposition on climate, biomes, and carbon use efficiency of vegetations ⁸, the resulting carbon stocks vary significantly across space and time. The differences in modelling these complex climate-biosphere dependencies, therefore, lead to large differences in Earth system model (ESM) predictions of carbon stocks ⁹,¹⁰ that are prevalent under the current climate and exacerbate under future climate change scenarios.
The ecosystem turnover and associated carbon losses and stocks, thus, represent major sources of uncertainties regarding carbon cycle – climate feedbacks ¹¹,¹² and the projections of future carbon budgets ⁵,¹³,¹⁴, and modelling and constraining them with observations still pose a significant challenge to ESMs ²⁻⁴.

Various studies have, therefore, investigated the relationship between land carbon stocks and their climate drivers. For example, the uncertainties in soil organic carbon and their responses to climate change have been extensively studied ¹⁵, but mostly focused on temperature, as the first principles dictate the key role of temperature in determining the current and future carbon cycle dynamics ¹⁶. The studies focusing only on energy-limited humid and cold regions, understandably, have shown strong associations of spatial variations of carbon stocks and temperature ¹⁷. When other climatic regions globally are considered, though, temperature alone only explains ~10% of the total spatial variation of the observation-based soil organic carbon ¹⁰ suggesting a larger influence of additional environmental factors. In particular, precipitation, which is the primary source of moisture for all land processes, is potentially a strong driver of spatial variation of turnover times, the τ ¹⁸, as demonstrated by the significance of moisture effects on decomposition ¹⁹ and the observation-based linkages between water and carbon cycles ²⁰. The moisture availability is especially critical in arid to semi-arid regions, which cover ~39% of the global vegetated land, and substantially influence the interannual variabilities of global biosphere-atmosphere carbon exchange ²¹⁻²³, but the effects on modelled τ has been largely ignored ²⁴.

In an ecosystem under a steady state, the temporal variations in total ecosystem carbon storage (hereafter $C_{total}$) become negligible as the net input (GPP) and output (total ecosystem respiration) carbon fluxes balance each other. The spatial variations of $C_{total}$ across ecosystems are, then, essentially defined by the differences in GPP and the carbon loss determined by decomposition rates and τ. The climate, though, has differential influences on and association with GPP and τ, which result in a unique spatial heterogeneity in $C_{total}$ compared to those of either GPP or τ. It is, therefore, critical that the sensitivities of GPP, τ, and $C_{total}$ to climatic variations are simultaneously evaluated, especially in ESMs where the uncertainties in $C_{total}$ may be related to not only GPP ² but to both τ and GPP ⁹.

Here, based on observation-based estimates of the carbon cycle, we first evaluate the apparent spatial sensitivities of climatological mean GPP and τ to two primary climatic drivers: mean annual air temperature (MAT) and mean annual precipitation (MAP). To infer effective or apparent climatological τ of an ecosystem, we assume that the ecosystem carbon
reaches a steady-state over multiple decades, and calculate $τ$ as the ratio of long-term averages of total ecosystem carbon stock and GPP <sup>17,18,25,26</sup>. The apparent spatial sensitivities of the climatological carbon cycle are assessed in a climate phase-space of temperature and precipitation for different climatic regions (arid to humid) that are delineated using an aridity index, defined as the ratio of mean annual precipitation and potential evapotranspiration (see Methods and **Figure A1**). While aridity itself is not directly mechanistically connected to physiological and decomposition processes within an ecosystem, it is a rather clear indicator of relative availability of limiting moisture and energy resources that define the soil moisture regime (**Figure A2**), and consequently, the vegetation responses and patterns <sup>27-29</sup>. The climate sensitivities of $τ$ and GPP are represented using non-linear relationships with temperature and precipitation (see Methods). The relationships are then used as the basis for evaluation of the offline carbon cycle model simulations of seven European ESMs from CRESCENDO project (see Methods), which participated in the Sixth Phase of Coupled Model Intercomparison Project (CMIP6).

## Observation-based climate sensitivities

Both $τ$ and GPP exhibit unique sensitivities to the spatial variabilities of precipitation and temperature in all climatic regions despite large heterogeneity within a climatic region (**Figure 1**, **Table A4**). First, $τ$ varies strongly across both temperature and precipitation gradients in all climatic regions. The sensitivity of $τ$ to temperature is well-documented for humid regions <sup>17</sup>. Interestingly, there is a significant offset in $τ$ as the climate gets drier with the longest $τ$ in arid regions ($τ$=178 years at 0°C) compared to humid regions (76 years). In fact, for any given temperature, $τ$ is longer in the arid regions compared to humid regions, suggesting an influence of, or covariation with, precipitation across climatic regions. The sensitivities to temperature, i.e., the slope of the fitted lines in **Figure 1a**, are all within ~17% across different climatic regions (**Table A3**). It should be noted that a significant number of grid cells, with a mean temperature less than 0°C, have longer $τ$ than under warmer temperatures within the same climatic region. Yet, the non-linear increase in temperature sensitivity with decreasing temperature is not as strong as reported previously for $τ$ of soil organic carbon <sup>17</sup> and the linear coefficients dominate the non-linear coefficients in different climatic regions (inset of **Figure 1**, and **Table A3**). While several factors may lead to such differences (e.g., differences in observed data, methodology, etc.), one key reason may also be the selection of climatic regions. For instance, in regions with temperature >10°C,
ignoring arid to semi-arid regions with a systematically longer τ than humid region would skew the overall distribution of τ, which would then lead to a hyper-logarithmically nonlinear τ-temperature relationship.

The apparent sensitivity of τ to precipitation is large when the precipitation is lower than ~1000 mm/year across all climatic regions (Figure 1b). Only within 0-1000 mm/year range of precipitation, τ varies by more than an order of magnitude. Contrasting to temperature, the τ-precipitation relationship saturates at higher precipitation (>1000 mm/year) in all regions except arid regions where precipitation never crosses the threshold. The overall apparent sensitivity of τ to precipitation is, therefore, hyper-logarithmically nonlinear, as indicated by a clear positive curvature. While the functional relationship of precipitation is almost the same for all but energy-limited humid regions, the sensitivity of τ to precipitation is smaller for humid regions compared to arid regions, indicating a saturation of the precipitation effect on τ. The difference of τ across different climatic regions is the smallest in the lowest precipitation ranges. Similar to the τ-temperature relationship, though, there is still a large variability of τ for given precipitation within all climatic regions (as indicated by low r² and higher r<sub>mad</sub> of fitted relationships in Figure 1 and Table A4).

GPP also has a clear relationship with temperature, the strength of which is dependent on the climatic region (Figure 1c). The temperature sensitivity is the largest in humid and the smallest in arid climatic region. In the humid region, GPP sensitivity to temperature increases with temperature. The GPP increases steadily for increasing precipitation with very small differences across different climatic regions (Figure 1d). The increase in GPP with precipitation is quasi-linear in all climates, as GPP saturates at the highest precipitation values, especially in the humid regions. This, again, suggests that precipitation plays an important role in determining GPP when the vegetation activities are likely to be limited by moisture. While a strong relationship of GPP with precipitation has been shown previously³⁰⁻³², the minimal difference of GPP across different climatic regions for given precipitation shows that the spatial variation of GPP is mainly related to precipitation alone.
<figure><img src="image_3.png" /><figcaption>**Figure 1.** Relationship between observation-based ecosystem turnover time of carbon ($\tau$, years) and gross primary productivity (GPP, kgC/m$^2$/year) with climate. In the top row, the relationship of $\tau$ with a) mean annual temperature (MAT, °C) and b) precipitation (MAP, mm/year) are plotted. The bottom row shows the same for GPP (c and d). The different colours indicate different climatic regions defined by the aridity index, and individual grid-cells are plotted as dots. The lines show a non-linear least square fit (see Methods) for the variation of $\tau$ and GPP with MAT and MAP within each climatic region. The inset text shows the parameters of the fit (non-linear coefficient | linear coefficient | constant) while the fitting performances are provided in Table A4. Note the logarithmic vertical axis for $\tau$ in a and b.</figcaption></figure>

## Climate sensitivities in Carbon Cycle models

In the CRESCENDDO model simulations, the apparent sensitivities of $\tau$ to climate have larger biases than those of GPP to climate, when compared against respective observation-based sensitivities (Figure 2). First, the comparison of the $\tau$-temperature relationship reveals that all models, except CLM4.5 and SURFEX, have a shorter $\tau$ than observation across all climatic regions while the linear correlation between the model and observation-based
relationships are generally high (first column, **Figure 2**). This is accompanied by a large bias in τ with most models, except CLM4.5, showing a clear underestimation. The differences between models and observation and among models also remain fairly similar across all climates. For example, the model with the longest τ in the arid region also has the longest τ in other climatic regions. This suggests that the temperature dependence of τ in a given model remains fairly consistent across different climatic regions. Of the models, only CLM5 shows a stronger sensitivity of τ to temperature with a hyper-logarithmically nonlinear increase in τ when the temperature decreases below 0°C (Figure 2e).

Similar to observation, the models also exhibit a tendency of non-linear increase in τ for decreasing precipitation, with the largest sensitivity in arid regions and the smallest sensitivity in humid regions (second column of **Figure 2**). Most models, though, show a smaller sensitivity to precipitation than the observation with a consistent underestimation bias across all climate, with the largest difference in the arid regions. In fact, only CLM4.5 and SURFEX show a significant increase of τ in the lower precipitation range that is akin to the observation.

For GPP, the models show increased sensitivity to temperature from arid to humid climatic regions (third column of **Figure 2**) except for CLM4.5 (Figure 2c), which shows a smaller increase in GPP at a higher temperature in all but the humid region, and LPJ-GUESS (Figure 2s) with much larger GPP in arid regions. In general, all models represent the sensitivity of GPP to temperature fairly well with a relatively smaller biases than the same of τ. The sensitivity of GPP to precipitation also shows a small spread among the models (fourth column of **Figure 2**). Only in the humid regions, a large number of models, e.g., CLM4.5 and JSBACH, over-predict GPP in the highest precipitation range, where the observation-based GPP shows a saturating tendency.
<figure><img src="image_4.png" /><figcaption>**Figure 2.** Evaluation of sensitivities of climatological carbon cycle dynamics to climate in CRESCENDO models. In the first and second columns, the relationships between ecosystem turnover time of carbon ($\tau$, years) versus mean annual temperature (*MAT*) and precipitation (*MAP*) are presented, followed by those for gross primary productivity (*GPP*, kgC/m$^2$/year) in the third and fourth columns. Along the row, the comparisons for different models against the observation are presented. The different colours indicate different climatic regions defined by the aridity index. The dotted lines indicate the observation-based relationship, and the solid lines indicate relationship from the model simulations. The inset text shows coefficient of determination ($r^2$) and mean relative bias between the fitted relationships from the models and observation. Note the logarithmic vertical axis for $\tau$ in the first and second columns.</figcaption></figure>
Partial correlations with climate

To elucidate the regional variations of τ, GPP and the resulting C<sub>total</sub>, and eliminate
collinearity between precipitation and climate, here, we evaluate the zonal variations and
their partial associations with precipitation and temperature.

In general, the large-scale zonal distribution of τ follows temperature, and that of GPP follows precipitation (first column of **Figure 3**, and **Figure A4**). The τ is the shortest in tropical regions with the highest temperature and the longest in high latitudes with the lowest temperature (**Figure 3a**). Similarly, GPP is the largest in the wettest tropical regions with the highest precipitation (**Figure 3d**). The zonal distribution of C<sub>total</sub> reveals a smaller variation across the latitude compared to τ and GPP (**Figure 3g**). Nonetheless, the largest C<sub>total</sub> occur in either the humid tropics with the largest GPP or in the high latitudes with the longest τ. In general, the CRESCENDO models produce zonal variations similar to observation-based estimates, with the smallest bias for GPP, and a consistent underestimation bias of τ and C<sub>total</sub> across the latitude.

The observation-based τ has a stronger negative correlation with temperature in the energy-
limited regions such as the tropics and high latitudes of both hemispheres compared to the
moisture-limited regions (Figure 3b). In general, the latitudinal variation of τ-temperature
correlation is much stronger in the models than in the observation. This is especially true for
sub-tropical mid-latitudes (40°S to 40°N) except the humid tropical regions. In the same
regions, the local variation of τ has a stronger correlation with precipitation than with
temperature (Figure 3c). The τ-precipitation relationships in the models have a larger spread,
and most models have a weaker τ-precipitation correlation than in the observation. This is
especially clear in the subtropical southern hemisphere and temperate northern hemisphere.
This weaker τ-precipitation correlation is concurrent with a stronger τ-temperature correlation
in the models suggesting a dominant temperature control on carbon cycle sensitivity to
climate. In these regions, only SURFEX shows a strong local-scale τ-precipitation correlation
that is consistently stronger than the observation, but it also exhibits a stronger bias in the
high latitudes.

Further, both the observations and models show a much stronger correlation of GPP with
precipitation (Figure 3f) than with temperature (Figure 3e) across most of the latitudes. Only
in the northern high latitudes over ~50°N (with MAT < 0°C), GPP has a stronger correlation
with temperature than with precipitation. In fact, in these regions, the low winter temperature
affects the MAT significantly, and correcting for winter reveals a clearer role of temperature
in the high latitudes (see **Figure A6**). The model spread is also relatively smaller for the
correlation of *GPP* with climate than of τ with climate. This shows that the models, in
general, reproduce both the global and local responses of *GPP* to temperature and
precipitation much better than those of τ.

Further, as expected, the observation-based relationship of $C_{total}$ and climate is a complex amalgam of those of $GPP$ and $\tau$. For example, $C_{total}$-temperature correlation is relatively small in magnitude (**Figure 3h**) due to the opposing $\tau$-temperature (negative) and $GPP$-temperature (positive) correlations. The $C_{total}$-precipitation correlation follows the same zonal variation as that of $GPP$ but with a lower magnitude (**Figure 3i**) due to predominantly negative $\tau$-precipitation correlation. The CRESCENDO models generally exhibit a stronger positive correlation of $C_{total}$ with climate than in the observation. This strong $C_{total}$-precipitation correlation in the models is due to a strong correlation between $C_{total}$ and $GPP$ (see **Figure A6**).
<figure><img src="image_5.png" /><figcaption>**Figure 3.** Zonal distribution of ecosystem turnover time of carbon (τ, years), gross primary productivity (GPP, kgC/m²/year), and total ecosystem carbon stock (C<sub>total</sub>, kgC/m²) and their relationships with climate. The zonal means are plotted in the left column, and the correlations with temperature and precipitation are plotted in the centre and right column, respectively. The correlation with precipitation is controlled for temperature and vice-versa. The Pearson's correlation coefficient for each latitude is calculated for a moving window of 10 grid cells along the latitude (5°). Only the coefficients that are statistically significant at 5% significance level are shown. The individual models are plotted in coloured thin lines, and the multimodel ensemble in thick blue lines. In the correlation plots, the thick dashed blue lines show the normalized mean correlation of all models with shades indicating variation within one standard deviation. The observation is plotted as a thick black line with shade indicating the range within the 5th and 95th percentiles.</figcaption></figure>
Model biases and agreement

<figure><img src="image_6.png" /></figure>

**Figure 4.** Global distributions of ecosystem turnover time of carbon (τ, years), gross primary productivity (GPP, kgC/m²/year), and total ecosystem carbon stock (C<sub>total</sub>, kgC/m²) and their biases. The multimodel ensemble, observation-based estimate, and the bias and agreement are presented in the first, second, and third row, respectively. Multimodel ensemble is calculated as the median of the seven CRESCENDO models. The bias is calculated as the ratio between multimodel ensemble and the corresponding observation. In the global maps of bias (third row), stippling indicates the regions where only two or fewer models fall within the range of observational uncertainties (5<sup>th</sup> and 95<sup>th</sup> percentiles).

Spatially, the CRESCENDO multi-model ensembles exhibit similar global distributions compared to the corresponding observation-based estimates of τ (Figure 4a, b), GPP (Figure 4d, e), and C<sub>total</sub> (Figure 4g, h). Globally, the observation-based τ is the shortest in tropical regions with high GPP as well as a relatively high C<sub>total</sub>, and the longest in high latitude regions with a relatively lower GPP but high C<sub>total</sub>. The longer τ is also prevalent in cold and dry arid regions, such as the surroundings of the Gobi Deserts, where both GPP and C<sub>total</sub> are lower than other regions. The observation-based C<sub>total</sub> shows a pattern of large carbon storages in either a region with high GPP or a longer τ. Additionally, larger C<sub>total</sub> are also evident in the Arctic North America and Boreal Eurasia characterized by occurrences of peat.
On a broad scale, the CRESCENDO multimodel ensemble $\tau$ also exhibits a similar spatial gradient with shorter $\tau$ in the tropics and longer $\tau$ in the northern high latitudes. Such spatial gradients are reproduced by individual models as well (Figure A8). Despite the similarity in spatial variability, the multimodel ensemble $\tau$ still has a substantial underestimation bias in the semiarid regions (sub-Saharan Sahel, central Asia, northern Australia, and western United States), where the multimodel ensemble is ~5 times shorter than the observation (Figure 4c). The models tend to agree with each other more in the northern high latitudes and the humid tropics than they do in the arid and semi-arid regions with large biases, as also shown previously for CMIP5 models (Carvalhais et al., 2014). Moreover, fewer than two models are within the observational uncertainty (hereafter referred to as low agreement) in ~22% of the total grid cells. In the semi-arid region, the underestimation of $\tau$ (the overestimation of turnover rate) is prevalent in all but three models (CLM4.5, JULES and SURFEX in Figure A7).

Both the spatial variability and magnitude of GPP in CRESCENDO models compare better with the corresponding observation than in the case of $\tau$ (see Figure A9 as well). In the tropical humid and semi-arid regions, the GPP bias is small in relative terms (Figure 4f). In semi-arid regions of south America and Australia, the relative bias in GPP is high due to relatively lower GPP values in the observation. But the largest overestimation bias can be seen in the northern high latitudes which have low GPP. The models also agree less in the regions with the largest bias with almost ~35% of global grid cells having a low model agreement. Note that such low agreement is also due to small uncertainty range in the ensemble of GPP observations (bar charts in Figure A7b). When the global and regional GPP are compared, almost all models are within the observational uncertainty globally due to better performance in the humid and sub-humid climate compared to other regions (Figure A7b).

Lastly, the spatial variability of $C_{total}$ in most CRESCENDO models is similar to that from observation-based estimate (Figure A10), even though the distinctly large storage in peatlands is not reproduced by most models. The bias in $C_{total}$ bears a striking similarity to the spatial pattern of bias of $\tau$. There are, however, also regions where the opposing biases in $\tau$ and GPP lead to unbiased $C_{total}$. For example, in the Iberian Peninsula and Hudson Bay, the overestimation of GPP is compensated by an underestimation of $\tau$ (overestimation of turnover rate) resulting in a relatively unbiased $C_{total}$. Due to such compounding effects, there is even more widespread occurrence of low model agreement for $C_{total}$ (~40% of global grid
cells), and biases, mostly similar with those of $τ$, are widespread across different climatic regions (Figure A7c).

To attribute the bias in $C_{total}$, we compare the biases in GPP, $C_{total}$, and $τ$ in each CRESCENDO model (Figure 5). Note that an ideal model would have low biases in all GPP, $τ$ and $C_{total}$. The contrast between the biases in GPP and $C_{total}$ reveals a dominant control of $τ$ on the $C_{total}$ bias. The JSBACH, LPJ-GUESS, and ORCHIDEE models show consistently lower $C_{total}$ than observation-based estimate, that is likely associated with an underestimation of $τ$, as the biases in GPP are relatively lower than those in $C_{total}$ (larger density of points along the axis of no bias in GPP). Other models perform better for both GPP and $τ$ in all but arid climatic region. Only CLM4.5 and SURFEX show a good agreement of $τ$ in arid region (red lines close to 1:1 line). CLM4.5, though, also has a slight overestimation bias in $C_{total}$ in all other climatic regions arising from overestimation of $τ$. In fact, in CLM5, the biases in $τ$ are reduced across all climatic regions. Only JULES and SURFEX produce a larger density of grid cells where biases are low for GPP, $τ$, and $C_{total}$. In JULES, $τ$ and $C_{total}$ are underestimated mainly in the arid and humid region. Globally, only CLM4.5 has larger range of spatial variability than in the observation (the slope of the fitted global line greater than 1).
<figure><img src="image_7.png" /><figcaption>**Figure 5.** Relationship of biases in gross primary productivity (GPP) and total ecosystem carbon stock ($C_{total}$) in CRESCENDO model simulations. The different colours indicate different climate defined by the aridity classes, and individual grid-cells are plotted as dots. The percentage values in the parenthesis of the title shows the fraction of the global grid cells that are within the range of bias between 0.1 and 4. The dashed vertical line shows the axis of no bias in GPP (ratio of GPP from model to that from observation = 1), the same for $C_{total}$ is shown by a horizontal dashed line. The grey solid line indicates the axis along which there is no bias in $τ$. An ideal point of no biases in GPP, $C_{total}$, and $τ$ is indicated by a cross ‘x’. The coloured lines indicate the main axis of variations of biases in GPP and $C_{total}$ (linearly fitted lines that passes through origin). The white contour lines indicate the density of grid cells, with higher density of lines showing larger occurrence of grid cells.</figcaption></figure>
Conclusions and discussion

Adding to a well-established association of carbon cycle with temperature, we show that precipitation also plays a key role in defining primary climate controls on spatial variabilities of GPP and carbon turnover times. The moisture control results in an emergent association of turnover time with aridity (Figure 1) that encompasses a wide range of precipitation and temperature regimes. Aridity regulates the moisture availability and, thus, modulates the apparent climate sensitivities of climatological carbon cycle dynamics. Despite uncertainties in the observation-based data, the presented observation-based climate sensitivities of carbon cycle are robust across full factorial of the latest estimates of GPP, soil and vegetation carbon stocks (Figure A11). We note that the apparent sensitivities presented here only reveals the primary controls, which is also indicated by a large spread within a climatic region (Figure 1). The additional heterogeneities may be associated with differences in soil and land properties, along with differences in secondary moisture effects such as photodegradation and pulsing of microbial activity from rainfall, drought-related mortality ³³, disturbances and fire regimes ³⁴,³⁵, etc.

We found that the offline simulations of the latest generation of Earth System Models from CRESCENDO project reproduce well the association of GPP with climate, but fall short for turnover times, especially in semiarid and arid regions leading to large uncertainties in simulated carbon stocks. The models with relatively lower biases in turnover time and carbon stock in arid and semiarid regions produce a better zonal variation of τ-precipitation relationship, while the poorer model performance is characterized by biases in τ-temperature relationship. This implies an insufficient model representation of moisture control on climatological carbon cycle dynamics even though all models include the moisture effects on both GPP and decomposition rates (Table A2).

The identification of exact mechanisms of moisture control on carbon cycle, especially without an observation-based soil moisture that extends beyond top few centimetres of soil, is still challenging. For example, we cannot clarify if the modelled soil moisture is itself biased or if the response of carbon cycle to soil moisture is misrepresented. Nevertheless, an evaluation of evapotranspiration shows a very consistent performance across models in all climatic regions (Figure A12), which should lead to a consistent soil moisture across models. Yet, the spatial covariation of carbon fluxes-moisture-temperature reveals diverse moisture-temperature relationships across different models (Figure A13). The temperature responses of GPP and respiration are highly consistent, but the moisture responses differ significantly
across different models. The model performing better in arid and semi-arid regions (e.g., SURFEX) has contrasting responses than the models with poorer performance providing secondary evidence of the potential weakness in the model representation of moisture controls. Factorial experiments of each model are necessary to identify the reasons behind, and to bridge the differences between, the apparent moisture controls presented in this study.

Lastly, the weaker performance of precipitation-turnover relationships leads to large uncertainties of carbon stocks especially in arid and semi-arid climatic regions, as the biases in $C_{total}$ are largely associated with biases in turnover time rather than those in $GPP$. Additionally, we found that biases of $GPP$ and turnover time manifest to a larger bias in $C_{total}$. This has serious implications in the predictions of changes in carbon stock under climate change, as the changes in precipitation, temperature, and thus aridity ³⁶ will have a non-negligible influence. The reduction of uncertainties in modelled carbon stock under global changes is, therefore, not a carbon-cycle only challenge and it must be addressed with a broader scope of improving the hydrological influences on the terrestrial carbon cycle.

391
Methods

Ecosystem carbon turnover time:

A turnover rate of a storage is broadly defined as the rate of fractional loss of storage per unit time. For an ecosystem under natural condition, the turnover time, an inverse of turnover rate, is, therefore, the time duration carbon stays in the ecosystem between carbon assimilation through photosynthesis and loss to atmosphere through respiration and decomposition processes. Under steady state assumption, the output carbon fluxes equilibrate with the input primary productivity, and temporal changes in carbon storage become small. Thus, the steady-state turnover time of an ecosystem can be effectively calculated as the ratio of carbon storage and the input flux to the ecosystem as,

$$ \tau = \frac{c_{\text{Total}}}{GPP} \qquad (1), $$

where, $\tau$ is the ecosystem turnover time (years), $C_{\text{total}}$ is the long-term average total ecosystem carbon storage per unit area (kgC/m²) and $GPP$ is the annual mean gross primary productivity (kgC/m²/year). As stated and used in previous studies ¹⁷,¹⁸,²⁵,²⁶, the $\tau$ in Eqn (1) is under the assumption of a steady state ecosystem and represents the apparent or effective turnover time of the whole ecosystem carbon storage. It emerges as the diagnostic property of an ecosystem, rather than the intrinsic property of decomposition processes that explicitly controls $C_{\text{total}}$.

Observation-based datasets:

Due to potential uncertainties in the global observation-based estimates, we used an ensemble of six GPP datasets, four soil carbon ($C_{\text{soil}}$) and four vegetation carbon ($C_{\text{veg}}$) stock datasets. The data ensembles, spanning a wide range of sources and methods, represent the current state-of-the-art of global observation-based estimates of the carbon cycle components and, likely, cover the full range of observational uncertainties. As we use only a single ensemble estimate from each product, we assume that the differences and uncertainties are larger across the datasets than within a single dataset.

The GPP ensemble includes Model Tree Ensembles (MTE) (Jung et al., 2011) and its recent successors from FLUXCOM based on remote sensing and that with additional meteorological forcing ³⁸, solar-induced fluorescence (SIF) based GOSIF GPP ³⁹, light use efficiency based GPP from vegetation photosynthesis model (VPM) ⁴⁰, and lastly, an independent machine learning prediction from FluxSat ⁴¹ that uses corrected satellite-based reflectance. All GPP products are either upscaled from or extensively evaluated against eddy covariance
observations of carbon fluxes from FLUXNET (www.fluxdata.org) sites (Baldocchi et al., 2001). For example, the MTE, FLUXCOM, and FluxSat products use different combinations and corrections of training data and drivers from satellite remote sensing and meteorological dataset to upscale site-level observation to the global scale using different machine learning algorithms. VPM, a light use efficiency model, is similar to MODIS GPP but with an additional validation for FLUXNET sites, and GOSIF GPP uses a set of GPP-SIF relationships to produce an ensemble of high resolution global GPP fields that are independent of reflectance-based remote sensing products. While the spatial variability of the mean GPP is one of the most robust features when comparing different observation-based GPP products, it is desirable to use an ensemble as no single data is superior to all others universally 43.

For C<sub>soil</sub>, we use the full depth soil organic carbon estimates including a data that combines inventories from Harmonized World Soil Database 44 with the Northern Circumpolar Soil Carbon Database 45 extrapolated to full depth 18; from SoilGrids that uses machine learning method to upscale soil profile measurements with land and climate characteristics as predictors46; and from Sanderman et al. that corrects for land use and forest cover 47. Due to differences in number and locations of observed soil profiles used, predictors, and prediction methods, the soil carbon estimates are uncertain, especially in high latitude regions, with a large C<sub>soil</sub> but a relatively fewer measurement profile. Nonetheless, the global distributions of C<sub>soil</sub> in these products are robust 48, and their differences reflect potential uncertainties across all observation-based global estimates. We note that the SoilGrids data has been recently updated, but the new version of the data, the LANDGIS, has not been used in this analysis owing to lack of extensive validation and potential over-estimation issue in the northern high latitudes 48,49. It should here be noted that using the LANDGIS instead of SoilGrids does not significantly affect the main findings of this study (see Figure 1 and Figure A3).

The C<sub>veg</sub> ensemble includes four different RADAR and LIDAR satellite-based estimates of aboveground biomass with a corresponding estimate for belowground biomass 48. As different data are based on different satellites and algorithms, and have been validated with observations whenever and wherever available, they are indicative of global vegetation biomass and associated uncertainties in observation-based estimates.

An ensemble of observation-based τ was then obtained using Eqn (1) for a full factorial combination of all C<sub>soil</sub>, C<sub>veg</sub>, and GPP products resulting in 96 different τ maps.
In this study, for GPP, $C_{total}$ and $\tau$, the ensemble median across data products was used as the representative observation-based estimate, and the 5th and 95th percentiles were used as uncertainty range.

Lastly, for an additional evaluation of CRESCENDO models, the ensemble estimates of evapotranspiration from FLUXCOM remote sensing products ⁵⁰ was used.

**Climatic regions based on aridity index:**

The aridity index, calculated as the ratio of mean precipitation and potential evapotranspiration (PET), is used to delineate different climatic regions based on relative availability of moisture and energy. For consistency, the CRU-NCEP precipitation, used to force the CRESCENDO model simulations, is also used for calculating the aridity index. The PET data is based on an estimate from the latest climate datasets at a high resolution ⁵¹.

Different climatic regions were then delineated based on the aridity index ranges suggested by UNEP ⁵² as: arid (<0.2), semi-arid, sub-humid, and humid (see **Figure A1**). The average annual precipitation (temperature) varies from 245 mm/year (7.6°C) in arid regions to 880.3 mm/year (0.9°C) in humid regions. These regions constitute 8.2%, 24.3%, 15.1%, and 52.4% of the total area considered in this study. In relative terms, the arid and semiarid regions contribute ~18% of the global GPP and hold ~24% of the global carbon stock (**Table A1**).

Combined, these regions have a $\tau$ of ~43 years, which is ~34% longer than the global $\tau$ of ~32 years.

**Climate sensitivities:**

The overarching aim of this study is to investigate the climate sensitivities of climatological mean carbon cycle dynamics across all major climatic regions globally and assess the apparent sensitivities of spatial covariations of carbon cycle with climate. Under humid climate, spatial sensitivity of $\tau$ is itself dependent on temperature ¹⁷. But, to what extent the same applies to other climatic regions and carbon cycle variables is unclear. This is especially critical with regard to precipitation that represents the potential moisture supply for an ecosystem that determines both the carbon assimilation and decomposition processes.

Further, we hypothesize that the relative availability of moisture (supplied by precipitation) and energy (determined by temperature) plays a central role in defining the carbon cycle dynamics across spatiotemporal scales. We, therefore, investigate the relationships between the carbon turnover time and GPP with precipitation and temperature across different
climatic regions characterized by an aridity index. We assume that the relationship between $\tau/GPP$ and climate are non-linear and assume it to be of a second-degree polynomial form as,

$$y = ax^2 + bx + c \quad (2),$$

where, $y$ is the response/dependent variable, $x$ is the independent variable, and $a, b$ and $c$ are the parameters of the quadratic equation. The terms $a$ and $b$ are the coefficients of the non-linear and linear terms, respectively, and $c$ is the constant term that defines the offset/intercept when the independent variable is zero. As $\tau$ is expected to have a non-linear exponential relationship with temperature, we log-normalize it and use $\log(\tau)$ as the dependent variable.

The parameters of Eqn (2) for each climatic region are estimated using a robust non-linear least square regression with Huber loss function 53 that is less sensitive to outliers in the data.

### CRESCENDO model simulations:

We use the observation-based climate sensitivities to evaluate the process representations in land surface schemes of (used in) the ESMs from seven different European research institutes. The stand-alone offline land simulations were carried out as a part of the CRESCENDO project (https://ukesm.ac.uk/crescendo/) to understand and evaluate the carbon and nitrogen cycle processes in the current state-of-the-art ESMs. The same land surface schemes were used in the ESM simulations for the sixth phase of coupled model intercomparison project (CMIP6). Following the TRENDY protocol 54, the models were forced by CRUNCEP v7 55 forcing dataset

(https://vesg.ipsl.upmc.fr/thredds/catalog/work/p529viov/cruncep/V8_1901_2016/catalog.html), observed atmospheric $CO_2$ concentration, nitrogen deposition, and annual land-use changes. The offline simulations forced with an observation-based dataset are suitable for evaluating the response of the land carbon cycle processes to the climate forcing, as they are less prone to biases and uncertainties arising from differences in carbon-climate feedbacks in the coupled simulations of ESM.

The data of CRESCENDO model simulations were last accessed in January, 2019. While the simulations are available for longer time period, the simulation results from 2001 to 2010 inclusive, consistent with the time period across different observation-based estimates of carbon cycle variables, were used for evaluations in this study. The $C_{total}$ was calculated as a sum of all the carbon pools respiring to the atmosphere. Similar to the observation, $\tau$ was calculated as the ratio of $C_{total}$ and $GPP$.
All models were forced in an offline mode with the same meteorological drivers, but at a different resolution with a different experimental and process setup (see **Table A2** for an overview). Regarding carbon cycle spinup, all models except JULES were initialized with zero carbo stock, and forced by the repeated meteorological data of the first few years for a total of 500-10000 years. It should be noted that, in essence, irrespective of the initial condition, the JULES model produces a consistent model state at the end of spinup period ⁵⁶, and, in general, by definition, the spin-up and initial condition are not systematically related to the biases in the model states. There are further differences in soil physics and model structure therein. For example, CLM5, JULES, and SURFEX have a finer discretization of soil layers and/or represent soil physics with freeze-thaw dynamics.

CLM4.5, the terrestrial component of the CMCC coupled model version 2 ⁵⁷ within CMIP6, was used in its Biogeochemical (BGC) configuration ⁵⁸,⁵⁹ for the CRESCENDO simulations. CLM4.5 describes photosynthetic, hydrologic, and decomposition processes. Photosynthesis is based on Ball-Berry model, and hydrology includes soil moisture and groundwater processes. The decomposition rates are dependent on soil temperature, soil moisture, oxygen and depth.

CLM5, the terrestrial component of NorESM, builds on CLM4.5, with major updates on soil hydrology and carbon coupling ⁶⁰. Soil hydrology is based on variable soil thickness with high resolution layers and spatially varying root profile. Photosynthesis is based on the Medlyn-model and includes nitrogen limitation using optimality principles. The representation of the decomposition process is updated with a new metric for the apparent soil carbon turnover ¹⁷ in which the temperature affects the moisture limitation of decomposition through freezing of liquid water.

JSBACH version 3.2 ⁶¹ is the terrestrial component of MPI-ESM1.2. As compared to its predecessor, it includes novel components of soil carbon, nitrogen limitation, a five-layer hydrology scheme, the wildfire model SPITFIRE, as well as improved land use representations ⁶². The soil carbon decomposition processes are based on the YASSO model ⁶³ and include five different soil carbon pools according to the chemical quality of the organic matter, each for woody and non-woody litter. The vertical distribution of soil carbon is not resolved and permafrost is not considered in the applied version. Decomposition rates depend on air temperature and precipitation, due to the foundation of YASSO on observed litter decomposition rates.
JULES<sup>56</sup>, the land component of UKESM1, includes the improvements in parameterization of the vegetation dynamics, canopy structural properties, and the parameters affecting the photosynthesis and respiration fluxes<sup>64</sup>. The nutrient availability limits the photosynthesis indirectly by controlling the biomass and leaf area index. The litter and exudate fluxes convert to the soil organic carbon through controls of nitrogen availability, and the soil decomposition process are controlled further by temperature and moisture.

LPJ-GUESS<sup>65</sup> is the dynamic vegetation model of EC-Earth used in CMIP6. LPJ-GUESS employs a two-layer leaky bucket soil hydrology scheme with percolation between layers and deep drainage. Photosynthesis is controlled by nitrogen limitation following whole plant optimal nitrogen content. The soil organic matter dynamics are based on the CENTURY soil model in which the decay rates depend on the moisture content of the top soil layer, soil temperature, texture, lignin fractions, tillage and nitrogen limitation.

ORCHIDEE, the land surface scheme of the IPSL-CM5 ESM, consists of a multi-layer soil that accounts for transport of water by diffusion and deep drainage, and of heat with improved thermodynamics and conduction process<sup>66</sup>. The resulting soil moisture and temperature are used for analytically solving soil organic matter dynamic that guarantees steady-state conditions. Photosynthesis is based on the Farquhar-model and is limited by the leaf nitrogen. The soil heterotrophic respiration is independent of the nitrogen content of soil organic matter.

SURFEX/ISBA-CTRIP, the land surface scheme of the CNRM-ESM2-1 in CMIP6<sup>67,68</sup> solves the energy and water balance of one vegetation canopy, 12 snow layers, and up to 14 soil layers in deep soils and permafrost. Soil texture, albedo and carbon content determine the thermal and hydraulic properties of the soil. The litter and soil organic matter processes are based on the soil carbon part of the CENTURY model, and the soil heterotrophic respiration is limited under high soil moisture. The nitrogen limitation leaf growth is empirically based on a meta-analysis of CO2 enrichment experiments that limit leaf nitrogen content and specific leaf area.

Zonal variations and correlation:

The zonal variations and correlations are computed using a moving window of 10 grid cells along the latitude (5° coverage). The zonal means of the GPP and $C_{total}$ are weighted by the area of the grid cell which vary along the latitude, and the zonal mean of $τ$ was estimated as
the ratio of zonal $C_{total}$ and GPP, and not as a zonal mean of $τ$ in different grid cells. The observational uncertainty band for the zonal means are calculated as 5th and 95th percentiles of the zonal value using different data products.

The correlations between $τ$ or GPP or $C_{total}$ and temperature or precipitation were calculated as the partial Pearson's correlation coefficient controlling for the other. To accommodate for the influence of the extreme cold winter temperature on the mean annual temperature in high latitude regions, the monthly temperature below -5°C were considered physiologically (for photosynthesis) and metabolically (for respiration) irrelevant, and these values were set to -5°C while calculating the mean annual temperature. Note that the processing is only relevant for high latitude regions where the duration of and temperature in winter vary significantly within a moving window (see **Figure 3** and **Figure A1**).

Within a moving window, one percent grid cells were discarded to minimize the effects of outliers on the correlation coefficient. Unless otherwise mentioned in the captions, the uncertainty band around the observation are the ranges within 5th and 95th percentile of the values calculated from different data products. The partial correlation coefficients were tested for statistical significance at 5% level of significance, and all insignificant correlations are masked out when plotting.
Acknowledgments

The CRESCENDO simulations and analysis for this study were carried out under the support of “Coordinated Research in Earth Systems and Climate: Experiments, kNowledge, Dissemination and Outreach (CRESCENDO)” project of the European Union's Horizon 2020 Framework Programme (grant agreement no. 641816). SK acknowledges the additional support of the “Erdsystemforschung: Afrikanische Grundwasserressourcen im Zuge des globalen Wandels” (Earth System Research: Groundwater Resources in Africa under Global Change) project of the Max Planck Society.

Author Contributions

SK and NC conceptually designed the study. SK carried out the analysis and prepared the manuscript. CJ, VB, CD, YF, VG, EJ, HL, SM, JN, DP, PP, DW, AW contributed to and or provided CRESCENDO model simulations. All authors had intellectual and/or direct input to the discussion of the results and completion of the manuscript.

Data and Code Availability

All the datasets used in this study are available in the public domain, and can be obtained by following the original publications that are cited in respective sections. The python code used to analyse the data and plot the results are available publicly at https://github.com/koir-su/c_cycle_eval.
Extended Tables

<table><caption>**Table A1.** Summary of the median and the range of observation-based gross primary productivity (GPP in pgC/year), total carbon storage ($C_{total}$ in pgC) and turnover time ($\tau$ in years) globally, and in different climatic regions. The median is calculated from the ensemble members of the observation-based data. The range indicates the values within 5th and 95th percentile of the ensemble members.</caption><thead><tr><th></th><th>Global</th><th>Arid</th><th>Semi-arid</th><th>Sub-humid</th><th>Humid</th></tr></thead><tbody><tr><th>GPP</th><td>109.5<br>(98.3-119.6)</td><td>2.7<br>(2.3-3.1)</td><td>16.8<br>(14.8-19.3)</td><td>12.8<br>(11.1-13.6)</td><td>77.6<br>(69.0-85.3)</td></tr><tr><th>C<sub>total</sub></th><td>3482.9<br>(2245.0-4804.8)</td><td>149.2<br>(105.3-162.4)</td><td>680.3<br>(424.7-811.5)</td><td>493.9<br>(289.3-698.0)</td><td>2150.4<br>(1418.0-3151.5)</td></tr><tr><th>τ</th><td>31.9<br>(18.9-47.4)</td><td>52.9<br>(35.1-73.2)</td><td>39.7<br>(22.9-54.1)</td><td>38.8<br>(21.4-62.1)</td><td>27.7<br>(16.8-44.3)</td></tr></tbody></table>
<table><caption>**Table A2.** An overview of the CRESCENDO models, the major processes therein, and the simulation setup. Human activities include human need-driven processes that affects the vegetation carbon stock such as crop harvest (H), pasture (P), wood harvest (W), deforestation (D), land use changes (LUC), and nitrogen deposition (NDep). All models include carbon losses from heterotrophic respiration (RH), and some models include the carbon losses from soil due to leaching of dissolved organic carbon (DOC).</caption><thead><tr><th>SN</th><th>Model Name (LSM/ES M)</th><th>Institution</th><th>Spinup (years)</th><th>Initial carbon stock</th><th>Forcing for spinup (repeat years)</th><th>Native spatial resolution (° latitude x ° longitude)</th><th>Dynamic vegetation process</th><th>Human activities</th><th>Soil physics (number of layers, total depth)</th><th>Soil carbon sink terms</th></tr></thead><tbody><tr><td>1</td><td>CLM4.5/CMCC-ESM</td><td>Euro Mediterranean Centre on Climate Change (CMCC) Foundation</td><td>1020 accelerated + 300 non-accelerated</td><td>0</td><td>30 years</td><td>1.25°x0.9375°</td><td>no</td><td>LUC, W, D</td><td>15 layers, 35.1776 m</td><td>RH</td></tr><tr><td>2</td><td>CLM5/No rESM</td><td>NORCE Norwegian Research Centre, Bergen, Norway</td><td>1526</td><td>0</td><td>30 years</td><td>0.5°x0.5°</td><td>no</td><td>LUC, W, D</td><td>20 layers, 8.5 m</td><td>RH; carbon cost for nutrient processes</td></tr><tr><td>3</td><td>JSBACH/ MPI-ESM</td><td>Max Planck Institute for Meteorology</td><td>> 10000</td><td>C stock from TRENDY v6 simulation</td><td>20 years</td><td>~1.875°x1.875° (T63)</td><td>not activated</td><td>LUC, NDep, W, H</td><td>Soil physics: 5 layers, 9.834 m; soil carbon: 1 layer</td><td>RH</td></tr><tr><td>4</td><td>JULES/U KESM</td><td>Met Office Hadley Centre, UK NERC</td><td>10000</td><td>C stock from independent simulation</td><td>20 years</td><td>~1.25°x1.875° (N96)</td><td>yes</td><td>LUC, NDep, H</td><td>4 layers, 3 m</td><td>RH</td></tr><tr><td>5</td><td>LPJ-GUESS/E C-Earth</td><td>Department of Physical Geography and Ecosystem Science, Lund University</td><td>Soil: 40500; Vegetation: 500</td><td>0</td><td>30 years, no IAV of temperature</td><td>0.5°x0.5°</td><td>yes</td><td>LUC, NDep, H, P</td><td>Soil moisture: 2 layers, 1.5 m; soil carbon: 1 layer</td><td>RH; DOC</td></tr><tr><td>6</td><td>ORCHID EE/IPSL-CM5</td><td>Institut Pierre Simon Laplace (IPSL), France</td><td>340 for litter input; cSoil: until steady state</td><td>0</td><td>30 years</td><td>0.5°x0.5°</td><td>no</td><td>LUC, W, H, D</td><td>Soil moisture: 11 layers, 2 m; soil carbon: 1 layer</td><td>RH</td></tr><tr><td>7</td><td>SURFEX/CNRM-CM5</td><td>CNRM, Meteo-France/CNRS/Université Fédérale de Toulouse</td><td>Soil: 8875; Vegetation: 470</td><td>0</td><td>20 years</td><td>1°x1°</td><td>no</td><td>LUC</td><td>Soil temperature: 14 layers, 12 m; soil moisture: 14 layers, till rooting depth (1m for grasses, 8m for tropical forests)</td><td>RH; DOC</td></tr></tbody></table>
<table><caption>**Table A3.** Summary of the parameters of the non-linear least square fitting of the relationships between $\tau$ and GPP and climate: a: coefficient for the quadratic term, b: coefficient for the linear term, and c: constant.</caption><thead><tr><th rowspan="2"></th><th rowspan="2"></th><th colspan="3">Arid</th><th colspan="3">Semi-arid</th><th colspan="3">Sub-humid</th><th colspan="3">Humid</th></tr><tr><th>a</th><th>b</th><th>c</th><th>a</th><th>b</th><th>c</th><th>a</th><th>b</th><th>c</th><th>a</th><th>b</th><th>c</th></tr></thead><tbody><tr><td rowspan="10">τ-MAT</td><td>Obs-based</td><td>2.61E-05</td><td>-3.45E-02</td><td>2.25</td><td>1.01E-04</td><td>-3.34E-02</td><td>1.97</td><td>1.33E-12</td><td>-3.01E-02</td><td>1.84</td><td>2.38E-04</td><td>-3.60E-02</td><td>1.88</td></tr><tr><td>CLM4.5</td><td>9.51E-04</td><td>-5.23E-02</td><td>2.13</td><td>1.36E-04</td><td>-3.48E-02</td><td>1.96</td><td>7.23E-16</td><td>-3.33E-02</td><td>1.92</td><td>1.92E-04</td><td>-3.32E-02</td><td>1.82</td></tr><tr><td>CLM5</td><td>1.01E-03</td><td>-6.36E-02</td><td>1.86</td><td>9.70E-04</td><td>-5.82E-02</td><td>1.53</td><td>4.41E-04</td><td>-3.96E-02</td><td>1.40</td><td>7.31E-04</td><td>-3.93E-02</td><td>1.44</td></tr><tr><td>JSBACH</td><td>1.04E-20</td><td>-1.62E-02</td><td>0.91</td><td>5.00E-04</td><td>-3.55E-02</td><td>1.00</td><td>1.56E-04</td><td>-3.11E-02</td><td>1.16</td><td>2.06E-05</td><td>-2.53E-02</td><td>1.29</td></tr><tr><td>JULES</td><td>3.94E-04</td><td>-2.56E-02</td><td>1.45</td><td>9.43E-20</td><td>-1.50E-02</td><td>1.54</td><td>1.52E-18</td><td>-1.11E-02</td><td>1.51</td><td>7.76E-16</td><td>-1.44E-02</td><td>1.43</td></tr><tr><td>LPJ-GUESS</td><td>5.86E-04</td><td>-3.81E-02</td><td>1.41</td><td>2.84E-04</td><td>-2.81E-02</td><td>1.41</td><td>1.70E-04</td><td>-2.36E-02</td><td>1.39</td><td>2.16E-04</td><td>-2.67E-02</td><td>1.42</td></tr><tr><td>ORCHIDEE</td><td>5.55E-04</td><td>-3.32E-02</td><td>1.21</td><td>4.82E-04</td><td>-2.49E-02</td><td>1.07</td><td>4.93E-04</td><td>-2.01E-02</td><td>1.00</td><td>1.05E-04</td><td>-1.50E-02</td><td>1.15</td></tr><tr><td>SURFEX</td><td>3.31E-14</td><td>-3.37E-02</td><td>2.23</td><td>1.48E-17</td><td>-2.98E-02</td><td>1.95</td><td>5.78E-20</td><td>-2.54E-02</td><td>1.75</td><td>2.85E-17</td><td>-2.84E-02</td><td>1.72</td></tr><tr><td rowspan="10">τ-MAP</td><td>Obs-based</td><td>1.05E-06</td><td>-2.64E-03</td><td>2.40</td><td>2.30E-06</td><td>-4.19E-03</td><td>3.05</td><td>1.11E-06</td><td>-2.86E-03</td><td>2.91</td><td>2.65E-07</td><td>-1.31E-03</td><td>2.60</td></tr><tr><td>CLM4.5</td><td>9.25E-07</td><td>-2.26E-03</td><td>2.19</td><td>2.03E-06</td><td>-3.90E-03</td><td>2.96</td><td>8.09E-07</td><td>-2.57E-03</td><td>2.93</td><td>2.63E-07</td><td>-1.27E-03</td><td>2.52</td></tr><tr><td>CLM5</td><td>1.54E-06</td><td>-3.44E-03</td><td>2.01</td><td>3.97E-06</td><td>-6.45E-03</td><td>3.20</td><td>2.00E-06</td><td>-4.32E-03</td><td>3.00</td><td>2.74E-07</td><td>-1.24E-03</td><td>2.18</td></tr><tr><td>JSBACH</td><td>2.86E-07</td><td>-6.45E-04</td><td>0.84</td><td>1.79E-06</td><td>-3.21E-03</td><td>1.83</td><td>1.22E-06</td><td>-2.99E-03</td><td>2.28</td><td>2.20E-07</td><td>-1.05E-03</td><td>1.84</td></tr><tr><td>JULES</td><td>7.30E-08</td><td>-1.87E-04</td><td>1.25</td><td>4.86E-07</td><td>-1.16E-03</td><td>1.81</td><td>1.80E-31</td><td>-4.95E-04</td><td>1.76</td><td>7.74E-08</td><td>-5.02E-04</td><td>1.72</td></tr><tr><td>LPJ-GUESS</td><td>4.23E-07</td><td>-1.02E-03</td><td>1.28</td><td>2.19E-06</td><td>-3.50E-03</td><td>2.28</td><td>9.63E-07</td><td>-2.25E-03</td><td>2.23</td><td>1.79E-07</td><td>-8.92E-04</td><td>1.92</td></tr><tr><td>ORCHIDEE</td><td>5.30E-07</td><td>-1.15E-03</td><td>1.18</td><td>1.65E-06</td><td>-2.61E-03</td><td>1.74</td><td>9.30E-07</td><td>-1.84E-03</td><td>1.68</td><td>9.53E-08</td><td>-4.91E-04</td><td>1.41</td></tr><tr><td>SURFEX</td><td>9.71E-07</td><td>-2.51E-03</td><td>2.38</td><td>9.44E-07</td><td>-2.69E-03</td><td>2.69</td><td>2.63E-07</td><td>-1.50E-03</td><td>2.41</td><td>1.76E-07</td><td>-1.01E-03</td><td>2.27</td></tr><tr><td rowspan="10">GPP-MAT</td><td>Obs-based</td><td>3.97E-04</td><td>1.09E-03</td><td>0.17</td><td>2.88E-04</td><td>1.54E-02</td><td>0.41</td><td>3.87E-21</td><td>3.22E-02</td><td>0.69</td><td>7.24E-04</td><td>4.83E-02</td><td>0.69</td></tr><tr><td>CLM4.5</td><td>1.35E-04</td><td>2.77E-04</td><td>0.15</td><td>3.68E-15</td><td>5.76E-03</td><td>0.38</td><td>3.85E-34</td><td>1.35E-02</td><td>0.59</td><td>4.17E-04</td><td>5.60E-02</td><td>0.90</td></tr><tr><td>CLM5</td><td>5.20E-04</td><td>-2.19E-03</td><td>0.14</td><td>5.74E-04</td><td>3.08E-03</td><td>0.38</td><td>4.42E-05</td><td>1.66E-02</td><td>0.73</td><td>6.07E-04</td><td>3.89E-02</td><td>1.00</td></tr><tr><td>JSBACH</td><td>3.57E-04</td><td>-6.90E-04</td><td>0.11</td><td>7.05E-04</td><td>6.56E-03</td><td>0.24</td><td>7.18E-04</td><td>1.97E-02</td><td>0.49</td><td>1.89E-03</td><td>3.95E-02</td><td>0.66</td></tr><tr><td>JULES</td><td>4.85E-15</td><td>4.02E-03</td><td>0.10</td><td>4.40E-04</td><td>1.50E-02</td><td>0.18</td><td>4.03E-04</td><td>3.02E-02</td><td>0.48</td><td>2.07E-04</td><td>5.62E-02</td><td>0.90</td></tr><tr><td>LPJ-GUESS</td><td>2.12E-18</td><td>1.97E-02</td><td>0.36</td><td>1.06E-15</td><td>1.80E-02</td><td>0.61</td><td>6.14E-22</td><td>1.87E-02</td><td>0.83</td><td>4.63E-15</td><td>4.74E-02</td><td>1.07</td></tr><tr><td>ORCHIDEE</td><td>4.04E-04</td><td>3.40E-03</td><td>0.05</td><td>6.45E-04</td><td>1.67E-02</td><td>0.26</td><td>1.54E-04</td><td>3.36E-02</td><td>0.66</td><td>8.37E-04</td><td>5.06E-02</td><td>0.78</td></tr><tr><td>SURFEX</td><td>2.61E-04</td><td>2.62E-03</td><td>0.07</td><td>5.66E-04</td><td>1.27E-02</td><td>0.24</td><td>5.08E-04</td><td>2.57E-02</td><td>0.49</td><td>1.64E-03</td><td>4.20E-02</td><td>0.51</td></tr><tr><td rowspan="10">GPP-MAP</td><td>Obs-based</td><td>-8.84E-08</td><td>1.09E-03</td><td>0.00</td><td>-1.87E-07</td><td>1.43E-03</td><td>0.00</td><td>-2.45E-07</td><td>1.61E-03</td><td>0.00</td><td>-1.58E-07</td><td>1.46E-03</td><td>0.00</td></tr><tr><td>CLM4.5</td><td>3.30E-07</td><td>5.79E-04</td><td>0.00</td><td>-7.28E-07</td><td>1.33E-03</td><td>0.00</td><td>-9.64E-07</td><td>1.84E-03</td><td>0.00</td><td>-1.01E-07</td><td>1.48E-03</td><td>0.00</td></tr><tr><td>CLM5</td><td>8.81E-08</td><td>9.87E-04</td><td>0.00</td><td>-2.28E-07</td><td>1.31E-03</td><td>0.00</td><td>-8.16E-07</td><td>1.96E-03</td><td>0.00</td><td>-2.27E-07</td><td>1.68E-03</td><td>0.00</td></tr><tr><td>JSBACH</td><td>2.44E-07</td><td>6.05E-04</td><td>0.00</td><td>6.06E-07</td><td>6.19E-04</td><td>0.00</td><td>3.00E-07</td><td>9.70E-04</td><td>0.00</td><td>-1.31E-08</td><td>1.40E-03</td><td>0.00</td></tr><tr><td>JULES</td><td>3.77E-07</td><td>4.79E-04</td><td>0.00</td><td>9.44E-07</td><td>3.75E-04</td><td>0.00</td><td>5.15E-07</td><td>8.24E-04</td><td>0.00</td><td>-2.40E-07</td><td>1.73E-03</td><td>0.00</td></tr><tr><td>LPJ-GUESS</td><td>-9.69E-07</td><td>2.55E-03</td><td>0.00</td><td>-1.33E-06</td><td>2.42E-03</td><td>0.00</td><td>-1.23E-06</td><td>2.47E-03</td><td>0.00</td><td>-2.34E-07</td><td>1.70E-03</td><td>0.00</td></tr><tr><td>ORCHIDEE</td><td>1.74E-07</td><td>7.45E-04</td><td>0.00</td><td>7.27E-07</td><td>8.20E-04</td><td>0.00</td><td>-4.85E-08</td><td>1.48E-03</td><td>0.00</td><td>-1.77E-07</td><td>1.62E-03</td><td>0.00</td></tr><tr><td>SURFEX</td><td>3.38E-08</td><td>6.52E-04</td><td>0.00</td><td>7.23E-07</td><td>6.34E-04</td><td>0.00</td><td>3.42E-07</td><td>9.49E-04</td><td>0.00</td><td>-1.09E-07</td><td>1.42E-03</td><td>0.00</td></tr></tbody></table>
<table><caption>**Table A4.** Performance metrics for least square regression of the relationship between $\tau$, GPP, and climate: $r^2$: coefficient of determination. $r_{mad}$: relative median absolute deviation calculated as the median of absolute deviation normalized by the interquartile range of the observation.</caption><thead><tr><th rowspan="3"></th><th rowspan="3"></th><th colspan="8">MAT</th><th colspan="8">MAP</th></tr><tr><th colspan="2">Arid</th><th colspan="2">Semi-arid</th><th colspan="2">Sub-humid</th><th colspan="2">Humid</th><th colspan="2">Arid</th><th colspan="2">Semi-arid</th><th colspan="2">Sub-humid</th><th colspan="2">Humid</th></tr><tr><th>r<sup>2</sup></th><th>r<sub>mad</sub></th><th>r<sup>2</sup></th><th>r<sub>mad</sub></th><th>r<sup>2</sup></th><th>r<sub>mad</sub></th><th>r<sup>2</sup></th><th>r<sub>mad</sub></th><th>r<sup>2</sup></th><th>r<sub>mad</sub></th><th>r<sup>2</sup></th><th>r<sub>mad</sub></th><th>r<sup>2</sup></th><th>r<sub>mad</sub></th><th>r<sup>2</sup></th><th>r<sub>mad</sub></th></tr></thead><tbody><tr><td rowspan="10">τ</td><td>Obs-based</td><td>0.06</td><td>0.25</td><td>0.45</td><td>0.14</td><td>0.44</td><td>0.14</td><td>0.37</td><td>0.13</td><td>0.00</td><td>0.27</td><td>0.58</td><td>0.14</td><td>0.57</td><td>0.14</td><td>0.00</td><td>0.18</td></tr><tr><td>CLM4.5</td><td>0.00</td><td>0.32</td><td>0.00</td><td>0.11</td><td>0.31</td><td>0.10</td><td>0.00</td><td>0.11</td><td>0.00</td><td>0.48</td><td>0.00</td><td>0.16</td><td>0.32</td><td>0.10</td><td>0.00</td><td>0.18</td></tr><tr><td>CLM5</td><td>0.00</td><td>0.36</td><td>0.00</td><td>0.18</td><td>0.00</td><td>0.25</td><td>0.00</td><td>0.24</td><td>0.00</td><td>0.37</td><td>0.00</td><td>0.30</td><td>0.01</td><td>0.26</td><td>0.00</td><td>0.35</td></tr><tr><td>JSBACH</td><td>0.23</td><td>0.42</td><td>0.40</td><td>0.22</td><td>0.34</td><td>0.14</td><td>0.65</td><td>0.16</td><td>0.01</td><td>0.44</td><td>0.40</td><td>0.29</td><td>0.48</td><td>0.15</td><td>0.62</td><td>0.20</td></tr><tr><td>JULES</td><td>0.00</td><td>0.39</td><td>0.00</td><td>0.31</td><td>0.01</td><td>0.30</td><td>0.20</td><td>0.17</td><td>0.00</td><td>0.49</td><td>0.00</td><td>0.38</td><td>0.01</td><td>0.32</td><td>0.22</td><td>0.17</td></tr><tr><td>LPJ-GUESS</td><td>0.17</td><td>0.31</td><td>0.10</td><td>0.19</td><td>0.23</td><td>0.14</td><td>0.11</td><td>0.14</td><td>0.00</td><td>0.47</td><td>0.11</td><td>0.22</td><td>0.25</td><td>0.14</td><td>0.00</td><td>0.19</td></tr><tr><td>ORCHIDEE</td><td>0.51</td><td>0.40</td><td>0.66</td><td>0.22</td><td>0.67</td><td>0.22</td><td>0.66</td><td>0.19</td><td>0.01</td><td>0.45</td><td>0.00</td><td>0.25</td><td>0.04</td><td>0.26</td><td>0.47</td><td>0.24</td></tr><tr><td>SURFEX</td><td>0.14</td><td>0.22</td><td>0.49</td><td>0.14</td><td>0.68</td><td>0.16</td><td>0.86</td><td>0.07</td><td>0.00</td><td>0.29</td><td>0.60</td><td>0.16</td><td>0.74</td><td>0.14</td><td>0.00</td><td>0.12</td></tr><tr><td rowspan="10">GPP</td><td>Obs-based</td><td>0.22</td><td>0.41</td><td>0.51</td><td>0.32</td><td>0.77</td><td>0.20</td><td>0.84</td><td>0.13</td><td>0.52</td><td>0.32</td><td>0.60</td><td>0.24</td><td>0.73</td><td>0.20</td><td>0.80</td><td>0.18</td></tr><tr><td>CLM4.5</td><td>0.03</td><td>0.47</td><td>0.11</td><td>0.54</td><td>0.23</td><td>0.51</td><td>0.54</td><td>0.30</td><td>0.69</td><td>0.32</td><td>0.23</td><td>0.47</td><td>0.29</td><td>0.48</td><td>0.69</td><td>0.31</td></tr><tr><td>CLM5</td><td>0.19</td><td>0.37</td><td>0.36</td><td>0.37</td><td>0.33</td><td>0.42</td><td>0.63</td><td>0.26</td><td>0.74</td><td>0.31</td><td>0.44</td><td>0.31</td><td>0.33</td><td>0.43</td><td>0.70</td><td>0.25</td></tr><tr><td>JSBACH</td><td>0.14</td><td>0.49</td><td>0.43</td><td>0.45</td><td>0.63</td><td>0.27</td><td>0.74</td><td>0.16</td><td>0.70</td><td>0.39</td><td>0.59</td><td>0.36</td><td>0.68</td><td>0.28</td><td>0.83</td><td>0.15</td></tr><tr><td>JULES</td><td>0.02</td><td>0.71</td><td>0.49</td><td>0.26</td><td>0.77</td><td>0.23</td><td>0.84</td><td>0.18</td><td>0.69</td><td>0.52</td><td>0.82</td><td>0.16</td><td>0.89</td><td>0.18</td><td>0.90</td><td>0.14</td></tr><tr><td>LPJ-GUESS</td><td>0.39</td><td>0.37</td><td>0.38</td><td>0.40</td><td>0.29</td><td>0.40</td><td>0.46</td><td>0.36</td><td>0.33</td><td>0.35</td><td>0.43</td><td>0.36</td><td>0.36</td><td>0.37</td><td>0.49</td><td>0.36</td></tr><tr><td>ORCHIDEE</td><td>0.23</td><td>0.37</td><td>0.59</td><td>0.25</td><td>0.73</td><td>0.21</td><td>0.82</td><td>0.12</td><td>0.60</td><td>0.43</td><td>0.71</td><td>0.20</td><td>0.71</td><td>0.22</td><td>0.79</td><td>0.17</td></tr><tr><td>SURFEX</td><td>0.19</td><td>0.34</td><td>0.61</td><td>0.24</td><td>0.79</td><td>0.19</td><td>0.85</td><td>0.10</td><td>0.57</td><td>0.33</td><td>0.78</td><td>0.17</td><td>0.80</td><td>0.13</td><td>0.78</td><td>0.17</td></tr></tbody></table>

637

638

639

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Extended Figures

<figure><img src="image_8.png" /><figcaption>**Figure A1.** Global distribution of climatic regions. The climatic regions are defined using the ranges of aridity index, which is calculated as the ratio of mean annual precipitation and potential evapotranspiration. The ranges of aridity (in square brackets) that define different climate regions are taken from UNEP (United Nations Environment, 1992). From the original UNEP classification, the hyper-arid climate was merged into arid climate because it only comprised 0.1% of grid cells after excluding the desert regions. The percentage values (in parenthesis) indicate the fraction of the valid grid cells with the climate.</figcaption></figure>
<figure><img src="image_9.png" /></figure>

**Figure A2. Covariation of climate and moisture.** Mean annual precipitation (MAP, mm/year), mean annual temperature (MAT, °C) and water availability index (WAI, -) <50 are plotted in X, Y and Z axes respectively. The different colours indicate different climatic regions defined by aridity index, and individual grid-cells are plotted as dots. The WAI is a proxy for soil moisture content based on the water balance concept, and it varies between 0 (dry) and 1 (wet).
<figure><img src="image_10.png" /><figcaption>**Figure A3.** Same and **Figure 1**, but using the LANDGIS ⁶⁹ instead of SoilGrids ⁴⁷ dataset in the observation-based ensemble of soil organic carbon estimates.</figcaption></figure>
<figure><img src="image_11.png" /></figure>

**Figure A4.** Zonal distributions of mean annual precipitation (mm/year) and mean air temperature (°C). The values for each latitude are calculated as mean within a moving window of 10 grid cells along the latitude (5°). The shaded region indicates the 5th and 95th percentiles within the latitudinal moving window.
<figure><img src="image_12.png" /></figure>

**Figure A5.** Same as **Figure 3** but using the average temperature that is corrected for low winter temperature below freezing point. For the correction, the temperature of months below 0°C are set at 0°C before calculating the mean annual temperature, which results in an estimate that only includes physiologically relevant months while considering the duration of the period with below freezing temperature.
<figure><img src="image_13.png" /></figure>

**Figure A6.** Zonal correlation between total ecosystem carbon stock (C<sub>total</sub>, kgC/m<sup>2</sup>) and gross primary productivity (GPP, kgC/m<sup>2</sup>/year). In a) correlation between C<sub>total</sub> and GPP, b) controlled for precipitation, and c) controlled for temperature are presented. The Pearson's correlation coefficient for each latitude is calculated for a moving window of 10 grid cells along the latitude (5°). The thick dashed blue lines show the normalized mean correlation of all models with shades indicating variation within 1 standard deviation. The observation is plotted as a thick black line with shade indicating the range within the 5<sup>th</sup> and 95<sup>th</sup> percentiles.

<figure><img src="image_14.png" /></figure>

**Figure A7.** Evaluation of a) ecosystem turnover time (τ, years), b) gross primary productivity (GPP, pgC/year), and c) total carbon storage (C<sub>total</sub>, pgC) over different climatic regions. In the bar charts, the observation and their uncertainties (5<sup>th</sup> and 95<sup>th</sup> percentiles) are plotted. In the colourmap matrix, horizontal axis shows different climatic regions and the global values, and the vertical axis shows different models or model ensembles. The colour indicates the bias, calculated as the ratio of modelled and observed values. The inset text shows τ or GPP or C<sub>total</sub> for a given model and climate. The colour of
the text indicates whether the modelled values are within the range of observational
uncertainty with green for those within and orange for those outside.
<figure><img src="image_15.png" /><figcaption>**Figure A8.** Comparison of the global distribution of ecosystem turnover times of carbon (τ, years) from observation-based estimate and CRESCENDO model simulations. Along the diagonal, the maps of τ from observation and model simulations are plotted. Above the diagonal, the biases (ratio of observation/model in column to observation/model along row) are plotted. Below the diagonal, density scatter plots are plotted with darker colour indicating larger density of points. The thin black line shows the 1:1 line, r and ρ indicate the spatial Pearson's and Spearman's correlation coefficient, respectively.</figcaption></figure>
<figure><img src="image_16.png" /><figcaption>**Figure A9.** Comparison of the global distribution of gross primary productivity (GPP, kgC/m²/year) from observation-based estimate and CRESCENDO model simulations. Along the diagonal, the maps of GPP from observation and model simulations are plotted. Above the diagonal, the biases (ratio of observation/model along column to observation/model along row) are plotted. Below the diagonal, density scatter plots are plotted with darker colour indicating larger density of points. The thin black line shows the 1:1 line, r and ρ indicate the spatial Pearson's and Spearman's correlation coefficient, respectively.</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>**Figure A10.** Comparison of the global distribution of total ecosystem carbon storage ($C_{total}$, kgC/m²) from observation-based estimate and CRESCENDO model simulations. Along the diagonal, the maps of $C_{total}$ from observation and model simulations are plotted. Above the diagonal, the biases (ratio of observation/model along column to observation/model along row) are plotted. Below the diagonal, density scatter plots are plotted with darker colour indicating larger density of points. The thin black line shows the 1:1 line, r and ρ indicate the spatial Pearson's and Spearman's correlation coefficient, respectively.</figcaption></figure>
<figure><img src="image_18.png" /><figcaption>**Figure A11.** Same as **Figure 1** of the main text but using the state-of-the-art observation-based datasets of soil carbon (cSoil) and vegetation carbon (cVeg) stocks, and gross primary productivity (GPP). In total, 3 different soil carbon datasets, 4 different vegetation carbon datasets, and 6 different GPP estimations were used (see Methods). In the first row, a full factorial of all datasets generating 72 members were used. The second, third and fourth rows consider the influence of using different cSoils (3), cVeg (4), and GPP (6), respectively, while the other two variables are set at the ensemble medians. The thick lines and shaded regions around them indicate the median and interquartile range of all fitted relationships, respectively. Different colours indicate different climatic regions. Note the logarithmic axis for τ in the first and second columns.</figcaption></figure>
<figure><img src="image_19.png" /><figcaption>**Figure A12.** Evaluation of sensitivities of evapotranspiration to climate in CRESCENDO models. The relationships between total evapotranspiration (ET, in mm/day) versus mean annual temperature (MAT) and precipitation (MAP) are presented in the first and second column, respectively. Along the row, the comparisons for different models against the observation⁵⁰ are presented. The different colours indicate different climatic regions defined by the aridity index. The solid lines indicate the observation-based relationship, and the broken lines indicate relationship from the model simulations. The inset text shows the ratio between the linear coefficients and constants from the least square fits for the model and observation for each climatic region. Note that for ET-MAP relationship, the constant/intercept term is always 0.</figcaption></figure>
<figure><img src="image_20.png" /><figcaption>**Figure A13.** Spatial sensitivities of climatological total soil moisture state and carbon fluxes in CRESCENDO model simulations. In the first column, the relationship between the spatial variability of mean annual temperature (*MAT*) and total soil moisture (*θ*) is presented. In the second, third and fourth columns, the relationships of spatial variabilities of heterotrophic respiration (*R*<sub>h</sub>), autotrophic respiration (*R*<sub>a</sub>), and gross primary productivity (*GPP*) with *MAT* are, respectively, presented. The fifth, sixth and seventh columns repeat the same but with *θ*. The different colours indicate different climatic regions defined by the aridity index. The lines are the least square fits for each climatic region. Along the row, the comparisons for different models against the observation are presented. For a consistent comparison across different variables and differences in sizes of soil column in different models, all variables are scaled by the 98th percentile within each climate region so that the spatial variability is roughly normalized between 0 and 1.</figcaption></figure>
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