Georgiou et al. (2022). Global stocks and capacity of mineral-associated soil organic carbon

& Margaret S. Torn

17,18

Soil is the largest terrestrial reservoir of organic carbon and is central for climate change

mitigation and carbon-climate feedbacks. Chemical and physical associations of soil carbon

with minerals play a critical role in carbon storage, but the amount and global capacity for

storage in this form remain unquanti

ﬁ

ed. Here, we produce spatially-resolved global esti-

mates of mineral-associated organic carbon stocks and carbon-storage capacity by analyzing

1144 globally-distributed soil pro

ﬁ

les. We show that current stocks total 899 Pg C to a depth

of 1 m in non-permafrost mineral soils. Although this constitutes 66% and 70% of soil carbon

in surface and deeper layers, respectively, it is only 42% and 21% of the mineralogical

capacity. Regions under agricultural management and deeper soil layers show the largest

undersaturation of mineral-associated carbon. Critically, the degree of undersaturation

indicates sequestration ef

ﬁ

ciency over years to decades. We show that, across 103 carbon-

accrual measurements spanning management interventions globally, soils furthest from their

mineralogical capacity are more effective at accruing carbon; sequestration rates average

3-times higher in soils at one tenth of their capacity compared to soils at one half of their

capacity. Our

ﬁ

ndings provide insights into the world

’

s soils, their capacity to store carbon,

and priority regions and actions for soil carbon management.

https://doi.org/10.1038/s41467-022-31540-9

OPEN

1

Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, Livermore, CA 94551, USA.

2

Department of Earth System Science,

Stanford University, Stanford, CA 94305, USA.

3

Woods Institute for the Environment, Stanford University, Stanford, CA 94305, USA.

4

Precourt Institute for

Energy, Stanford University, Stanford, CA 94305, USA.

5

Department of Biology, University of Antwerp, Antwerp 2000, Belgium.

6

Institute for Environmental

Studies, Charles University, Prague 128 01, Czech Republic.

7

Laboratoire des Sciences du Climat et de l

’

Environnement, Gif-sur-Yvette F-91191, France.

8

Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37830, USA.

9

Deptartment of Physical Geography and Ecosystem Science,

Lund University, Lund SE-22100, Sweden.

10

Agricultural Resources and Regional Planning, Chinese Academy of Agricultural Sciences, Beijing 10081, China.

11

U.S. Geological Survey, Menlo Park, CA 94035, USA.

12

Department of Plant Sciences, University of Cambridge, Cambridge CB2 3EA, UK.

13

Cambridge

Conservation Institute, University of Cambridge, Cambridge CB2 3EA, UK.

14

Agricultural Research Service, U.S. Department of Agriculture, Temple, TX

76502, USA.

15

Department of Ecosystem Science and Sustainability, Colorado State University, Fort Collins, CO 80523, USA.

16

Granular, Inc, San Francisco,

CA 94103, USA.

17

Climate and Ecosystem Sciences, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA.

18

Energy and Resources Group,

University of California, Berkeley, Berkeley, CA 94720, USA.

✉

email:

georgiou1@llnl.gov

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123456789

0():,;

S

oil organic carbon (SOC) is an integral component of ter-
restrial ecosystems and plays an important role in ecosys-
tem resilience and productivity. Soil organic matter contains

nutrients that support plant growth and yield, retains water and
reduces runoff, and resists erosion

. Globally, SOC contains more

carbon than the atmosphere and vegetation combined

–

. Cli-

mate- and land-use-induced changes to soil may alter SOC
cycling and drive large terrestrial carbon sinks or sources; indeed,
human land-use and land-cover change have resulted in a sig-
ni

ﬁ

cant net loss of soil carbon over the past two centuries

Improved soil management practices that promote soil carbon
sequestration, especially in stable carbon pools, are needed to
reverse this trajectory and mitigate climate change

8

9

.

Field observations suggest that more than half of soil organic

carbon is chemically or physically associated with soil
minerals

10

(Supplementary Fig. 1). These interactions limit

microbial access to otherwise decomposable substrates

12

,

13

and,

consequently, mineral-associated organic carbon (MOC) can
have turnover times up to 1000 times longer (reaching
100

–

10,000 years) than particulate organic carbon (POC) at the

same depth

14

15

. Thus, increasing MOC may be a key to lasting

carbon sequestration in soils

16

. However, despite its unique role,

it is still unclear how much MOC presently exists, and how much
could be accrued, in soils globally across depths and geographic
regions. The capacity of soils to store MOC and other persistent
forms of SOC will in

ﬂ

uence the long-term trajectory of the ter-

restrial carbon sink. Furthermore, it is unknown whether the
proximity of a given soil to its carbon-storage capacity will
in

ﬂ

uence the rate of C accrual, and thus the ef

ﬁ

cacy of soil C

sequestration efforts. These knowledge gaps hinder climate
change mitigation pathways and soil management initiatives, and
limit long-term projections of Earth system models.

Soil organic matter decomposition, and its response and

feedback to climate, depends on the physico-chemical form of the
organic matter. To improve projections of long-term soil-climate
feedbacks, it is imperative to predict the amount, distribution, and
dynamics of MOC

. Yet, little attention has been afforded to the

explicit representation and parameterization of mineral-organic
associations in Earth system models

18

. Organic matter and

minerals form associations via myriad mechanisms, including
ligand exchange, hydrophobic interactions, and cation bridging

19

and the appropriate

—

representative yet tractable

—

mathematical

formulation of MOC dynamics in these models is still the subject
of research

20

21

. Nevertheless, existing and candidate approaches

require a means to constrain the maximum mineralogical capa-
city (MOC

max

). This MOC

max

is a property of the soil

mineralogy

22

23

. A data-driven approach to convert readily

measured soil mineralogical variables to MOC

max

is therefore

needed to achieve advances in modeling and to enable robust
estimates of carbon sequestration capacity.

Here we synthesized MOC observations from 1144 soil pro

ﬁ

les

spanning diverse biomes, soil types, and climates worldwide. Our
synthesis included soils with a wide range of clay plus silt mineral
content (CS; 1.5

–

100%), mean annual temperature (MAT;

−

2.9

–

29 °C),

and

mean

annual

precipitation

(MAP;

79

–

3806 mm yr

−

1

), as well as different vegetation types and land-

uses (Supplementary Figs. 2 and 3). We leveraged these obser-
vations, with insights from theory and process-based models, and
demonstrated that MOC

max

can be inferred as an emergent

property from readily measured soil mineralogical variables. We
explored the variability of observed MOC and used a machine
learning approach to elucidate the role of environmental vari-
ables, including climate and vegetation, in driving the observed
departures from mineralogical saturation. We categorized sites
into natural/less-managed (forest and grassland) and intensively
managed (cropland) ecosystems to further investigate the effects

of vegetation type and management on the degree of MOC
undersaturation across soil depths. Finally, to explore how this
undersaturation affects the sequestration ef

ﬁ

cacy of soils over

decadal timescales, we examined 103 carbon-accrual measure-
ments spanning management interventions globally.

Results and discussion

Carbon capacity of low- and high-activity mineral soils

. Studies

have presented con

ﬂ

icting results on the importance of clay plus

silt content (CS) as a single linear predictor of MOC

24

–

26

, with

many of these analyses focusing on the prediction of bulk SOC,
which contains additional pools of non-mineral-associated
organic carbon (e.g., POC). As we present here, theory and
model insights, as well as our extensive global data analysis, all
suggest that there is no universal linear relationship between
MOC (or SOC) and CS (Supplementary Figs. 4

–

6). Rather, this

relationship depends, to a

ﬁ

rst-degree, on the combined effect of

the C loading on minerals (g C m

−

2

mineral) which is a function

of environmental conditions and management practices

27

, and

the effective mineral area on which C can bind (m

2

g

−

1

mineral)

which is a function of the type of mineral

. However, since

MOC

max

is driven primarily by the amount (g mineral kg

−

1

soil)

and type of mineral

23

28

, we hypothesized that if soils were par-

titioned based on their dominant mineral type, CS would emerge
as a signi

ﬁ

cant predictor of MOC

max

globally.

To test this hypothesis, we classi

ﬁ

ed soils according to their

mineral type and explored whether the upper quantiles of
observed MOC form distinct boundaries for different mineral
categories, i.e., whether a distinct MOC

max

speci

ﬁ

c to each

mineral type arises (Supplementary Figs. 6 and 7). Here, we
classi

ﬁ

ed soils as containing high- or low-activity minerals (HM

or LM, respectively) based on their primary composition of high-
activity (illite, smectite, vermiculite, chlorite) and low-activity
(kaolinite, gibbsite) clays

29

–

(see

“

Methods

”

for the robustness

of results to additional categories).

Indeed, our data synthesis quanti

ﬁ

es and supports this

hypothesis, demonstrating that a robust MOC

max

estimate can

emerge as a function of only CS and the type of mineral (Fig.

;

and irrespective of vegetation type, Supplementary Fig. 8). We
obtained a conservative estimate of MOC

max

as the 95th quantile

of MOC values for each mineral type, resulting in MOC

max

estimates of 86 ± 9 and 48 ± 6 mg C g

−

1

mineral for HM and LM,

respectively (Fig.

; slope ± 90% con

ﬁ

dence interval, following a

unit conversion). These data-derived estimates of MOC

max

provide a maximum carbon potential for a given CS and mineral
type, which can be used to inform the location and management
practices of soil restoration and sequestration efforts (Supple-
mentary Discussion). These values broadly agree with regional
studies that have included high-activity minerals at comparable
soil depths

, but are signi

ﬁ

cantly greater than studies that

have omitted mineral activity

. Given the important role of

mineralogy (Supplementary Fig. 4), our data-driven MOC

max

estimates are also a notable update to regional studies that have
reported a maximum carbon potential across European soils (e.g.,
45

–

50 g C kg

−

1

soil based on model-predicted values in ref.

).

While it may be dif

ﬁ

cult for soils to reach MOC

max

in practice,

the proximity of a given soil to its maximum capacity is an
important factor for determining its effectiveness in sequestering
additional carbon (see Supplementary Fig. 9 for a conceptual
schematic)

38

,

39

and, consequently, underestimating MOC

max

can

have signi

ﬁ

cant implications for estimates of carbon de

ﬁ

cit and

potential accrual.

Vegetation and management controls on carbon under-
saturation across depths

. Our analysis suggests that many soils

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are substantially below their mineralogical capacity (Fig.

). This

mineralogical undersaturation may be attributed to environ-
mental (e.g., climate and plant C inputs) limitations on MOC
storage and decomposition, management practices that result in
MOC losses, or both. To explore where and why soils contain less
MOC than they could based on their mineralogy alone, we cal-
culated the mineralogical % C saturation for a given soil as the
ratio of observed MOC to MOC

max

(see

“

Methods

”

; Supple-

mentary Fig. 10). Across all sites, soils averaged 40 ± 2% C
saturation (±95% con

ﬁ

dence interval of the mean). Land-use

change and/or poor management practices that degrade soils can
decrease MOC, a result evident in the shift of C saturation dis-
tributions from less-managed to more intensively managed eco-
systems (Fig.

a). The former (namely, grasslands and forests),

which we refer to here as natural ecosystems for brevity, had on
average higher levels of C saturation than did agricultural systems
(

p

< 0.0001; Fig.

a). Indeed, whereas soils in natural ecosystems

averaged 46 ± 3% C saturation, agricultural systems averaged only

31 ± 2% C saturation. This contrast suggests that restoring
degraded or intensively managed lands could push their soils
towards higher C saturation levels (i.e., their highest attainable
MOC given the site-speci

ﬁ

c environmental factors that limit

stocks below MOC

max

) and allow them to serve as a substantial C

sink.

We also observed that deeper soils were further from C

saturation than were surface soils (

p

< 0.0001; Fig.

b). On

average, surface soils (0

–

30 cm) were 43 ± 2% C saturated, as

compared to 19 ± 3% C saturation for deeper soils (30

–

120 cm).

This difference is likely due, in part, to lower rates of C inputs
with depth

40

41

. The location and type of C inputs are also

important, as a higher proportion of plant C is retained in SOC
from belowground root inputs than from aboveground litter
inputs

42

–

44

. We may then expect a difference in C saturation

levels between grasslands and forests, which have different root
depth distributions

45

. Indeed, although there was no signi

ﬁ

cant

difference in the level of saturation between grasslands and forests

0

25

50

75

100

Crop

Forest

Grassland

Deep

Surface

0

25

50

75

100

Managed

Natural

% C satur

a

tion

% C satur

a

tion

a

b

Fig. 2 Percent mineralogical carbon saturation across ecosystems and soil depths.

Percent mineralogical C saturation (%C saturation)

—

i.e., the

proximity of a soil to its mineralogical carbon capacity (MOC

max

)

—

was calculated for each measurement in our observational synthesis.

a

%C saturation

grouped by managed (

n

=

573) and natural (

n

=

862) ecosystems across depths (see

“

Methods

”

).

b

%C saturation by ecosystem (cropland, forest, and

grassland) and depth (surface < 30 cm and deep > 30 cm). Only categories with >5 observations for both surface (cropland

n

=

425; forest

n

=

242;

grassland

n

=

355) and deep (cropland

n

=

21; forest

n

=

53; grassland

n

=

136) soils are shown. Box plots indicate the medians (horizontal lines), 1st and

3rd quartiles (boxes), 1.5× interquartile range (whiskers), and means (diamonds).

0

40

80

120

0

25

50

75

100

Clay and silt content (%)

Miner

al−associated C (g C kg

−

1

soil)

Low-activity minerals

Natural

Managed

95

th

quantile

High-activity minerals

Natural

Managed

95

th

quantile

0

10

20

30

40

50

60

70

80

90

100

Cl

ay

(%)

Silt (%)

Sand (%)

0

1000

2000

3000

4000

10

0

10

20

30

MAT (°C)

1

2

3

4

5

6

7

8

9

Boreal Forest
Cropland
Grassland
Savanna
Shrubland
Temperate Forest
Tropical Forest

a

b

c

MAP

(

mm y

r

-1

)

Fig. 1 Maximum mineral-associated carbon as a function of clay and silt content for high- and low-activity mineral soils estimated from a global
observational synthesis. a

Mineral-associated organic carbon (MOC; g C kg

−

1

soil) as a function of clay and silt content (CS; %) across sites. The

maximum slope (

ﬁ

t as the 95th quantile) for each soil type represents the intrinsic capacity of minerals to store carbon and depends on mineral

composition. High-activity minerals (HM) include soils dominated by illite, smectite, vermiculite, and chlorite (

n

=

1303) and low-activity minerals (LM)

include soils dominated by kaolinite and gibbsite (

n

=

93). Shading depicts 90% con

ﬁ

dence intervals on the slope. Soils near the upper quantiles are closer

to MOC saturation. Within HM and LM soils,

ﬁ

lled markers and crosses denote natural and managed ecosystems, respectively.

b

,

c

Distribution of soil

texture (

b

) and climate (

c

) across sites. Black polygons depict Whittaker

’

s biomes

119

according to mean annual temperature (MAT; °C) and mean annual

precipitation (MAP; mm yr

−

1

) values, following: (1) tropical rainforest; (2) tropical seasonal rainforest/savanna; (3) subtropical desert; (4) temperate

rainforest; (5) temperate seasonal forest; (6) woodland/shrubland; (7) temperate grassland/desert; (8) boreal forest; and (9) tundra.

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in surface soils (0

–

30 cm), grasslands were closer to C saturation

in deeper horizons (30

–

120 cm) than forests were (

p

< 0.005;

Fig.

b). This pattern con

ﬁ

rms that root pro

ﬁ

les and rates of C

inputs in

ﬂ

uence the achieved MOC levels. This is an additional

reason to expect that deeper-rooted vegetation may be more
effective in sequestering C, and should thus be examined for
restoring degraded lands and selecting cover crops

41

46

.

Climate controls on mineral-associated organic carbon

. Cli-

mate also affects the achieved MOC in soil and its departure from
saturation. However, MOC does not vary linearly with extrinsic
factors such as temperature, but rather its response is governed by

‘

pedogenic thresholds

’

and nonlinearities

47

. We thus used a

machine learning approach to determine the signi

ﬁ

cance of key

covariates and reveal emergent relationships of each variable, as
well as variable interactions, on MOC (i.e., partial dependence
plots; see

“

Methods

”

). This approach illuminates not only the

overall sensitivity of MOC to individual variables but also the
conditional relationship and rate of change with respect to a given
variable (i.e., the partial derivative), without imposing a particular
(e.g., linear) relationship. Speci

ﬁ

cally, we optimized a random

forest (RF) model using key environmental covariates (see

“

Methods

”

;

R

2

=

0.60, Supplementary Fig. 11). We then calcu-

lated partial dependence relationships of MOC as a function of
each variable alone (Supplementary Fig. 12), as well as condi-
tional on interactions between variables (Fig.

).

Clear predictive relationships emerged for MOC as a function

of each variable. We found a linear partial dependence relation-
ship between MOC and CS (Supplementary Fig. 12a), which can
be attributed to an underlying increase in total mineral surface
area and pore space

22

48

. This result supports studies that

ﬁ

nd

correlations between MOC and CS, but illustrates the importance
of controlling for the variability introduced by environmental
covariates. With POC, we observed a saturating relationship in
MOC (Fig.

a), corresponding to an increase in C loading up to

an effective saturation of mineral surfaces

48

49

. Although not all of

this POC may be able to sorb onto mineral surfaces, it emerged as
a signi

ﬁ

cant variable in our analysis (Supplementary Figs. 11 and

12), likely as an indicator of rapidly decomposing material and
the production of microbial necromass and dissolved organic
carbon. In contrast, machine learning predictions of the
conditional relationship between MOC and aboveground litter
inputs showed a weaker dependence, consistent with other

ﬁ

ndings that aboveground productivity and litterfall are often not

good proxies for carbon inputs to mineral soils

42

.

We observed a decline in MOC with MAT (Fig.

b and

Supplementary Fig. 12c) which is consistent with increased
relative desorption with increasing temperatures

50

51

, and sug-

gests a potential global vulnerability of MOC to warming. This
decline with MAT also emerged across different ranges of POC,
but interestingly, with signi

ﬁ

cant differences in magnitude

(Fig.

b); low POC regimes (which are furthest from MOC

saturation; Fig.

a) exhibited greater temperature sensitivities

compared to high POC regimes (soils closer to saturation;
Fig.

a). Distinct temperature-dependence regimes of saturating

sorption curves are corroborated by theory (Supplementary
Fig. 6) and experiments

52

. Speci

ﬁ

cally, when available carbon

concentrations are low, MOC depends on the equilibrium
constant

K

eq

¼

f

ð

T

Þ

(i.e., the ratio of adsorption to desorption

rate constants; Supplementary Fig. 6) which is a strong function
of temperature, whereas when concentrations are high, MOC
approaches MOC

max

≠

f

ð

T

Þ

and hence exhibits a weaker

temperature dependence. Thus, our

ﬁ

ndings suggest that

restoring degraded soils towards their mineralogical capacity
through improved land management may not only contribute to
carbon sequestration efforts

53

but also impart a greater resiliency

of soils to future warming.

Finally, we leveraged a machine learning approach to predict

current MOC globally, excluding tundra, peatlands, and deserts (see

“

Methods

”

;

R

2

=

0.79, Supplementary Figs. 13 and 14). We

estimated that MOC stocks total 899 Pg C (5

–

95% range: 668,

1074 Pg C) to a depth of 1 m, with 448 Pg C (296, 536) in topsoils
(0

–

30 cm) and 451 Pg C (372, 538) in subsoils (30

–

100 cm) (Fig.

and Supplementary Fig. 15; Supplementary Tables 1 and 2).
Globally, MOC made up a smaller proportion of total SOC in
topsoils (0.66 ± 0.13; mean ± s.d.) compared to in subsoils
(0.70 ± 0.17) (0.69 ± 0.15 to a depth of 1 m; Supplementary Fig. 16).
Soils had a smaller proportion of MOC to SOC in boreal regions
than in tropical and temperate regions, suggesting a larger
proportion of non-protected carbon (i.e., POC) at high latitudes
that may be vulnerable to warming

54

(Supplementary Discussion).

Our global estimates of MOC stocks, and as a fraction of total SOC,
are to our knowledge the

ﬁ

rst such spatially- and depth-resolved

data products, providing a crucial link for understanding soil carbon
vulnerability, benchmarking soil carbon models

, and assessing the

mineralogical potential for carbon sequestration globally.

10

20

30

0

10

20

30

POC (g C kg

−

1

soil)

Predicted MOC (g C kg

−

1

soil)

10

20

30

0

5

10

15

20

25

MAT (

°

C)

Predicted MOC (g C kg

−

1

soil)

b

a

H

M

L

H

M

L

Fig. 3 Data-driven predictive relationships of mineral-associated organic carbon as a function of individual controlling factors and interactions.

A

random forest model was used to disentangle the signi

ﬁ

cance and emergent relationships of individual covariates, using partial dependence relationships

that describe the marginal effect of each variable on the predicted mineral-associated carbon (MOC) response (see

“

Methods

”

).

a

Predicted MOC as a

function of particulate organic C (POC). For each plot, the points show random forest model predictions; best

ﬁ

t lines and shading show 99% con

ﬁ

dence

intervals on each trend.

b

Predicted MOC as a function of mean annual temperature (MAT), conditional on three distinct subsets of POC

—

namely, low (L),

medium (M), and high (H) POC corresponding to unsaturated to saturated regimes. The breakpoints were selected as the median and third quartile of the
POC distribution, which also correspond to approximate saturation thresholds in the partial dependence plot of POC alone.

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Global soil mineralogical carbon capacity

. We used the same

classi

ﬁ

cation of mineral types from our observational synthesis to

map high- and low-activity minerals (HM and LM, respectively;
see

“

Methods

”

, Supplementary Fig. 14). Together with a global

map of CS and our derived relationships for MOC

max

in HM and

LM soils, we calculated the corresponding MOC

max

globally

(Fig.

and Supplementary Fig. 17). This spatially explicit and

depth-resolved global product provides insights into the capacity
of the world

’

s soils to store MOC. Globally, we estimate that the

soil mineralogical C capacity is 1443 ± 141 Pg C and 3153 ± 312
Pg C in topsoils and subsoils, respectively, totaling 4596 Pg
C ± 453 Pg C to a depth of 1 m (excluding tundra, peatlands, and
deserts; Supplementary Table 1). Many sites in temperate and
subequatorial zones show the greatest mineralogical C de

ﬁ

cit

(MOC

max

minus MOC), and thus potential for additional MOC

storage, in part because of the prevalence of agricultural soils
there (Fig.

c and Supplementary Figs. 18

–

20). Indeed, we esti-

mate that the mineralogical C de

ﬁ

cit of croplands is 184 Pg C

(5

–

95% range: 148, 225) and 509 Pg C (439, 569) in topsoils and

subsoils, respectively (Supplementary Table 1). While reaching
MOC

max

is dif

ﬁ

cult and strongly limited by climate (Fig.

), if

these soils achieved the average %C saturation levels of natural
lands (Fig.

), this potential sequestration would total nearly 104

Pg C to a depth of 1 m (62 and 42 Pg C in topsoils and subsoils,
respectively) (Supplementary Table 1). Grazing lands also show a
large mineralogical C de

ﬁ

cit covering a large expanse globally, but

will require tailored strategies for soil C restoration, especially in
arid and semi-arid regions that are additionally limited by climate
(e.g., the Southwestern United States and Ustyurt Plateau). Our
maps reveal hotspots of mineralogical C de

ﬁ

cit, often associated

with long-standing cropping and grazing lands (Fig.

and Sup-

plementary Figs. 20 and 21), and highlight priority regions for soil
C restoration efforts.

Current MOC stocks correspond to global average C saturation

levels of 42% (5

–

95% range: 24%, 61%) and 21% (14%, 30%) in

topsoils and subsoils, respectively (Fig.

c and Supplementary

Figs. 18 and 19; Supplementary Table 2). However, as
explained earlier, reaching C saturation is not necessarily feasible
(given climate limitations, for example) or a recommended target.
Rather, the potential lies initially in restoring the natural %C
saturation in managed areas (Supplementary Figs. 18

–

22; Sup-

plementary Table 1) and, especially, those furthest from %C
saturation (Supplementary Fig. 9; Supplementary Discussion).
We identify geographic locations with the most promise (namely,
temperate and subequatorial zones in the northern hemisphere;
Fig.

c) and highlight the potential bene

ﬁ

t of practices that

sequester C deeper in the soil pro

ﬁ

le, where soil minerals are

further from %C saturation (Supplementary Figs. 18

–

20). In

addition to practices that leverage deeper-rooted vegetation

41

,

recent studies have indicated that new approaches to deep
ploughing

55

or other practices resulting in topsoil-subsoil

ﬂ

ipping

56

may lead to considerable overall C sequestration,

0

2

4

6

0

50

100

150

200

%C saturation

C accr

ual (t ha

−

1

yr

−

1

)

a

b

d

c

Fig. 4 Global soil mineralogical carbon capacity, mineral-associated carbon stocks, and potential for carbon accrual. a

Mineralogical carbon capacity

(MOC

max

; kg C m

−

2

soil),

b

mineral-associated organic carbon (MOC; kg C m

−

2

soil), and

c

percent mineralogical carbon saturation (%C saturation) in

topsoil (0

–

30 cm) at 0.5° resolution, excluding tundra, peatlands, and deserts. MOC

max

was estimated using our data-derived relationships with the

amount and type of mineral. MOC was predicted using a random forest model trained on our observational dataset. %C saturation was calculated as
MOC/MOC

max

. Low %C saturation corresponds to a greater C de

ﬁ

cit, and therefore highlights regions where targeted soil management could lead to

higher C sequestration.

d

Carbon accrual in topsoil (t ha

−

1

yr

−

1

; mean depth

=

29 cm) as a function of %C saturation across sites, based on our global

synthesis of studies that measured C accrual following management interventions (

n

=

103). Nonlinear

ﬁ

t depicts asymptotic regression model with

shaded areas representing 10th and 90th quantiles.

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5

although the cost and full impact of such practices on other soil
functions needs to be better understood.

In addition to informing locations for targeted restoration and

carbon sequestration, our data and results are also an essential
input for Earth system models (ESMs) that seek to represent soil
mineral-organic associations explicitly

—

directly informing the

mineralogical C capacity and constraining the proportion of total
SOC that is mineral-associated (Supplementary Figs. 16 and
17)

. Our global estimate of MOC

max

constitutes an effective

potential for sorption on minerals, unlike that derived from
laboratory DOC sorption experiments alone

57

58

. Laboratory

assays tend to underestimate maximum sorption potential,
especially if they use native soil which already has some carbon
loading on mineral surfaces

57

58

. Moreover, microbial necromass

and residues contribute substantially to MOC measured in the

ﬁ

eld

59

, and thus, our estimates have the potential to uniquely

improve model parameterizations beyond those obtained from
laboratory measurements.

Carbon sequestration implications and future perspectives

.

Geographic regions with higher C de

ﬁ

cit can be used to inform soil

C sequestration efforts, such as the

“

4 per 1000

”

initiative

60

61

and

categories

”

for classi

ﬁ

cation details). We also collected other auxiliary soil

properties, including dithionite- and oxalate-extractable iron (Fe

d

and Fe

o

,

respectively), oxalate-extractable aluminum (Al

ox

), cation exchange capacity

(CEC), speci

ﬁ

c surface area (SSA), and total reserve bases (TRB), though these

measurements were sparse across the collected studies. A complete list of studies
and their location, climate, and vegetation is provided in Supplementary Table 3.

Studies in our synthesis spanned intensively managed (e.g., crop) to natural/

less-managed (e.g., grassland, forest) ecosystems across diverse climates and soil
types (Fig.

and Supplementary Fig. 2). We obtained a representative mix of MOC

measurements from managed (

n

=

559 pro

ﬁ

les) and natural (

n

=

585 pro

ﬁ

les)

lands. We focused on the current management status herein, but note that future
studies may consider information on historical management, where available.
Within natural lands, there was a greater representation of temperate ecosystems,
as opposed to tropical and boreal ecosystems (Supplementary Figs. 2, 3, and 14)

—

especially when including the European LUCAS database

(Supplementary

Fig. 2b, d), but our model and results were robust to its exclusion. Furthermore,
measurements in tundra and deserts were limited, highlighting the need for studies
in these regions (Fig.

c, Supplementary Figs. 2 and 3). Nevertheless, our

observational synthesis spanned diverse climates and soil types: MAT ranged from

−

2.9 to 29 °C, MAP from 79 to 3806 mm yr

−

1

, and CS from 1.5 to 100%, across

different mineral and vegetation types (Fig.

b, c and Supplementary Fig. 2).

Indeed, our synthesis spanned the majority of the climate-edaphic covariate space
encompassed by the world

’

s soils in WoSIS (World Soil Information Service)

93

(Supplementary Fig. 3a, b). We further illustrated the global representativeness of
our synthesis within a multi-dimensional covariate space using a principal
component analysis (PCA) and comparing to randomly sampled WoSIS pro

ﬁ

les

(Supplementary Fig. 3c). We note that even WoSIS soil pro

ﬁ

les showed a greater

representation in temperate ecosystems compared to tropical and boreal
ecosystems

94

(Supplementary Fig. 3b), further highlighting the need for additional

measurements in these regions.

De

ﬁ

ning and evaluating ecosystem categories

. Here we classi

ﬁ

ed soils into two

broad categories of mineral type and activity; namely, low-activity minerals (LM)
and high-activity minerals (HM). We used soil order from each individual study
and, when provided, details on clay composition to categorize the soil of each site.
Phyllosilicate clay minerals

—

composed of tetrahedral silicate sheets and octahedral

hydroxide sheets

—

are composed of either 1:1 (one tetrahedral and one octahedral

sheet) or 2:1 (one octahedral sheet sandwiched between two tetrahedral sheets)
clays. 1:1 clays are prevalent in kaolinitic soils and generally have a lower
SSA

; therefore, such soils generally exhibit a lower capacity to stabilize

carbon and can be characterized as LM. In contrast, 2:1 clays are present in
smectitic (e.g., montmorillonitic) and illitic soils and can be characterized as HM,
on account of their high SSA

,

. Finally, soils with amorphous, poorly

crystalline minerals and mineraloids (e.g., allophane) also depicted high stabiliza-
tion (described in greater detail below) and were grouped with HM.

Soil orders (USDA taxonomy) represented in this study include Al

ﬁ

sols,

Andisols, Aridisols, Entisols, Gelisols, Inceptisols, Mollisols, Oxisols, Spodosols,
Ultisols, and Vertisols; we excluded organic soils in wetlands and peat, and, thus,
Histosols were not considered. When detailed information on mineral composition
(e.g., the dominant presence of 2:1 vs. 1:1 clays) was not explicitly stated in the
original studies, the following categorization was used based on the primary
mineral composition by soil order

: Oxisols and Ultisols at all depths were LM;

and Al

ﬁ

sols, Aridisols, Gelisols, Inceptisols, Mollisols, Spodosols, and Vertisols

were HM. Andisols and Entisols were HM in the topsoil (0

–

30 cm) and LM in the

subsoil (30

–

100 cm). We note that, in future studies, allophanic soils with large

amounts of amorphous minerals (i.e., Andisols) could be treated as a third category
due to their propensity to form stable Al- and Fe-complexes and accumulate
SOC

14

,

32

; however, we did not observe a signi

ﬁ

cant difference in their MOC as

compared to HM soils in our synthesis. Furthermore, there are complexities,
including the amount and type of metal oxides and hydroxides, that can make the
distinction between low- and high-activity minerals dif

ﬁ

cult in certain soils

29

96

(and can also complicate the comparison of soil clays and

“

reference

”

or synthetic

clays

97

), the classi

ﬁ

cation of LM and HM soils has been widely used and

,

,

and emerges from our data globally (Fig.

and Supplementary

Figs. 7 and 8). Indeed, the MOC patterns were consistent within our classi

ﬁ

cations

and, thus, these categories were deemed suf

ﬁ

cient for the scope of this global-

scale study.

We retained the classi

ﬁ

cation of vegetation type, and all details on management

practices or lack thereof, reported in the original studies and assigned one of eight
land cover types (Fig.

b

–

c). Land cover types included boreal forest, temperate

forest, tropical forest, grassland, savanna, shrubland, and cropland (Supplementary
Fig. 14). To further compare managed and natural lands, we grouped sites into
broad categories of forests, grasslands (including savannas), and croplands. We
observed stark differences between natural or less-managed ecosystems (namely,
forest and grassland) and more intensively managed (crop) ecosystems (Fig.

). We

calculated the %C saturation of soils (as depicted in Supplementary Fig. 10) to
compare ecosystems and management practices.

Boundary line analyses

. To estimate the mineralogical carbon capacity (MOC

max

)

as a function of soil mineralogy, we conducted a boundary line analysis across the
full range of clay and silt (CS) for each mineral category (LM and HM, see section

“

De

ﬁ

ning and evaluating ecosystem categories

”

; Supplementary Fig. 26). Speci

ﬁ

-

cally, we explored the relationship of MOC (y-axis; g C kg

−

1

soil) as a function of

CS (

x

-axis; %) and

ﬁ

t the 95th quantile for natural ecosystems of each mineral type

to obtain maximum boundary-line slopes for HM and LM (Fig.

; quantile sen-

sitivity analysis in Supplementary Fig. 7). We chose the 95th quantile as a con-
servative approximation of this boundary line, given existing experimental
uncertainty of individual observations (i.e., total % recovery of C from size frac-
tionations ranged from ~80 to 120% among studies). We used MOC observations
from clay and silt (<63

μ

m) size classes to derive MOC

max

(Fig.

) and note that our

results were robust to the choice of particle size (e.g., <20

μ

m or <63

μ

m; Sup-

plementary Fig. 5). The 63

μ

m silt size threshold chosen is also that used in global

datasets and mapped products of soil clay and silt

,

. We also note that our

estimates of MOC

max

for HM and LM were robust across topsoils and subsoils.

Both topsoils and subsoils approached MOC

max

(Fig.

b), and thus, a separate

MOC

max

for each depth was not theoretically or empirically warranted. While it is

more dif

ﬁ

cult to reach MOC

max

in subsoils due to lower carbon inputs, MOC

max

is

an intrinsic property of the soil mineralogy and constitutes a theoretical upper limit
that is independent of depth; indeed, this depth-independence is important for
capturing MOC stocks and ages in process-based soil carbon models

99

100

. Our

estimates of MOC

max

for HM and LM were also robust across vegetation types

(Supplementary Fig. 8), which corroborates studies showing that microbial pro-
cessing and reactive minerals act as effective

ﬁ

lters that lessen chemical differences

in organic matter inputs

59

101

. Theory and models further support this

ﬁ

nding and

suggest that, while litter quality may affect the approach of a given soil to its
mineralogical capacity, the value of MOC

max

is independent of vegetation

. Regressions for both mineral types were

ﬁ

t with a forced intercept

through the origin, since, by de

ﬁ

nition, no clay- and silt-associated organic carbon

(i.e., MOC) can exist without clay and silt minerals present. While some size
fractionation studies report MOC in sandy soils with very low amounts of clay and
silt minerals

, further exploration is needed to understand the relative contribu-

tion of

ﬁ

ne POC and DOC in such soils

16

.

Statistical modeling and predictive relationships

. Due to potential nonlinear

relationships between MOC and environmental variables, we used an ensemble
machine learning method

—

namely, Random Forest (RF)

—

to identify key pre-

dictors and their effects on MOC. This method has been shown to reduce over-

ﬁ

tting to a training dataset compared to other machine learning methods, and does

not suffer from multi-collinearity (i.e., the linear dependence among predictor
variables), as do multiple regression analyses

103

. We used the RandomForest

package in R for RF analyses

103

104

. We used an ensemble of 300 independently

trained RF models (using a 75

–

25% train-test split; 400 decision trees each) with

bootstrapped sampling to robustly assess model performance

105

—

mean absolute

error (MAE) and mean-squared error (MSE) to quantify the model error and

R

2

to

estimate the proportion of variance in MOC explained by the model (Supple-
mentary Fig. 11). Our aim was to: (i) elucidate key variables by assessing their
relative contribution to the MSE of test-set predictions when removed or permuted,
(ii) calculate the total variance explained by selected predictors, and (iii) predict the
response of MOC to a given variable while controlling for all other variables.

RF is often used to rank the importance of each variable in a regression through

permutations of the data

103

, as implemented herein. After preliminary

investigation to select the most important variables, while also considering
variables that were measured in suf

ﬁ

cient studies to retain the greatest number of

complete observations, we identi

ﬁ

ed CS, MAT, MAP, and POC as key continuous

predictors and vegetation (land cover) and mineral type as key categorical
predictors (Supplementary Fig. 11;

R

2

=

0.60 ± 0.06). Speci

ﬁ

cally, variables were

ranked from most to least important, where the most important variables showed
the highest increase in MSE of test set predictions when permuted in the model.

We then investigated the underlying relationship of MOC to key variables

(Fig.

and Supplementary Fig. 12). RF allowed us to explore the effect of each

individual variable on MOC, by integrating the predicted response over the
contribution of all other variables (i.e., partial dependence plot)

106

. That is, for a

variable

x

s

and complement set of all other variables

x

C

, the general model function

is

f x

s

;

x

C

and depends on all input variables. The partial dependence function of

x

s

, denoted

^

f

x

s

x

s

, then describes the marginal effect of

x

s

on the prediction, and is

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7

estimated as:

^

f

x

s

x

s

¼

1

n

∑

n

i

¼

1

f x

s

;

x

C

ð

i

Þ

ð

3

Þ

This was calculated for each predictor variable over the full range of the other

predictor variables (Supplementary Fig. 12), and also over relevant subsets of the
other predictor variables to explore conditional partial dependencies and visualize
two-way variable interactions (e.g., Fig.

). For the case of MAT and POC, we

explored the temperature sensitivity of MOC (i.e., the partial dependence
relationship with MAT) conditional on low (L), medium (M), and high (H) values
of POC that corresponded to different saturation regimes

—

unsaturated, medium,

and saturated (Fig.

a). The breakpoints for these three regimes were selected as the

median and third quartile of the POC distribution (namely, 4 and 10 g C kg

−

1

soil,

respectively), which also correspond to approximate saturation thresholds in the
partial dependence plot of POC (Fig.

a).

Our approach permits us to disentangle the role of each controlling variable and

two-way interactions on the response variable of interest (here MOC) and uncovers
emergent (linear, monotonic, or nonlinear) relationships, providing unique insights
for MOC response to future climate and management interventions (e.g.,
increasing POC or CS). For comparison, we also repeated the above analysis with a
generalized linear model (GLM) and

ﬁ

nd qualitatively similar, though linearized,

trends between MOC and the individual environmental predictors.

Global mineral-associated carbon predictions and uncertainty

. Following the

exploration of underlying climatic and edaphic properties, we trained a RF model
on our observational synthesis to predict MOC globally. Speci

ﬁ

cally, we trained the

RF model to predict MOC from MAT, MAP, CS, SOC, vegetation type, and
mineral type (Supplementary Fig. 26). We note that a global map of POC values
did not exist to be used as an explanatory variable, as was used in the attribution
analyses (Supplementary Fig. 11); rather, global POC values can be derived as a
product of this study.

The Scikit-learn Library in the Python environment was used for global

predictions and Matplotlib Basemap for global mapping. We again used an
ensemble of 300 independently trained RF models (using a 75

–

25% train-test split;

400 decision trees each) with bootstrapped sampling to rigorously assess model
performance

105

. For these RF models that included SOC, a comparison of

predicted and observed MOC on the independent test datasets across the ensemble
yielded an

R

2

=

0.79 ± 0.05 (mean ± s.d.; Supplementary Fig. 13). We note that,

while the predictability of SOC is often lower across large global datasets

107

, the

predictability of MOC is generally high given readily measured SOC, climate, and
edaphic variables (e.g., see refs.

,

on a regional scale). Indeed, the

R

2

was

consistently high across the ensemble cross-validation (Supplementary Fig. 13b).
We also performed a spatially buffered leave-one-out cross-validation

108

to ensure

that spatial auto-correlation did not signi

ﬁ

cantly compromise the RF model.

Namely, for each leave-one-out test data point, all data within a given buffer radius
(0

–

150 km) were excluded from the training set; i.e., only data points outside the

buffer zone were used to train each RF model.

R

2

values did not vary with buffer

radius (regression slope not statistically different from zero;

p

=

0.81) and were in

agreement with the ensemble cross-validation approach (Supplementary Fig. 13c).
Furthermore, we also used a hold-out (or block) cross-validation

109

on the basis of

soil order to assess extrapolation performance and con

ﬁ

rm the robustness of our

RF estimates across soil types

—

i.e., all soil pro

ﬁ

les from a given soil order were

completely withheld from the training dataset and then used to independently test
the resulting RF model. Model performance was consistently high across the out-
of-sample test datasets (

R

2

=

0.75 ± 0.11; mean ± s.d. across soil orders); only

Andisols (which span ~1% of the ice-free land surface) were more dif

ﬁ

cult to

predict when completely withheld from the training dataset (

R

2

=

0.40), and we

encourage more measurements in these soils (see section

“

De

ﬁ

ning and evaluating

ecosystem categories

”

). Hold-out cross-validation on the basis of individual studies

also con

ﬁ

rmed the robustness of our RF estimates to additional data (e.g., our

results were insensitive to adding the independent LUCAS dataset

;

Supplementary Fig. 2). We rigorously demonstrate the RF model performance and
provide uncertainty ranges for the 90% prediction intervals, derived from the 5th
and 95th quantiles (Supplementary Fig. 13a).

The climatic and edaphic driver variables used for the global predictions were

all re-gridded to 0.5° × 0.5° resolution (Supplementary Fig. 14). Mean annual
temperature (MAT) was estimated from the CRU data set (version 3.10)

110

, and

mean annual precipitation (MAP) from the GPCC dataset

111

, both as 30-year

annual averages. Clay and silt (CS) content was obtained from the Harmonized
World Soil Database (HWSD)

. Soil organic carbon (SOC) was obtained from

both the HWSD and SoilGrids

, and also as the average of the two gridded data

products

112

(Supplementary Fig. 19 and Supplementary Table 2). Land cover

(vegetation type) was obtained from the MODIS MCD12C1 product

113

, and the 16

categories were combined into 10 for consistency with those reported in the
observations (Fig.

b, c and Supplementary Fig. 14 for details). The primary

mineral type was calculated from global estimates of mineral composition

(Supplementary Fig. 14; see section

“

Estimating the global soil mineralogical

carbon capacity

”

). We focused our analysis on mineral soils, and thus excluded grid

cells containing a majority of organic soils (i.e., >50% Histosols and Gelisols)

114

,

115

.

Tundra and deserts were also excluded, due to data limitations in these regions

(Supplementary Figs. 2 and 14). We used two depth intervals for SOC, CS, and
primary mineral type, namely topsoil (0

–

30 cm) and subsoil (30

–

100 cm).

The predictive RF model (

R

2

=

0.79 ± 0.05; Supplementary Fig. 13), trained on

the observational data, was then used to predict MOC globally for each depth
interval to 1 m (Supplementary Fig. 15; Supplementary Tables 1 and 2 summarize
results for all SOC data products). We include MOC uncertainty ranges for the
90% prediction intervals (5th and 95th quantiles) globally (Supplementary Fig. 15;
Supplementary Table 2). Interestingly, we note that the distributions of MOC and
SOC (and %C saturation) from our globally distributed observational dataset most
closely agreed with SOC and predicted MOC (and %C saturation) from the
averaged data product (Supplementary Figs. 18 and 19; Supplementary Table 2),
whereas the distribution of SOC (and %C saturation) from SoilGrids was higher
and HWSD was substantially lower (Supplementary Fig. 19; Supplementary
Table 2). We focus here on reporting results using the averaged SOC data product,
as a conservative estimate of MOC stocks given the uncertainty and range between
soil carbon data products, and note that more accurate estimates and consensus on
current soil carbon stocks are critical for improved predictions

116

.

Leveraging our global MOC predictions, we calculated the proportion of SOC

that is mineral-associated globally (Supplementary Fig. 16). Our global estimates of
MOC/SOC ratios agree with those observed in our observational synthesis and
con

ﬁ

rm the dominant contribution of MOC to soil carbon at the global scale

(Supplementary Figs. 1 and 16). Furthermore, our predictions suggest that high-
latitudes have a lower fraction of MOC/SOC globally, and thus a higher fraction of
particulate organic carbon (POC), but data limitations of mineral-associated
carbon measurements at high-latitudes warrant further exploration of these
patterns.

Estimating the global soil mineralogical carbon capacity

. To estimate the

spatially explicit mineralogical carbon capacity (MOC

max

) globally, we used global

data products of clay and silt content (CS), soil order and mineral composition, and
bulk density (BD), together with our derived relationship for MOC

max

(Eq.

;

Fig.

). Global maps of % clay, % silt, and BD were obtained from the HWSD

. A

map of soil mineral composition

was used to generate a corresponding map of

primary mineral type (Supplementary Fig. 14; see section

“

De

ﬁ

ning and evaluating

ecosystem categories

”

). Our focus here was on mineral soils, and thus, we excluded

organic soils (grid cells with >50% Histosols and Gelisols) from the estimation of
global MOC storage potential. Tundra and deserts were also excluded due to data
limitations (Supplementary Figs. 2 and 14). We calculated CS content and applied
our MOC

max

relationship (Fig.

; slope ± 90% con

ﬁ

dence intervals) for each

mineral type (HM and LM) globally to obtain MOC

max

(gC kg

−

1

soil) at 0.5° × 0.5°

resolution. For a global total (in Pg C; 1 Pg

=

10

15

g), we used BD to calculate

MOC

max

stocks (in kg C m

−

2

soil) and then summed over all grid cells containing

mineral soils (Supplementary Tables 1, 2).

The mineralogical capacity MOC

max

(Supplementary Fig. 17) was then

compared to predicted MOC stocks (Supplementary Fig. 15) to calculate the
mineralogical C de

ﬁ

cit (by subtracting MOC from MOC

max

) and %C saturation

(by dividing MOC/MOC

max

) globally (Fig.

; Supplementary Figs. 18

–

20). We note

that this limit is based on mineralogy alone, and many lands may be further limited
by climate. Thus, in addition to the C de

ﬁ

cit relative to the mineralogical capacity

(MOC

max

), we also estimated the C de

ﬁ

cit relative to an environmental limit

calculated using the natural land average %C saturation (i.e., average MOC/
MOC

max

) observed in our MOC synthesis at each depth (Fig.

; i.e., 51 and 19% for

topsoil and subsoil, respectively). These results are summarized in Supplementary
Table 1. We note that our estimates of C de

ﬁ

cit and %C saturation using SoilGrids

are the most conservative for potential accrual, given their higher current SOC (and
consequently MOC) stocks (Supplementary Table 2). However, our estimates using
the averaged soil carbon data product agree with the distributions of MOC stocks
and %C saturation in our observational synthesis (Supplementary Fig. 19;
Supplementary Table 2), and provide a robust estimate that incorporates the range
of current soil carbon stocks.

Our spatially explicit, depth-resolved global estimates highlight regions where

larger C de

ﬁ

cits (lower %C saturation) can be targeted for soil restoration and C

sequestration efforts, especially on managed lands (Fig.

c; Supplementary Figs. 21

and 22). While environmental conditions may make carbon accumulation more
dif

ﬁ

cult in some regions than in others (Supplementary Fig. 12), this estimate

constrains MOC

max

for a given soil mineralogy and provides a starting point for

areas to focus on management (Supplementary Discussion). Furthermore, while
deep soils have the largest C de

ﬁ

cit, surface soils in lands already dominated by

management may be the most cost-effective areas on which to focus.

Observational synthesis and analysis of carbon accrual

. Here we aimed to

quantify the ability of topsoils ranging in mineralogical carbon saturation to further
accrue carbon. We hypothesized that soils further from their mineralogical capacity
(i.e., lower MOC saturation) would accrue carbon faster than soils closer to their
capacity. To this end, we performed an observational synthesis from manipulation
and chronosequence studies that included initial and

ﬁ

nal carbon stocks or con-

centrations to calculate these stocks, bulk density, experimental duration, and
edaphic properties; namely, clay and silt content, texture class or soil series to
estimate these contents and soil classi

ﬁ

cation or other information that would

allow us to assign the soil to a high- or low-activity mineral type.

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For each entry (a pair of initial and

ﬁ

nal carbon stocks), we calculated the

maximum mineralogical capacity (MOC

max

) using the data-derived relationships

(Fig.

) with an amount (% clay

+

silt; CS) and type (high- or low-activity; HM or

LM, respectively) of mineral in each soil layer and used respective bulk densities to
calculate the layer MOC

max

stocks (t C ha

−

1

) which were then summed across the

considered depth to obtain the pro

ﬁ

le MOC

max

stock (t C ha

−

1

). In cases where

initial and

ﬁ

nal soil pro

ﬁ

les differed in clay and silt content, their average was used.

However, if the difference resulted in these soil pro

ﬁ

les falling into different texture

classes, they were excluded from further analysis. Furthermore, to calculate initial
and

ﬁ

nal stocks, we considered initial and

ﬁ

nal pro

ﬁ

les that were taken at equal

depths, which ranged between 10 and 40 cm across studies. Where necessary, initial
and

ﬁ

nal SOC stocks were standardized to equal depths using the maximum depth

of the shallower pro

ﬁ

le as a cutoff ranging between 30 and 39 cm (

n

=

5 pro

ﬁ

les).

We calculated the mineralogical %C saturation as the initial MOC stock divided

by the initial MOC

max

stock. Because MOC was not measured in all accrual studies,

we used the measured SOC and CS values to calculate the corresponding MOC
using our random forest model trained on the MOC synthesis data with analogous
SOC and CS predictors (

R

2

=

0.70 ± 0.06; using Scikit-Learn in Python, see section

“

Global mineral-associated carbon predictions and uncertainty

”

).

Carbon accrual (t C ha

−

1

y

−

1

) was calculated as the difference between

ﬁ

nal and

initial C stock divided by the time period between the repeated samplings (

n

=

32),

the duration of the experiment in the case of a paired plot experimental design
(

n

=

30), the age difference between two sites of a chronosequence (

n

=

24), the

time span at which a regression across multiple samplings was used to obtain an
average rate for a chronosequence (

n

=

10), or the time of soil formation after

emergence of a SOC-free parent material (

n

=

7).

Accrual studies spanned crop, pasture, grassland, and forest ecosystems across

different climates and soil types (Supplementary Table 4; Supplementary Fig. 23).
We focused on studies in which carbon inputs were manipulated or land-use was
altered in a way that carbon accrual could be expected. These included improved
agriculture (cover cropping, no till, crop-livestock rotation, deep ploughing, grazing
reduction), land use change (conversion of cropland to grassland or forest),
doubled litter or wood input from the DIRT (Detrital Input and Removal
Experiment) network, and natural revegetation and mine reclamation (formerly
degraded lands or newly exposed land surfaces as a result of mining, landsliding,
alluviation, or marine terrace uplift, where soil C accrual can be expected as a
consequence of natural or human-accelerated revegetation and soil formation). We
note that most studies did not explicitly quantify C inputs over time, especially
those where changes in C inputs stemmed from downstream impacts on
vegetation, and we strongly urge the reporting of C input estimates in future
studies. After the initial compilation, pro

ﬁ

les were excluded in which the studied

soil depth was lower than 15 cm (

n

=

2) and in which organic amendments were

applied annually, in an initial one-time application higher than 20 t ha

−

1

without a

control plot or at unknown intensity (

n

=

11).

Our accrual synthesis included 103 observations from 34 studies, with depths

ranging between 15 and 40 cm (mean

=

29 cm). The synthesis included soils with

both high-activity minerals (

n

=

84), especially Entisols (

n

=

41) and Al

ﬁ

sols

(

n

=

20), and low-activity minerals (

n

=

19), belonging to Oxisols (

n

=

10) and

Ultisols (

n

=

9). There was a greater representation of temperate climates,

highlighting the need for additional studies in poorly represented regions including
tropical and boreal climates in future work. However, globally, our study suggests
that the greatest potential for accrual (i.e., lowest %C saturation) often occurs in
these temperate regions (Fig.

b) and was thus a focus of our work.

While most soils in the C accrual synthesis fell below 100% C saturation, we

note that MOC

max

was derived as a conservative estimate from the 95th quantile of

our MOC synthesis (Fig.

; see section

“

Boundary line analyses

”

) and therefore, by

de

ﬁ

nition, soils can fall near or above this maximum. Indeed, in our MOC

synthesis, ~200% C saturation values were observed for soils with low values of
MOC and MOC

max

. Of the 103 accrual measurements, one sandy soil (i.e., low

MOC and MOC

max

) displayed seemingly high %C saturation, yet still within

expected ranges (Fig.

d). Furthermore, this soil was categorized as an Andisol,

which could be treated as a third category in future studies (see section

“

De

ﬁ

ning

and evaluating ecosystem categories

”

), due to its propensity to form stable Al- and

Fe-complexes and accumulate carbon

14

. Nevertheless, removing this individual

measurement, or even all Andisols (

n

=

6) in the C accrual synthesis, did not

change the

ﬁ

tted model.

Furthermore, we note that the reclaimed mine soils in our dataset constituted

two major categories of abandonment and regeneration

—

those with and without

topsoil application (Supplementary Fig. 23b). Mine reclamation that employs the
application of topsoil (usually a 30 cm layer, originally excavated before mining and
stored in stockpiles;

n

=

31) is, in terms of management procedures, comparable to

the conversion of cropland (disturbed by tillage and/or erosion) to grassland or
forest. Reclamation can involve some mechanical preparation of soil, application of
fertilizer or other organic amendments, and planting vegetation. This reapplied
topsoil is sampled as a baseline and subsequent sampling in the following years is
used to monitor C accrual. In reclamation without topsoil application (

n

=

13),

vegetation either spontaneously establishes itself or is planted directly into the
parent material. Such conditions represent early stages of soil formation and are
parallel to the restoration of soils heavily impacted by erosion that has led to the
complete loss of topsoil with only the infertile parent material left behind. While
mine soils are well-described systems suitable for the study of soil management,

included in previous syntheses of soil carbon dynamics after land-use
change

117

118

, the

ﬁ

tted model and observed negative trend in C accrual with %C

saturation were robust to their exclusion (Supplementary Fig. 23c).

Statistical analyses were conducted using the

‘

nls

’

package in R to

ﬁ

t a nonlinear

asymptotic relationship between carbon accrual rates and the mineralogical percent
saturation of the respective soil pro

ﬁ

les. Speci

ﬁ

cally, we used a three-parameter

self-starting asymptotic regression model (SSAsymp) on the 103 rate
measurements (

R

2

=

0.18; Fig.

d). The same approach was also used to

ﬁ

t the

10th and 90th quantiles (Fig.

https://doi.org/10.5281/zenodo.5987415

d). There was substantial variability in observed

accrual rates for a given %C saturation, due to differences in climate and land use
across sites (Supplementary Fig. 23). However, most of this variability appeared in
soils furthest from C saturation, where environmental and management factors
also play a role in observed accrual rates. In soils closest to saturation, this
variability was far lower as carbon accrual rates tended towards zero, illustrating
the importance of the mineralogical limit. Our focus here was on constraining an
average empirical rate of carbon accrual as a function of %C saturation and
investigating whether soils furthest from C saturation achieve higher carbon
accrual rates. We also note that the variability in C accrual rates was better
explained by %C saturation (

R

2

=

0.18) than by initial SOC (

R

2

=

0.04-0.10;

Supplementary Fig. 24), further demonstrating the relevance of the
mineralogical limit.

We used the nonlinear asymptotic regression to provide a spatially explicit

global estimate of potential C accrual rates in topsoils dominated by management
(Supplementary Fig. 22). While such accrual rates would be dif

ﬁ

cult to achieve

everywhere, our spatially explicit estimates of potential C accrual rates highlight
priority regions for future soil restoration and C sequestration initiatives and
provide an independent estimate of global soil C sequestration potential.

Data availability

The globally gridded maps of mineral-associated carbon and mineralogical carbon
capacity derived in this study are freely available and archived at Zenodo (

https://doi.org/

10.5281/zenodo.6539765

). The observational syntheses (mineral-associated carbon and

accrual measurements) in support of these

ﬁ

ndings are detailed in Supplementary

Tables 3 and 4, and archived at Zenodo (

).

Code availability

All code relating to this study is available from the corresponding author upon request,
and is archived at Zenodo (

https://doi.org/10.5281/zenodo.6539765

).

Received: 20 January 2022; Accepted: 9 June 2022;

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Acknowledgements

K.G. was supported as a Lawrence Fellow at Lawrence Livermore National Laboratory
(LLNL) and by a U.S. Department of Agriculture NIFA Postdoctoral Fellowship (Grant
No. 2018-67012-27982). Work at LLNL was conducted under the auspices of DOE
Contract DE-AC52-07NA27344 and was supported by the LLNL-LDRD Program under
Project No. 21-ERD-045. O.V. and R.Z.A. were supported by the European Union

’

s

Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie
grant agreement No. 793485 (O.V.) and No. 834169 (R.Z.A.). R.Z.A. was also supported
by the US DOE, Of

ﬁ

ce of Science, Of

ﬁ

ce of Biological and Environmental Research at

Oak Ridge National Laboratory, which is managed by UT-Battelle, LLC, for the US DOE
under contract DE-AC05-00OR22725. M.S.T. and W.J.R. were supported by the US
DOE, Of

ﬁ

ce of Science, Of

ﬁ

ce of Biological and Environmental Research under contract

number DE-AC02-05CH11231. We thank Jan Frouz, Kate Lajtha, Derek Pierson, István
Fekete, and Zsolt Kotroczó for helpful comments regarding the carbon accrual synthesis.

Author contributions

K.G. conceived the study. K.G., R.B.J., and M.S.T. designed the study, with contributions
from O.V., R.Z.A., J.W.H., H.W.P., and W.J.R. on the study development. K.G., O.V.,
A.A., A.F.A.P., W.F., and J.L.S. collected and contributed data. K.G. and O.V. performed
statistical and model analyses. K.G. wrote the manuscript, with contributions from all
authors.

Competing interests

The authors declare no competing interests.

Additional information

Supplementary information

The online version contains supplementary material

available at

https://doi.org/10.1038/s41467-022-31540-9

.

Correspondence

and requests for materials should be addressed to Katerina Georgiou.

Peer review information

Nature Communications

thanks Emanuele Lugato and the

other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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http://www.nature.com/reprints

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