Fourel et al. (2026). Compact CNN-Transformers match larger models for spatially-robust soil organic carbon mapping at regional scale

https://github.com/ValerianFoure

d

,

Thomas

Scholten

d

,

e

a

University

of

Hamburg

Business

School,

Professorship

of

Statistics

with

Applications

in

Business

Administration,

University

of

Hamburg, Moorweidenstraße

18, Hamburg, 20148, Hamburg, Germany

b

Bavarian

State

Research

Center

for

Agriculture,

Institute

for

Agroecology

and

Organic

Farming, Vöttinger

Straße

38, Freising, 85354, Bavaria, Germany

c

The

LandBanking

Group

GmbH, Sophienstraße

5, Munich, 80333, Bavaria, Germany

d

Department

of

Geosciences,

Soil

Science

and

Geomorphology,

University

of

Tübingen, Rümelinstraße

19-23, Tübingen, 72070, Baden-Württemberg, Germany

e

Cluster

of

Excellence

Machine

Learning:

New

Perspectives

for

Science,

University

of

Tübingen, Maria-von-Linden-Straße

6, Tübingen, 72076, Baden-Württemberg, Germany

A

R

T

I

C

L

E

I

N

F

O

Handling

Editor:

Budiman

Minasny

Dataset

link:

l/SOCmapping

,

https://huggingface.co/dataset

s/ValerianFourel/sgt-bavaria-soc-2002-2023-la
rge

,

https://huggingface.co/datasets/ValerianF

ourel/SOCrebuttal

Keywords:

Remote

sensing

Machine

learning

Soil

organic

carbon

Bavaria
Mapping
Spatial

cross-validation

Transformer
CNN

A

B

S

T

R

A

C

T

Soil

Organic

Carbon

(SOC)

is

a

global

reservoir

in

the

carbon

cycle,

and

accurate

regional

monitoring

is

needed

for

soil

assessment

and

climate-change

mitigation.

Most

Digital

Soil

Mapping

(DSM)

studies

treat

SOC

as

a

static

spatial

target

and

report

accuracy

on

random

data

splits,

which

spatial

autocorrelation

inflates.

We

evaluate

a

family

of

architectures,

gated

and

ungated

CNN-Transformer

hybrids,

plain

Transformers,

CNN–LSTM,

Random

Forest,

and

XGBoost,

on

16,514

Bavarian

topsoil

samples

(2007–2023)

with

a

43-band

multi-temporal

covariate

stack,

under

10-fold

longitude-blocked

spatial

cross-validation.

Every

attention

model

clusters

within

one

fold

standard

deviation,

so

a

compact

gated

CNN-Transformer

(

≈

87k

parameters,

𝑅

2

= 0

.

375 ± 0

.

100

)

comes

within

one

fold

standard

deviation

of

a

≈

45.1M-parameter

pure

Transformer

(

𝑅

2

= 0

.

401 ± 0

.

097

)

at

roughly

500×

fewer

parameters.

Neither

the

convolutional

front-end

nor

the

gated

residual

network

yields

a

separable

gain,

and

added

capacity

does

not

help.

Tree

ensembles

trail

only

modestly

on

the

full

domain

(Random

Forest

0.342,

XGBoost

0.317).

This

edge

is

modest

(0.05–0.07

in

fold-mean

𝑅

2

,

within

the

fold-to-fold

spread)

but

consistent

in

sign

across

longitude-,

latitude-,

and

cluster-blocked

folds,

and

it

is

land-use

stratified:

on

cropland

alone,

a

low-variance

regime,

gradient-boosted

trees

are

far

stronger

(

𝑅

2

≈ 0

.

66

versus

≈ 0

.

21

),

reproducing

prior

cropland-only

Bavarian

studies.

The

appropriate

regional

product

is

therefore

a

land-use-stratified

map

with

tree

ensembles

on

cropland

and

attention

models

on

the

high-variance

organic

remainder,

rather

than

a

single

model.

The

contribution

is

thus

not

a

new

architecture

for

SOC

mapping

but

a

rigorous,

spatially-

validated

architecture

comparison

and

the

land-use-dependent

inversion

of

model

performance

it

reveals.

The

recommended

compact

model

produces

a

wall-to-wall

2023

SOC

map

of

Bavaria

at

250

m

resolution.

1.

Introduction

The

distribution

of

SOC

is

driven

by

complex

interactions

among

topography,

climate

and

land

management

(

,

),

and

laboratory

assessment

does

not

scale

to

regional

extents.

Digital

Soil

Mapping

(DSM)

instead

leverages

Earth

Observation

data

;

,

),

where

Random

Forest

valerian.fourel@gmail.com

Breiman

,

2001

)

and

XGBoost

(

are

the

industry

stan-

dard

,

,

)

but

treat

SOC

as

a

static

spatial

target,

correlating

instantaneous

or

time-averaged

covariates

with

current

stocks

(

).

Yet

SOC

accu-

mulates

over

decades

of

productivity,

litter

decomposition

and

stabi-

lization,

so

current

stocks

carry

a

legacy

that

no

single-date

snapshot

∗

Corresponding

author.

E-mail

addresses:

(V.

Fourel),

martin.wiesmeier@lfl.bayern.de

(M.

Wiesmeier),

nkakhani@gmail.com

(N.

Kakhani),

thomas.scholten@uni-tuebingen.de

(T.

Scholten).

encodes.

Without

attempting

to

recover

that

full

multi-decadal

legacy,

we

test

whether

a

short,

recent

multi-year

covariate

window

carries

more

signal

than

static

covariates

,

);

hybrid

CNN-

Transformer

models

have

been

reported

to

capture

such

multi-year

trajectories

with

gains

over

static

baselines

,

though,

as

we

find,

the

advantage

proves

modest

and

land-use-dependent

rather

than

decisive.

Recent

studies

have

successfully

employed

deep

learning

and

hy-

perspectral

imagery

to

map

SOC

with

increasing

precision

;

;

,

Models

consistently

underperform

in

carbon-rich

environments

due

to

data

scarcity

and

fail

https://doi.org/10.1016/j.geoderma.2026.117933

Received

31

March

2026;

Received

in

revised

form

2

July

2026;

Accepted

3

July

2026

Available

online

14

July

2026

0016-7061/©

2026

The

Authors.

Published

by

Elsevier

B.V.

This

is

an

open

access

article

under

the

CC

BY

license

(

http://creativecommons.org/licenses/by/4.0/

V.

Fourel

et

al.

Fig.

1.

ESA

Landcover

map

for

Bavaria.

to

generalize

well

across

diverse

ecoregions

).

Under-

standing

these

dynamics

is

crucial

because

land

use

strongly

dictates

storage

potential;

for

instance,

grasslands

typically

store

significantly

more

carbon

than

croplands,

a

distinction

that

static

models

often

struggle

to

resolve

without

temporal

phenology

data

(

,

).

To

address

these

limitations,

we

evaluate

a

family

of

architectures

for

temporally-aware

SOC

prediction,

with

particular

focus

on

how

spatial-generalization

performance

scales

with

model

size.

Drawing

on

the

Temporal

Fusion

Transformer

and

hybrid

CNN-Transformer

designs

(

we

systematically

compare

architectures

ranging

from

tree-based

baselines

to

attention

models

spanning

multiple

orders

of

magnitude

in

parameter

count

(from

≈

87k

to

≈

45.1M),

all

trained

on

a

43-band

multi-temporal

co-

variate

stack

and

evaluated

under

10-fold

longitude-blocked

spatial

cross-validation,

isolating

which

inductive

biases

transfer

to

spatially

held-out

regions

and

how

accuracy

depends

on

parameter

count

at

the

modest

sample

sizes

typical

of

regional

soil

monitoring.

The

concrete

prediction

target

is

the

2023

SOC

concentration

across

Bavaria;

the

2007–2023

covariate

archive

lets

each

sample

draw

on

a

five-year

preceding

window,

matching

the

multi-year

timescale

on

which

SOC

responds

to

climate

and

management

(

,

The

bare-soil

reflectance

composite

is

the

most

direct

spectral

pre-

dictor

of

topsoil

SOC

and

underpins

every

prior

Bavarian

mapping

study

;

;

,

;

It

is

constructed

by

capped-median

compositing

of

repeat-

edly

bare

Landsat

pixels

,

;

,

;

,

with

the

Normalized

Burn

Ratio

2

(NBR2)

and

a

bare-

soil

index

(BSI)

screening

crop

residue

and

partial

vegetation

cover

(

,

and

chromatic

coordinates

capturing

the

organic-matter

darkening

of

soil

colour

(

,

);

its

shortwave-infrared

bands

in

particular

carry

the

CH/NH/CO

overtone

absorptions

diagnostic

of

soil

organic

matter

(

,

;

,

The

dynamic

MODIS/SRTM

backbone

rep-

resents

the

SCORPAN

energy

and

organism

factors,

with

NPP,

LAI,

and

the

thermal

and

water-balance

controls

on

decomposition

(LST,

ET,

soil

evaporation)

(

,

;

,

,

;

).

Static

soil

properties

(texture,

pH,

bulk

density,

CEC)

encode

the

capacity

of

the

mineral

matrix

to

stabilize

organic

carbon

);

terrain

derivatives

capture

the

lateral

redistribution

of

water

and

carbon

across

the

landscape

(

,

and

the

climate

and

phenology

layers

summarize

the

seasonal

moisture

and

growth

regime

governing

carbon

input

and

turnover

(

,

Provenance

and

independence

of

the

soil-property

covariates.

Five

of

the

43

bands

are

static

soil

properties

(clay,

sand,

pH,

bulk

density,

CEC)

taken

at

0–10

cm

from

two

global

modelled

digital

soil-mapping

prod-

ucts,

OpenLandMap

)

and

SoilGrids

2.0

,

at

250

m

(sources

in

1

Because

they

are

modelled

surfaces

they

raise

a

potential

circularity,

but

the

risk

is

limited:

they

are

causal

mineral-matrix

controls

on

carbon

stabilization

(texture,

base

saturation,

aggregate

density

(

rather

than

SOC

derivatives,

are

predicted

independently

of

the

Bavarian

SOC

used

here

and

without

SOC

as

a

predictor,

and

carry

their

own

uncertainty

that

is

largest

in

the

carbon-rich

soils

where

any

leakage

would

matter

most.

We

treat

the

dependence

as

a

limitation

(Section

4.6

);

the

full

independence

argument

is

given

in

Supplementary

Text

S2.

As

the

direct

test,

we

retrained

the

recommended

model

without

these

five

soil-property

bands:

fold-mean

𝑅

2

falls

by

only

0.01–0.03

under

the

same

10-fold

longitude-blocked

spatial

cross-validation.

The

static

soil

layers

are

therefore

marginal

contributors

rather

than

primary

drivers

of

fit,

so

the

SOC

information

they

could

re-introduce

is

small

and

circular

leakage

is

unlikely

to

be

material;

we

retain

them

because

they

add

modest,

independent

pedological

context

at

negligible

parameter

cost.

The

architecture

is

band-agnostic:

a

grouped

input

convolution

accommodates

the

full

stack

with

negligible

additional

parameters,

so

the

parameter-efficiency

conclusions

reported

here

are

properties

of

the

architecture

rather

than

of

any

particular

input

width.

2.3.

SOC

distribution

and

temporal

analysis

2.3.1.

Statistical

distribution

The

SOC

distribution

across

Bavaria

exhibits

a

strong

positive

skew

(3.26)

and

high

kurtosis

(12.71),

characteristic

of

temperate

soil

datasets

).

The

mean

concentration

(

22

.

5 g kg

−1

)

notably

exceeds

the

median

(

16

.

5 g kg

−1

),

with

approximately

90%

of

samples

falling

Geoderma

472

(2026)

117933

4

V.

Fourel

et

al.

Table

1

The

43-band

covariate

stack

summarized

by

thematic

group,

with

the

dominant

SCORPAN

factor

in

parentheses

and

the

source

dataset,

native

resolution

and

static/dynamic

status

of

each

group.

Native

resolutions

are

the

source

resolutions

before

all

layers

are

resampled

to

the

common

250

m

modelling

grid.

The

five

static

soil-property

bands

are

taken

from

global

modelled

digital

soil-mapping

products

(OpenLandMap,

SoilGrids

2.0);

their

provenance

and

independence

are

discussed

below.

The

complete

channel-ordered

enumeration

(band

name,

source

asset,

native

resolution,

units,

epoch

and

static/dynamic

status)

is

provided

in

the

supplementary

material.

Only

the

five

soil-property

bands

carry

a

per-pixel

uncertainty

estimate

from

their

source

products

(SoilGrids

2.0/OpenLandMap),

largest

in

the

carbon-rich

organic

soils;

the

remaining

covariates

are

direct

observational

or

reanalysis

products

without

per-band

uncertainty

layers.

Abbreviations:

SRC,

soil

reflectance

composite;

SWIR,

shortwave

infrared;

BSI,

bare-soil

index;

NBR2,

normalized

burn

ratio

2;

RCC/BCC,

red/blue

chromatic

coordinate;

NDVI/EVI,

normalized-difference/enhanced

vegetation

index;

LAI,

leaf

area

index;

NPP,

net

primary

productivity;

LST,

land-surface

temperature;

ET,

evapotranspiration;

TWI,

topographic

wetness

index;

TPI,

topographic

position

index;

TRI,

terrain

ruggedness

index;

CEC,

cation-exchange

capacity.

Group

(SCORPAN)

#

Source

(native

res.;

type)

Representative

members

Soil

reflectance

composite,

SRC

(

𝑠

)

11

Landsat

C2

L2

capped-median

bare-soil

composite,

30

m

(dynamic,

1984–2023)

blue–SWIR2,

BSI,

NBR2,

RCC/BCC,

exposure

count

Terrain

(

𝑟

)

8

SRTM

GL1

+

MERIT

Hydro,

30

m

(static)

slope,

aspect,

TWI,

TPI

(90/300/1000

m),

TRI,

roughness

Climate

(

𝑐

)

7

ERA5-Land

reanalysis,

≈

9

km

(dynamic,

2007–2023)

precipitation,

air

temperature,

soil

temperature,

snow

depth,

frost

days,

growing-degree

days,

climatic

water

balance

Vegetation

&

phenology

(

𝑜

)

6

MODIS

MOD13Q1/MCD15A3H,

250–500

m

(dynamic,

2000–2023)

NDVI,

EVI,

LAI,

seasonal

NDVI/EVI

amplitude,

NDVI

integral

Soil

properties

(

𝑠

)

5

OpenLandMap

v02

(texture,

pH,

bulk

density)

+

SoilGrids

2.0

(CEC),

250

m

(static,

modelled)

clay,

sand,

pH,

bulk

density,

cation-exchange

capacity

Energy

&

evapotranspiration

(

𝑐

,

𝑜

)

3

MODIS

MOD17/MOD11/MOD16,

0.5–1

km

(dynamic)

NPP,

LST,

ET

Hydrology

(

𝑐

)

2

ERA5-Land

vol.

soil

water

+

bare-soil

evaporation,

≈

9

km

(dynamic)

soil

moisture

(0–7

cm),

soil

evaporation

Elevation

(

𝑟

)

1

SRTM

GL1,

30

m

(static)

SRTM

DEM

elevation

Total

43

Fig.

4.

SOC

Histogram

and

Kernel

Density

Distribution

(KDE)

of

the

study

area.

below

50 g kg

−1

.

The

heavy

tail

represents

occasional

high-carbon

outliers

found

in

distinct

ecoregions.

2.3.2.

Temporal

variability

and

spatiotemporal

dynamics

Annual

analysis

reveals

substantial

inter-annual

variability

in

both

central

tendency

and

dispersion

The

violin

plots

display

con-

siderable

heterogeneity

across

years,

with

sample

sizes

ranging

from

55

(2023)

to

3034

(2012),

and

mean

SOC

values

spanning

from

13

.

1 g kg

−1

(2007)

to

75

.

2 g kg

−1

(2023).

The

sharp

increase

of

the

mean

and

median

SOC

concentration

in

2022

and

2023

coincides

with

small,

spatially

non-representative

campaigns

that

disproportionately

sam-

pled

carbon-rich

sites,

and

is

examined

as

a

sampling

artefact

in

the

Discussion.

To

characterize

the

raw

temporal

signal

in

the

observed

data,

we

fitted

a

multivariate

regression

of

SOC

on

both

altitude

and

sampling

year.

The

fitted

plane

equation:

SOC

= −9

.

14 + 0

.

752 × (

Year

− 2007) + 0

.

0581 ×

Altitude

(1)

yields

𝑅

2

= 0

.

246

,

confirming

that

altitude

accounts

for

substantial

SOC

variance.

The

year

coefficient

(

+0

.

752 g kg

−1

year

−1

)

is

the

altitude-

controlled

variant

(V5)

in

the

sensitivity

analysis

of

2

;

this

Geoderma

472

(2026)

117933

5

V.

Fourel

et

al.

Fig.

5.

Annual

distribution

of

SOC

concentrations

(2007–2023)

showing

violin

plots

with

sample

means

(blue

diamonds)

and

medians

(pink

circles).

Table

2

Sensitivity

of

the

estimated

annual

SOC

trend

to

model

specification

and

sample

weighting.

The

coefficient

ranges

from

+0

.

75

to

+2.42

g

kg

−1

year

−1

across

reasonable

variants,

indicating

that

it

is

governed

by

the

uneven

sampling

distribution

rather

than

a

robust

temporal

signal.

Variant

Specification

𝑛

Year

coef.

adj.

𝑅

2

(g

kg

−

1

yr

−

1

)

V1

OLS,

year

only

16,514

+1

.

192

0.042

V2

OLS,

excluding

2022–2023

16,335

+0

.

895

0.024

V3

WLS,

weight

1∕

𝑛

year

16,514

+2

.

423

0.150

V4

OLS,

years

with

𝑛

≥

100

16,459

+1

.

067

0.034

V5

OLS,

year

+

altitude

16,514

+0

.

752

0.246

coefficient

is

highly

sensitive

to

the

uneven

year-by-year

sampling

distribution

and

should

not

be

interpreted

as

a

robust

soil–carbon

trend

(

,

This

interpretation

is

reinforced

by

the

sampling

record

itself.

An-

nual

sample

sizes

range

from

55

(2023)

to

over

3000

(2012),

and

the

sharp

rise

in

mean

SOC

in

2022–2023

5

)

coincides

with

small,

spatially

non-representative

campaigns

that

disproportionately

sampled

carbon-rich

sites.

This

is

most

parsimoniously

read

as

a

bias

in

the

observational

record

rather

than

as

regional

carbon

accumulation,

consistent

with

independent

Bavarian

assessments

that

report

only

slight

change

or

decline

,

;

,

2.3.3.

Implications

for

architecture

design

The

spatiotemporal

structure

revealed

by

this

analysis

motivates

the

architectural

choices

evaluated

in

this

study.

Three

observations

are

relevant:

First,

the

temporal

signal

motivates

explicit

temporal

modelling.

Since

altitude

remains

constant

for

each

location

while

environmen-

tal

conditions

vary

year

by

year,

models

that

ignore

this

temporal

dimension

leave

a

modest,

land-use-dependent

amount

of

explanatory

power

unused

,

).

By

treating

time

as

the

dynamic

variable,

we

capture

systematic

year-to-year

changes

in

climate

patterns,

management

practices,

and

vegetation

dynam-

ics

that

influence

SOC

accumulation,

which

are

variations

that

occur

independently

of

the

fixed

topographic

context

defined

by

altitude.

Second,

the

limited

variance

explained

by

the

altitude-year

plane

(

𝑅

2

= 0

.

246

)

demonstrates

that

static

topographic

and

simple

temporal

features

capture

less

than

one-quarter

of

SOC

variability.

This

under-

scores

the

need

for

richer

environmental

covariates

(NPP,

LST,

moisture

regimes)

and

their

temporal

sequences

to

model

the

complex

drivers

of

SOC

dynamics.

Third,

the

persistence

of

both

spatial

and

temporal

structure

moti-

vates

an

architecture

that

combines

a

spatial

encoder

with

a

temporal

sequence

model.

The

compact

CNN-Transformer

hybrid

evaluated

here

addresses

this

with

a

hybrid

design:

a

CNN

extracts

spatial

features

from

each

multi-channel

time

step,

while

a

Transformer

self-attention

block,

optionally

refined

by

a

gated

residual

network,

captures

dependencies

across

the

5-year

sample-relative

input

window

(Section

2.4

).

By

com-

bining

these

complementary

inductive

biases,

the

model

maps

cumula-

tive

environmental

histories

to

observed

SOC

levels

rather

than

relying

on

spurious

spatial

autocorrelation

or

oversimplified

trend

extrapo-

lation

(

Whether

the

gated

residual

network

earns

its

parameters,

and

how

performance

depends

on

model

size,

are

treated

as

explicit

ablations

(Sections

3.2.1

–

3.2.3

)

rather

than

assumed.

2.4.

Model

architectures

We

evaluate

a

family

of

architectures

spanning

the

spectrum

from

tree

ensembles

to

deep

spatiotemporal

models,

each

comparison

isolat-

ing

one

design

choice.

The

recommended

model

is

a

compact

gated

CNN-Transformer

(

𝑑

= 32

,

2

heads,

1

layer,

≈

87k

parameters),

described

first;

the

ablations

and

baselines

against

which

it

is

com-

pared

follow.

All

neural

models

share

the

same

input

tensor,

temporal

Geoderma

472

(2026)

117933

6

V.

Fourel

et

al.

Fig.

6.

Architecture

of

the

recommended

compact

gated

CNN-Transformer

(

𝑑

= 32

,

2

heads,

1

layer,

≈

87k

parameters):

a

convolutional

spatial

encoder,

a

gated

residual

network

(GRN),

a

Transformer

temporal

block,

and

an

MLP

head.

The

gating

ablation

removes

the

GRN;

the

scaling

ablation

varies

the

embedding

dimension

and

depth.

window

and

training

protocol,

so

that

performance

differences

are

attributable

to

architecture

rather

than

to

data

handling.

2.4.1.

Recommended

model:

compact

gated

CNN-transformer

(87k

param-

eters)

The

recommended

model

takes

each

sample

as

a

tensor

of

shape

(

𝐵, 𝑇

= 5

,

43

,

5

,

5)

:

a

5

×

5

spatial

window

(

1

.

25 × 1

.

25

km

on

the

250

m

grid)

of

all

43

covariates

over

a

five-year,

sample-relative

time

window.

For

a

sample

collected

in

year

𝑦

the

window

is

{

𝑦

−4

,

…

, 𝑦

}

,

which

prevents

temporal

leakage,

since

no

covariate

post-dates

the

mea-

surement,

and

matches

the

multi-year

scale

on

which

SOC

responds;

samples

before

2011

are

dropped

when

fewer

than

four

preceding

years

of

MODIS

coverage

exist.

The

network

has

four

stages

6

):

a

weight-shared

CNN

encodes

each

time

step

into

a

length-

𝑑

feature

vector

(

𝑑

= 32

);

a

gated

residual

network

(GRN)

,

;

,

)

reweights

these

features

through

learnable

sigmoid

gates;

a

small

self-attention

encoder

(2

heads,

1

layer)

with

positional

encoding

and

attention

pooling

aggregates

the

five

steps;

and

an

MLP

head

maps

the

result

to

SOC.

In

this

smallest

configuration

the

model

has

only

≈

87k

parameters

yet

matches

much

larger

ones

within

fold

noise

(Section

3.2

).

We

compare

two

output

heads:

a

plain

MLP

head,

and

a

crisp

linear-skip

head

that

adds

a

direct

linear

projection

of

the

pooled

features.

They

differ

only

in

output

dynamic

range;

the

effect

on

map

calibration

is

reported

with

the

gating

ablation

(Section

3.2.3

,

12

).

2.4.2.

Ablations

and

baselines

Three

controlled

comparisons,

each

sharing

the

recommended

model’s

input

tensor,

window

and

training

protocol,

isolate

one

design

choice.

Gating:

removing

the

GRN

leaves

an

otherwise-identical

un-gated

CNN-

Transformer

(

𝑑

= 64

,

≈

118k

parameters),

so

the

difference

measures

whether

the

GRN

earns

its

parameters;

the

gated

design

is

the

architec-

ture

originally

introduced

as

the

Spatiotemporal

Gated

Transformer.

Front-end

and

scale:

pure

self-attention

models

with

no

CNN

encoder

are

evaluated

at

a

lightweight

≈

313k

size

and

at

a

large

≈

45.1M

size

(embedding

tied

to

the

flattened

input),

testing

whether

the

CNN

front-

end

adds

value

at

matched

capacity

and

whether

brute-force

scale

can

substitute

for

inductive

bias.

Baselines:

Random

Forest

and

XGBoost,

the

current

state

of

practice,

aggregate

the

five-year

window

into

static

per-band

statistics,

while

a

CNN–LSTM

(

)

replaces

attention

with

recurrence;

together

they

test

whether

explicit

spatial

and

temporal

modelling

is

necessary.

The

transformer

family

thus

spans

≈

87–118k

(gated

and

un-gated

hybrids)

through

≈

313k

and

≈

45.1M

(pure

Transformers).

2.5.

Experimental

design

The

primary

evaluation

is

10-fold

longitude-blocked

spatial

cross-

validation.

The

study

area

is

partitioned

into

ten

contiguous

west–east

bands

of

approximately

equal

sample

count

(

7

);

each

band

is

held

out

in

turn

as

the

validation

fold

while

the

remaining

nine

train

the

model.

A

1.2

km

buffer

is

enforced

at

every

fold

boundary,

so

that

no

validation

sample

lies

within

the

1

.

25 × 1

.

25 km

input

window

of

any

training

sample;

this

prevents

the

spatial-autocorrelation

leakage

that

random

splits

permit

(

;

,

Because

each

fold

withholds

an

entire

geographic

region,

the

result-

ing

fold-mean

𝑅

2

±

standard

deviation

estimates

genuine

out-of-region

generalization

rather

than

interpolation

between

nearby

points.

We

report

fold-mean

𝑅

2

and

its

standard

deviation

across

the

ten

folds

as

the

primary

performance

summary,

and

let

the

per-fold

results

(Section

3.2

)

identify

which

regions

are

hardest

rather

than

assuming

a

single

worst

fold

a

priori.

Final

inference

for

the

published

2023

SOC

map

13

)

is

per-

formed

by

feeding

the

recommended

model

covariate

sequences

span-

ning

2019–2023

across

the

full

Bavarian

250

m

grid,

yielding

a

single

SOC

prediction

surface

representative

of

2023.

Model

performance

was

evaluated

using

four

standard

metrics:

•

Coefficient

of

determination

(

𝑅

2

):

𝑅

2

= 1 −

SS

res

SS

tot

,

we

have

SS

res

=

∑

𝑛
𝑖

=1

(

𝑦

𝑖

−

̂

𝑦

𝑖

)

2

and

SS

tot

=

∑

𝑛
𝑖

=1

(

𝑦

𝑖

−

̄

𝑦

)

2

•

Root

Mean

Squared

Error

(RMSE):

RMSE =

√

1

𝑛

∑

𝑛
𝑖

=1

(

𝑦

𝑖

−

̂

𝑦

𝑖

)

2

•

Mean

Absolute

Error

(MAE):

MAE =

1

𝑛

∑

𝑛
𝑖

=1

|

𝑦

𝑖

−

̂

𝑦

𝑖

|

•

Ratio

of

Performance

to

Interquartile

Distance

(RPIQ):

RPIQ =

𝑄

3

−

𝑄

1

RMSE

(

,

,

,

We

have

𝑦

𝑖

representing

observed

values,

̂

𝑦

𝑖

represents

predicted

values,

̄

𝑦

is

the

mean

of

observed

values,

𝑛

is

the

number

of

observa-

tions,

and

𝑄

1

and

𝑄

3

are

the

first

and

third

quartiles

of

the

observed

data,

respectively.

2.6.

Training

protocol

Training

procedures

differed

between

the

deep

learning

models

and

the

ensemble

baselines.

The

neural

networks

(the

gated

and

un-gated

CNN-Transformer

hybrids,

the

simple

Transformer,

and

CNN–LSTM)

were

trained

with

the

Adam

optimizer

(

,

using

ReLU

activations.

The

training

objective

was

the

mean

absolute

error

between

predicted

̂

𝑦

𝑖

and

observed

𝑦

𝑖

,

both

on

the

log-transformed

SOC

target:



(

𝜃

) =

1

𝑁

∑

𝑖

=1

|

𝑦

𝑖

−

̂

𝑦

𝑖

|

,

(2)

given

𝑁

is

the

mini-batch

size

and

𝜃

denotes

the

model

parameters.

The

𝐿

1

formulation

was

preferred

over

mean

squared

error

because

of

its

reduced

sensitivity

to

the

heavy-tailed

residuals

characteris-

tic

of

carbon-rich

peatland

samples.

Generalization

was

controlled

by

dropout

(

𝑝

= 0

.

3

)

applied

after

each

fully

connected

block

and

𝐿

2

weight

decay

(

𝜆

= 10

−5

)

applied

through

the

Adam

optimizer.

Input

co-

variates

were

standardized

per

channel

using

statistics

computed

on

the

Geoderma

472

(2026)

117933

7

V.

Fourel

et

al.

Fig.

7.

The

ten

longitude-blocked

cross-validation

folds.

Bavaria

is

partitioned

into

ten

contiguous

west–east

bands

of

approximately

equal

sample

count

(colour

=

fold);

each

band

is

held

out

in

turn

as

the

validation

fold

while

the

remaining

nine

train

the

model,

and

a

1.2

km

buffer

at

every

band

boundary

prevents

overlap

between

the

1

.

25 × 1

.

25 km

input

windows

of

training

and

validation

samples.

Coordinates

are

in

UTM

zone

32N.

training

set

only,

and

the

SOC

target

was

log-transformed

to

stabilize

its

skewed

distribution

,

);

the

same

target

transformation

was

applied

to

the

ensemble

baselines

(Random

Forest,

XGBoost)

for

comparability.

Ensemble

hyperparameters

were

selected

via

grid

search

with

internal

cross-validation

on

the

training

set.

3.

Results

3.1.

Spatial

and

statistical

residual

analysis

Residual

analysis

for

the

recommended

model

indicates

spatially

independent

errors

with

a

residual

structure

dominated

by

the

heavy

upper

tail

of

the

SOC

distribution.

The

residual

maps

and

Q–Q

panels

below

are

rendered

for

the

recommended

model,

and

the

residual

summary

statistics

reported

in

this

section

are

computed

from

its

training-fold

and

longitude-blocked

hold-out

predictions.

Spatial

distribution.

Residual

maps

for

both

training

and

validation

sets

display

a

predominantly

random

pattern

across

the

study

area.

There

is

no

systematic

clustering

of

over-

or

under-estimation

in

either

the

southern

alpine

regions

(high

SOC)

or

the

northern

agricultural

lowlands

(low

SOC).

This

confirms

that

model

performance

remains

consistent

across

diverse

geographical

and

land-use

contexts

(see

9

Statistical

characteristics.

Error

distributions

are

centred

near

zero

but

exhibit

non-normal

behaviour.

Training

residuals

show

a

mean

of

0

.

818 g kg

−1

(SD

=

8.874),

while

validation

residuals

show

a

mean

of

−1

.

238 g kg

−1

(SD

=

5.966)

with

a

slight

negative

tail.

Q–Q

plots

reveal

tail

deviations

from

normality,

indicating

persistent

systematic

structure

rather

than

pure

noise.

This

is

attributed

to

the

skewed

nature

of

SOC

data

and

the

resolution

gap

between

coarse

250 m

predictors

and

fine-scale

heterogeneity;

higher-resolution

inputs

(e.g.,

10–20 m)

could

potentially

reduce

these

structural

deviations

;

;

,

The

training

residual

SD

(8.87

g

kg

−

1

)

exceeding

the

validation

residual

SD

(5.97

g

kg

−

1

)

is

unusual,

since

validation

error

normally

equals

or

exceeds

training

error.

The

most

plausible

explanation

is

distributional

rather

than

a

sign

of

underfitting:

the

heavy

upper

tail

of

the

SOC

distribution

(peatland

and

high-organic

alpine

samples)

is

concentrated

in

the

training

partition,

whereas

the

spatially-blocked

validation

partition

for

this

diagnostic

contains

proportionally

fewer

such

extreme-SOC

samples.

Because

these

high-SOC

samples

generate

the

largest

absolute

residuals,

they

inflate

the

training-set

residual

SD

relative

to

the

validation

set.

Limitation

in

carbon-rich

zones.

While

the

model

avoids

spatial

bias,

it

tends

to

underestimate

the

highest

SOC

values:

in

carbon-rich

environ-

ments

(peatlands,

high-organic

alpine

soils)

predictions

are

compressed

towards

the

densely-sampled

low-to-moderate

range.

This

is

a

conse-

quence

of

the

strong

positive

skew

of

the

training

distribution

rather

than

a

hard

numerical

ceiling,

and

it

means

SOC

maps

should

be

read

as

conservative

in

carbon-rich

areas.

3.2.

Comparative

model

performance

3

compares

the

best

configuration

of

each

architecture

fam-

ily

under

10-fold

longitude-blocked

spatial

cross-validation

on

16,514

Bavarian

soil

samples

and

the

43-band

covariate

stack.

Three

findings

emerge:

increasing

model

capacity

provides

no

reliable

gain,

neither

the

convolutional

front-end

nor

gating

separates

the

attention

models

beyond

fold-to-fold

noise,

and

the

practical

contribution

is

therefore

parameter

efficiency.

Geoderma

472

(2026)

117933

8

V.

Fourel

et

al.

Fig.

8.

Out-of-fold

residuals

(predicted

−

actual)

of

the

recommended

compact

gated

CNN-Transformer

at

every

soil

sample,

pooled

across

the

ten

longitude-

blocked

hold-out

folds.

Red

indicates

over-prediction

and

blue

under-prediction;

the

colour

scale

is

clipped

at

±

18

g

kg

−

1

(90th

percentile

of

|

residual

|

).

Errors

are

largely

spatially

unstructured

apart

from

a

few

dense

sampling

clusters.

Fig.

9.

Normal

Q–Q

plots

of

the

recommended

compact

gated

CNN-Transformer’s

residuals

(predicted

−

actual,

g

kg

−

1

):

(a)

training

residuals

and

(b)

validation

(held-out)

residuals.

Both

distributions

are

markedly

heavy-tailed

and

non-Gaussian.

We

have

sample

quantiles

fall

well

below

the

reference

line

in

the

lower

tail

and

above

it

in

the

upper

tail,

and

the

two

panels

are

closely

similar,

indicating

that

the

non-normal

residual

structure

is

intrinsic

to

the

heavy-tailed

SOC

distribution

rather

than

an

artefact

of

the

held-out

split.

The

large

negative

residuals

reflect

under-prediction

of

the

rare

carbon-rich

samples,

consistent

with

the

conservative

behaviour

of

the

prediction

map

in

high-SOC

areas.

3.2.1.

Scale

provides

no

advantage

Adding

capacity

does

not

improve

out-of-region

accuracy.

The

largest

model

evaluated

is

a

≈

45.1M

pure

Transformer

which

attains

𝑅

2

= 0

.

401 ± 0

.

097

,

a

≈

313k

transformer

attains

0

.

385 ± 0

.

100

,

and

the

≈

87k

gated

CNN-Transformer

attains

0

.

375 ± 0

.

100

.

The

≈

87k

hybrid

and

the

≈

313k

Transformer

are

statistically

indistinguishable,

whereas

the

≈

45.1M

model

is

marginally

but

significantly

higher

(

𝛥𝑅

2

= 0

.

026

,

𝑝

= 0

.

01

;

3

);

the

spread

across

this

∼

500

×

range

of

param-

eter

counts

nonetheless

stays

within

one

fold

standard

deviation.

A

∼

500

×

larger

model

therefore

buys

only

a

marginal

0.026

gain

that

Geoderma

472

(2026)

117933

9

V.

Fourel

et

al.

Table

3

Architecture

comparison

under

10-fold

longitude-blocked

spatial

cross-validation

on

16,514

Bavarian

soil

samples

and

the

43-band

covariate

stack

(SOC

≤

150

g

kg

−

1

).

Configurations:

pure

Transformer

𝑑

=

𝐶

⋅

𝐻

⋅

𝑊

(input-tied),

ℎ

= 4

,

𝐿

= 1

;

lightweight

Transformer

𝑑

= 128

,

ℎ

= 4

,

𝐿

= 1

;

un-gated

CNN-Transformer

𝑑

= 64

,

ℎ

= 4

,

𝐿

= 1

;

recommended

gated

CNN-Transformer

(

⋆

)

𝑑

= 32

,

ℎ

= 2

,

𝐿

= 1

;

CNN–LSTM

hidden

𝑑

= 64

,

𝐿

= 1

;

Random

Forest

1000

trees,

unlimited

depth;

XGBoost

1000

trees,

depth

8,

𝜂

= 0

.

05

(

𝑑

,

ℎ

,

𝐿

are

the

transformer

embedding

dimension,

attention

heads

and

encoder

layers).

𝑅

2

is

the

fold

mean

±

per-fold

standard

deviation

with

the

95%

confidence

interval

(Student-

𝑡

,

𝑑𝑓

= 9

);

RMSE

and

MAE

are

fold

means

±

the

half-width

of

the

95%

CI;

parameter

counts

are

approximate;

𝑝

is

a

paired

Wilcoxon

signed-rank

test

of

per-fold

𝑅

2

against

the

recommended

gated

model

(all

models

share

identical

geographic

folds).

All

attention-based

models

cluster

within

roughly

one

fold

standard

deviation

(

𝑅

2

= 0

.

375

–0.401):

the

lightweight

Transformer,

un-gated

CNN-Transformer

and

CNN–LSTM

are

not

significantly

different

from

the

≈

87k

gated

model

(

𝑝 >

0

.

1

),

whereas

the

≈

45.1M

pure

Transformer

is

marginally

but

significantly

higher

(

𝛥𝑅

2

= 0

.

026

,

𝑝

= 0

.

01

,

∼

500

×

the

parameters

for

a

0.026

gain).

The

gated

CNN-Transformer

is

significantly

above

both

tree

ensembles

(RF

𝑝

= 0

.

03

,

XGBoost

𝑝

= 0

.

002

),

which

trail

only

modestly.

Neither

the

convolutional

front-end

nor

gating

separates

the

attention

models

beyond

fold-to-fold

noise;

the

practical

contribution

is

parameter

efficiency,

so

the

gated

CNN-Transformer

is

recommended

on

that

basis

rather

than

as

the

single

highest-scoring

model

and

).

⋆

recommended

configuration.

Family

𝑅

2

95%

CI

RMSE

MAE

Params

𝑝

mean

±

SD

𝑑𝑓

= 9

g kg

−

1

g kg

−

1

vs.

⋆

Pure

Transformer

(no

CNN)

0

.

401 ± 0

.

097

[0

.

33

,

0

.

47]

14

.

6 ± 1

.

8

.

2 ± 1

.

2

45.1 M

0.010

Lightweight

Transformer

0

.

385 ± 0

.

100

[0

.

31

,

0

.

46]

14

.

8 ± 1

.

9

8

.

0 ± 1

.

1

313 k

0.432

CNN-Transformer

(un-gated)

0

.

381 ± 0

.

096

[0

.

31

,

0

.

45]

14

.

9 ± 1

.

9

8

.

1 ± 1

.

1

118 k

0.695

Gated

CNN-Transformer

⋆

0

.

375 ± 0

.

100

[0

.

30

,

0

.

45]

14

.

9 ± 1

.

8

.

1 ± 1

.

0

87

k

–

CNN–LSTM

0

.

352 ± 0

.

125

[0

.

26

,

0

.

44]

15

.

1 ± 1

.

7

8

.

2 ± 1

.

1

99 k

0.105

Random

Forest

0

.

342 ± 0

.

095

[0

.

27

,

0

.

41]

15

.

4 ± 2

.

1

8

.

7 ± 1

.

2

–

0.027

XGBoost

0

.

317 ± 0

.

106

[0

.

24

,

0

.

39]

15

.

6 ± 2

.

1

8

.

8 ± 1

.

1

–

0.002

its

parameter

cost

does

not

justify,

and

the

compact

model

is

preferred

purely

on

efficiency

grounds

(

10

ranks

all

families;

11

resolves

performance

fold

by

fold).

3.2.2.

The

CNN

front-end

is

not

decisive

With

a

properly

calibrated

output

head,

the

convolutional

spatial

encoder

does

not

separate

the

strongest

models.

The

two

highest-

scoring

architectures

are

pure

(no-CNN)

Transformers,

the

≈

45.1M

model

(0.401)

and

the

≈

313k

model

(0.385),

both

of

which

edge

out

the

CNN-Transformer

hybrids

(un-gated

0.381,

gated

0.375);

all

four

differences

lie

within

the

fold-to-fold

standard

deviation

(

≈

0.10),

so

attention

does

not

require

a

CNN

front-end

to

be

competitive

here.

The

tree

ensembles

(RF

0.342,

XGBoost

0.317)

are

clearly

positive

under

spatial

blocking

and

trail

the

attention

models

only

modestly,

while

the

recurrent

CNN–LSTM

(0.352)

is

comparable

to

the

trees.

The

deep

models

thus

deliver

a

small,

consistent

edge

over

the

tree

baselines

that

is

attributable

to

self-attention

rather

than

to

the

convolutional

front-

end

specifically.

Output-head

calibration

partly

governs

the

ranking

among

the

neural

families,

an

effect

taken

up

with

the

gating

ablation

(Section

3.2.3

3.2.3.

Gating

is

accuracy-neutral

but

supplies

output

dynamic

range

On

held-out

accuracy

the

recommended

gated

model

(0.375)

and

the

otherwise-identical

un-gated

CNN-Transformer

(0.381)

are

indis-

tinguishable:

the

difference

is

well

within

the

fold-to-fold

standard

deviation

(

≈

0.10),

and

if

anything,

the

ungated

variant

is

marginally

ahead.

We

therefore

make

no

accuracy

claim

for

gating

and

do

not

advance

the

gated

residual

network

(GRN)

as

a

source

of

predictive

skill

The

gate

nonetheless

changes

behaviour

as

it

is

operationally

vis-

ible

and

modifies

the

calibration

of

the

output

map.

SOC

is

strongly

right-skewed

(skewness

3.26;

∼

90%

of

samples

below

50 g kg

−1

),

and

under

an

𝐿

1

objective

a

plain

prediction

head

regularized

with

dropout

and

weight

decay

is

pulled

towards

the

median,

compressing

its

out-

put

variance

and

washing

the

map

out.

The

GRN

counteracts

this

without

touching

average

accuracy:

its

residual

path

lets

the

high-

variance

feature

directions

pass

forward

without

being

squashed

by

the

nonlinear

stack,

while

the

sigmoid

gate

makes

that

amplification

context-dependent,

opening

where

the

input

reads

high-carbon

and

falling

back

to

a

conservative

baseline.

The

crisp

linear-skip

head

isolates

the

same

effect

independently

(

12

):

it

lifts

the

under-calibrated

plain-head

models

substantially

(pure

Transformer

+0

.

069

,

CNN–LSTM

+0

.

092

,

lightweight

Transformer

+0

.

038

)

but

is

neutral

for

the

gated

CNN-Transformer

(

−0

.

008

),

whose

GRN

already

supplies

that

range.

The

two

experiments

together

identify

the

GRN’s

role

as

output

dynamic

range

rather

than

accuracy,

and

the

consequence

is

visible

in

the

maps

(

15

):

the

gated

model’s

predicted-SOC

spread

is

wider

than

the

equally-accurate

un-gated

hy-

brid

and

closer

to

both

the

≈

45.1M

Transformer

and

the

observed

distribution.

We

therefore

recommend

the

gated

configuration

as

the

better-calibrated

wall-to-wall

product

at

the

smallest

parameter

count,

supplying

its

own

dynamic

range

without

a

separate

post-hoc

calibra-

tion

head.

3.3.

Underestimation

in

carbon-rich

environments

The

recommended

model,

like

all

models

evaluated

here,

com-

presses

predictions

towards

the

densely-sampled

low-to-moderate

SOC

range

and

underestimates

the

most

carbon-rich

sites.

We

do

not

report

a

single

numerical

ceiling:

the

degree

of

compression

depends

on

the

training

distribution

and

the

SOC

cutoff,

and

a

precise

figure

such

as

the

120 g kg

−1

value

obtained

under

a

log-

𝐿

1

objective

is

specific

to

that

configuration

rather

than

fundamental.

The

recommended-model

2023

map,

for

instance,

has

a

95th

percentile

near

23 g kg

−1

,

reflecting

the

predominance

of

mineral

soils

across

Bavaria.

For

operational

applications,

SOC

maps

in

peatland

and

high-

altitude

regions

should

be

interpreted

as

conservative

lower

bounds.

Future

work

could

address

this

through

targeted

oversampling

of

carbon-rich

environments,

asymmetric

loss

functions

that

penalize

underestimation

more

heavily

at

high

SOC

values,

or

ensemble

ap-

proaches.

4.

Discussion

4.1.

Architecture–data

alignment

The

pattern

of

results

points

to

an

accuracy

ceiling

set

by

the

data

and

the

spatial-extrapolation

task

rather

than

by

any

single

architec-

ture.

Under

longitude-blocked

cross-validation

every

attention-based

model

clusters

within

roughly

one

fold

standard

deviation,

so

nei-

ther

the

CNN

spatial

encoder

nor

the

gated

residual

network

earns

a

statistically

separable

improvement,

and

capacity

well

beyond

∼

100k

parameters

adds

no

practically

useful

skill

(Section

3.2.1

).

The

tree

ensembles

are

competitive

and

clearly

positive

under

spatial

blocking,

so

the

deep

models

contribute

a

modest,

consistent

edge

from

combin-

ing

self-attention

with

the

5-year

covariate

sequence

(

,

not

the

rescue

of

a

task

on

which

classical

Geoderma

472

(2026)

117933

10

V.

Fourel

et

al.

Fig.

10.

Best-per-family

fold-mean

𝑅

2

under

10-fold

longitude-blocked

spatial

cross-validation

(43-band

stack,

SOC

≤

150

g

kg

−

1

),

with

per-fold

standard-deviation

error

bars

and

parameter

counts.

The

recommended

compact

gated

CNN-Transformer

(

⋆

,

≈

87k)

lies

within

the

error

bars

of

every

other

attention-based

model,

including

the

≈

45.1M

pure

Transformer.

Fig.

11.

Per-fold

𝑅

2

for

each

architecture

family

across

the

ten

longitude-blocked

hold-out

folds

(rows

sorted

by

fold

mean;

right

column

gives

mean

±

per-fold

SD).

The

westernmost

block

(fold

F0)

is

the

hardest

fold

for

every

family

and

drives

most

of

the

fold-to-fold

variance.

methods

fail;

this

edge

holds

under

latitude-

and

cluster-blocked

cross-

validation

as

well

(Section

4.2

The

practical

lesson

is

that,

with

∼

16,500

samples

and

coarse

covariates,

the

spatial-extrapolation

dif-

ficulty

bounds

accuracy

far

more

than

the

choice

among

competitive

architectures,

and

keeping

the

model

small

costs

nothing

(

,

;

,

4.2.

Land-use

stratification

of

SOC

predictability

The

architecture

ranking

established

above

is

a

property

of

the

heterogeneous,

multi-land-use

domain

on

which

it

was

measured,

not

of

SOC

mapping

in

general:

it

inverts

when

the

analysis

is

restricted

to

cropland.

This

regime

dependence

is

distinct

from

the

choice

of

spatial-CV

geometry,

the

longitude-,

latitude-,

and

cluster-blocked

folds

vary

where

a

model

must

extrapolate,

whereas

the

all-land-use

versus

cropland-only

contrast

varies

which

data

regime

it

must

learn.

The

two

axes

are

summarized

in

and

On

the

full

multi-land-use

domain

the

attention

family

out-generalizes

the

strongest

tree

ensem-

bles

under

every

geometry,

by

+0

.

059

(longitude),

+0

.

072

(cluster),

and

+0

.

054

(latitude)

in

fold-mean

𝑅

2

.

The

margin

is

modest

relative

to

the

fold-to-fold

spread

(

≈

0.08–0.11)

but

consistent

in

sign

across

all

three

blockings,

which

is

the

defensible

form

of

the

claim

that

the

deep

models

generalize

better.

Restricting

the

same

data

to

cropland

Geoderma

472

(2026)

117933

11

V.

Fourel

et

al.

Fig.

12.

Effect

of

the

crisp

linear-skip

output

head

on

spatial-CV

𝑅

2

,

per

neural

family

(original

plain

MLP

head

vs.

linear-skip

head,

𝛥𝑅

2

).

The

linear-skip

head

substantially

helps

the

under-calibrated

plain-head

models

(CNN–LSTM

+0

.

092

,

pure

Transformer

+0

.

069

,

lightweight

Transformer

+0

.

038

)

and

is

approximately

neutral

for

the

gated

CNN-Transformer

(

−0

.

008

),

whose

gated

residual

network

already

supplies

output

dynamic

range.

The

tree

baselines

have

no

neural

head

and

are

unaffected.

Fig.

13.

Predicted

2023

topsoil

SOC

map

of

Bavaria

from

the

recommended

compact

gated

CNN-Transformer

(

𝑑

= 32

,

ℎ

= 2

,

𝐿

= 1

,

≈

87k

parameters),

across

the

full

250

m

grid.

Inference

uses

covariate

sequences

spanning

2019–2023.

The

colour

scale

is

fixed

to

0–150

g

kg

−

1

(PowerNorm

𝛾

= 0

.

7

);

built-up

areas

(black)

and

water

bodies

(deep

blue)

are

masked

from

prediction.

The

map

is

read

as

conservative

in

carbon-rich

areas.

which

is

a

low-variance

regime

(SOC

mean

≈

17,

SD

≈

11

g

kg

−

1

)

inverts

the

ranking

decisively

and

consistently:

the

tree

ensembles

reach

𝑅

2

≈ 0

.

66

under

all

three

geometries

while

the

attention

family

falls

to

≈ 0

.

16

–0.23,

a

gap

of

0.43–0.51.

This

cropland

advantage

is

not

an

artefact

of

variance

normalization,

it

is

equally

clear

on

the

absolute

metrics,

where

the

tree

ensembles

more

than

halve

the

attention

model’s

error

(RMSE

≈

3.7

vs

≈

8.5

g

kg

−

1

,

MAE

≈

2.5

vs

≈

4.8)

and

more

than

double

its

RPIQ

(

≈

2.2

vs

≈

0.9;

An

attention

model’s

advantage

is

its

capacity

to

exploit

variance

and

signal

that

lives

in

spatial

neighbourhoods

and

multi-year

covariate

trajectories;

a

gradient-boosted

tree

instead

reads

per-band

statistics

directly

from

a

flat

feature

vector

and

is

near-optimal

when

the

target

is

a

smooth

function

of

those

statistics.

Cropland

offers

little

of

the

former,

so

the

tree’s

higher-bias

prior

is

the

better

match,

and

the

attention

model,

with

little

spatial

or

temporal

structure

to

recover,

overfits

region-specific

detail

that

does

not

transfer

under

blocking.

The

Geoderma

472

(2026)

117933

12

V.

Fourel

et

al.

Table

4

Performance

scoreboard

under

10-fold

spatial

cross-validation

(43-band

stack,

maximum

SOC

150

g

kg

−

1

).

The

first

block

is

the

full

leading

comparison

on

the

longitude-blocked,

all-land-use

domain,

with

per-fold

standard

deviations

(the

same

seven

families

are

listed

with

parameter

counts

in

3

);

the

remaining

blocks

contrast

the

pure

Transformer

(the

leading

network)

and

the

recommended

compact

gated

CNN-Transformer

against

the

leading

tree

ensemble

under

the

cluster-

and

latitude-blocked

geometries

and

on

cropland.

All

metrics

are

fold

means;

RMSE

and

MAE

are

in

g

kg

−

1

.

RF

=

Random

Forest;

XGB

=

XGBoost.

Model

𝑹

𝟐

RPIQ

MAE

RMSE

Longitude-blocked

⋅

all

land

use

(leading

comparison)

Pure

Transformer

(45.1M)

0

.

401 ± 0

.

097

0.794

8.17

14.59

Lightweight

Transformer

(313k)

0

.

385 ± 0

.

100

–

CNN-Transformer,

un-gated

(118k)

0

.

381 ± 0

.

096

0.779

8.12

14.86

Gated

CNN-Transformer

(87k)

0

.

375 ± 0

.

100

0.776

8.10

14.89

CNN–LSTM

(99k)

0

.

352 ± 0

.

125

0.766

8.15

15.10

Random

Forest

0

.

342 ± 0

.

095

0.756

8.72

15.36

XGBoost

0

.

317 ± 0

.

106

–

Cluster-blocked

⋅

all

land

use

Pure

Transformer

0.292

0.766

8.33

14.56

gated

CNN-Transformer

0.284

0.759

8.38

14.69

Random

Forest

0.220

0.730

9.05

15.37

Latitude-blocked

⋅

all

land

use

Pure

Transformer

0.235

0.725

8.63

14.48

gated

CNN-Transformer

⋆

0.198

0.707

8.39

14.84

Random

Forest

0.181

0.701

8.73

15.00

Longitude-blocked

⋅

cropland

Pure

Transformer

0.226

0.991

4.77

8.38

gated

CNN-Transformer

⋆

0.208

0.974

4.85

8.51

XGBoost

0.657

2.191

2.45

3.69

Cluster-blocked

⋅

cropland

Pure

Transformer

0.161

0.858

4.95

8.56

gated

CNN-Transformer

⋆

0.157

0.855

4.98

8.63

XGBoost

0.657

2.147

2.56

3.65

Latitude-blocked

⋅

cropland

Pure

Transformer

0.163

0.907

4.84

8.52

gated

CNN-Transformer

⋆

0.139

0.901

4.97

8.69

XGBoost

0.670

2.174

2.51

3.71

full

domain

restores

both

ingredients:

the

heavy-tailed

organic

carbon

of

forest,

peat,

and

wetland

soils

and

the

broad

geographic

gradients

across

Bavaria

are

exactly

the

structured,

high-variance

signal

that

attention

is

built

to

model.

The

full-domain

advantage

is

nonetheless

modest,

and

because

𝑅

2

is

variance-relative

it

is

partly

leveraged

by

a

small

number

of

high-carbon

sites

that

enlarge

the

variance

denomina-

tor.

The

edge

is

not

solely

an

𝑅

2

effect,

however:

on

the

full

domain

the

attention

model

also

carries

a

consistently

lower

fold-mean

RMSE

under

every

geometry

(

≈

14.5

vs

≈

15.0–15.4

g

kg

−

1

;

).

Pedological

basis

of

the

land-use

dependence.

The

statistical

contrast

above

has

a

concrete

pedological

reading.

Bavarian

SOC

is

governed

first

by

soil

type

and

land

use

):

the

carbon-rich,

high-variance

tail

sits

in

groundwater-influenced

Gleysols

and

Fluvisols

and

in

the

Histosols

of

drained

fens

and

bogs

of

the

Alpine

foreland,

together

with

the

cool,

wet

forests

and

grasslands

of

the

south,

where

waterlogging

and

low

temperatures

slow

decomposition

and

produce

the

structured

signal

attention

models

exploit

,

).

The

intensively

managed

arable

lowlands,

by

contrast,

are

dominated

by

mineral

Cambisols

and

Luvisols

whose

topsoil

carbon

has

been

driven

by

tillage

and

liming

towards

a

narrow,

near-stationary

equilibrium

(mostly

below

≈

2%

SOC,

with

little

decadal

change

(

)),

a

low-variance

regime

where

a

higher-bias

tree

ensemble

is

the

better

match.

The

land-use

inversion

of

the

model

ranking

is

thus

a

reflection

of

how

carbon

is

stabilized

across

Bavaria’s

soils,

not

a

modelling

artefact.

This

stratification

reconciles

with,

rather

than

competes

against,

the

existing

Bavarian

SOC

literature

All

five

comparable

regional

studies

are

cropland-only:

bare-soil

reflectance

compositing,

the

basis

of

those

studies,

requires

periodically

bare

soil

and

there-

fore

restricts

coverage

to

arable

land

,

,

;

,

,

Cropland

is

precisely

the

low-variance

regime

in

which

tree-

and

shallow-CNN

models

are

near-optimal,

so

their

convergence

near

𝑅

2

≈ 0

.

6

–0.7

under

random

validation

is

the

expected

result,

and

our

own

tree

baselines

reproduce

it

(

≈ 0

.

66

)

on

a

matched

cropland

subset

under

blocked

cross-validation.

The

contribution

here

is

not

a

higher

cropland

number

but

the

multi–land-use

scope,

which

no

prior

Bavarian

study

possessed

and

without

which

the

regime

dependence

is

invisible,

combined

with

longitude-blocked

evaluation

that

removes

the

spatial-autocorrelation

inflation

inherent

in

the

random-split

metrics

those

studies

report.

For

a

wall-to-wall

product

these

results

argue

for

a

regime-aware

rather

than

a

single-model

map:

tree

ensembles

where

the

surface

is

arable,

the

regime

they

map

best,

and

where

external

benchmarks

exist,

and

the

attention

family

across

the

high-variance

organic

re-

mainder.

A

single

deep-learning-everywhere

map

is

not

supported:

it

would

be

weakest

precisely

on

cropland,

the

most

scrutinized

and

most

benchmarked

land

use.

We

frame

the

stratified

product

as

indicated

by

the

per-regime

results

rather

than

demonstrated

end-to-end:

a

formal

evaluation

of

the

stitched

map

against

either

single

model,

including

its

behaviour

at

land-cover

seams,

remains

to

be

carried

out.

4.3.

Validating

for

generalization

Because

every

fold

withholds

an

entire

west–east

band

of

Bavaria

behind

a

1.2

km

buffer,

the

fold-mean

𝑅

2

reported

here

measures

genuine

out-of-region

extrapolation

rather

than

interpolation

between

environmentally

similar

neighbours

,

,

,

).

One

property

of

𝑅

2

matters

when

reading

these

scores:

being

variance-normalized,

it

need

not

track

RMSE

fold

to

fold.

A

fold

withholding

a

low-variance

region

leaves

little

explainable

variance,

so

even

small

absolute

errors

can

yield

a

low

or

negative

𝑅

2

,

whereas

a

heavy-tailed

high-carbon

fold

raises

RMSE

while

enlarging

the

variance

denominator.

The

fold-mean

𝑅

2

≈ 0

.

375

–0.40

for

the

best

attention

models

should

therefore

be

read

as

a

measure

of

out-of-region

difficulty

under

variance

normalization,

not

a

failure

of

absolute

pre-

diction,

which

is

why

each

mean

is

reported

with

its

per-fold

standard

deviation

(

≈

0.08–0.11),

with

the

full

per-fold

breakdown

in

11

Geoderma

472

(2026)

117933

13

V.

Fourel

et

al.

Fig.

14.

Best-per-class

hold-out

𝑅

2

(mean

±

per-fold

SD

over

the

ten

folds)

for

the

strongest

neural

model

(best

NN,

blue)

versus

the

strongest

tree

ensemble

(best

tree,

orange),

across

the

two

axes

of

:

data

regime

(all

land

use

vs.

cropland,

shaded)

and

spatial-CV

geometry

(longitude-,

cluster-,

and

latitude-blocked).

On

the

full

multi–land-use

domain

the

attention

model

out-generalizes

the

trees

under

every

geometry;

on

cropland

the

ordering

inverts

decisively,

with

the

gradient-boosted

trees

reaching

𝑅

2

≈ 0

.

66

while

the

attention

model

falls

to

≈ 0

.

16

–0.23.

Best

NN

is

the

pure

(no-CNN)

Transformer

throughout;

best

tree

is

Random

Forest

on

the

full

domain

and

XGBoost

on

cropland.

All

models

use

the

43-band

stack

with

SOC

≤

150

g

kg

−

1

.

While

design-based

validation

is

the

appropriate

estimator

for

a

probability

sample

(

,

),

our

16,514

records

are

a

spatially

clustered

composite

of

monitoring

and

survey

campaigns

(LUCAS,

LfL,

LfU),

not

a

probability

sample

of

Bavaria,

so

no

design-

based

estimate

is

available.

Longitude-blocked

spatial

cross-validation

therefore

remains

the

most

rigorous

available

estimator

of

out-of-

region

extrapolation,

and

we

read

the

fold-mean

𝑅

2

as

a

deliberately

conservative

lower

bound

for

operational

mapping

rather

than

a

figure

characterizing

every

pixel.

15

pairs

the

predicted

2023

SOC

with

the

width

of

the

cal-

ibrated

90%

prediction

interval

for

three

representative

models.

The

intervals

are

conformal,

calibrated

on

the

spatial-CV

out-of-fold

resid-

uals

and

binned

by

predicted

level

(empirical

held-out

coverage

0.90).

All

three

share

the

same

uncertainty

geography

tight

over

the

densely-

sampled

low-carbon

cropland

(

≈

11–15

g

kg

−

1

)

and

wide

over

the

carbon-rich

peat,

alpine

and

forest

soils

(

≈

105–116

g

kg

−

1

).

The

un-

certainty

measures

are

asymmetric,

widening

on

the

upper

side

as

the

spatially-explicit

signature

of

the

conservative

bias

at

high

SOC

(Section

2.3.1

).

The

≈

45.1M

pure

Transformer

and

the

≈

87k

gated

CNN-Transformer

produce

near-identical

uncertainty

fields

while

XG-

Boost

is

most

confident

over

the

cropland

where

it

is

strongest.

For

each

model

we

take

its

out-of-fold

residuals

from

the

10-fold

spatial

cross-validation,

compute

their

5th

and

95th

percentiles

within

bins

of

predicted

SOC,

and

attach

that

level-dependent

band

to

every

grid

pixel

as

its

90%

prediction

interval.

The

mapped

uncertainty

is

therefore

the

empirical

spread

of

the

model’s

own

held-out

errors,

conditioned

on

the

predicted

value.

4.4.

Covariate

sufficiency

and

environmental

representation

Static

topographic

and

simple

temporal

features

explain

less

than

one-quarter

of

SOC

variability

(

𝑅

2

= 0

.

246

;

Section

2.3.2

),

so

the

model

is

instead

driven

by

the

43-band

multi-temporal

stack

(Sec-

tion

2.2

),

assembled

to

populate

the

SCORPAN

soil-forming

factors

rather

than

to

maximize

feature

count

(

,

a

dynamic

MODIS/SRTM

core

with

LST

LAI

(

),

NPP

(

soil

evaporation,

and

evapotranspiration

),

complemented

by

a

bare-

soil

reflectance

composite,

vegetation

and

phenology

layers,

a

climate

block,

static

soil

properties

,

and

terrain

derivatives

spanning

the

remaining

factors

(full

stack

in

1

).

The

central

empirical

point

is

that

this

breadth

did

not

require

a

larger

model:

Expanding

the

stack

to

43

bands

left

the

most

compact

configuration

as

the

best

performer

(Section

3.2

At

this

sample

size,

predictive

accuracy

is

therefore

bounded

by

the

information

that

coarse

(250–1000 m)

covariates

carry

about

fine-scale

SOC,

not

by

feature-

space

breadth

or

model

capacity

(

,

as

we

reach

the

same

ceiling,

read

from

the

covariate

side,

that

the

parameter-scaling

results

report

from

the

architecture

side.

To

better

capture

management

effects,

an

explicit

land

use/land

cover

time

series

from

ESA

Sentinel-2

imagery

is

a

natural

further

covariate.

4.5.

Pedological

interpretation

of

the

temporal

component

By

integrating

a

multi-year

sequence

of

environmental

covariates,

the

recommended

architecture

aligns

with

the

temporal

factor

of

soil

formation,

and

this

temporal

grounding,

rather

than

any

specific

gat-

ing

mechanism,

is

its

principal

conceptual

contribution.

Unlike

static

models

that

treat

soil

samples

as

isolated

pixels

;

a

temporally-aware

model

encodes

that

SOC

stocks

are

the

cumulative

result

of

historical

biomass

inputs

balanced

against

decomposition

over

years

to

decades

,

The

Transformer

module

lets

the

model

proxy

this

cumulative

pedo-

genesis,

approximating

the

temporal

factor

(

𝑡

)

of

soil

formation

(

;

,

Two

caveats

bound

that

inter-

pretation:

the

series

begins

only

in

2007,

so

longer-term

SOC

memory

that

is

the

imprint

of

past

climate,

vegetation,

and

management

on

current

stocks

(

,

,

is

not

captured,

and

NPP

represents

above-

but

not

below-ground

carbon

inputs

(

while

elevation

interacts

with

SOC

in

complex,

landscape-

dependent

ways

,

Within

the

2007–2023

window,

however,

the

model

does

exploit

covariate

trajectories

such

as

temperature

and

moisture

controls

on

decomposition

(

,

)

and

the

NPP/LAI

dynamics

that

separate

stable

from

changing

ecosystems

(

Grunwald

,

2021

)

that

static

models

omit.

A

temporally-aware

model

thus

shifts

the

task

modestly

from

purely

correlative

mapping

towards

more

process-informed

prediction

at

the

out-of-region

accuracy

achieved

here

it

captures

temporal

structure

that

static

regressions

omit,

but

it

does

not

by

itself

recover

the

physical

mechanisms

of

carbon

input,

stabilization,

and

turnover

;

,

Geoderma

472

(2026)

117933

14

V.

Fourel

et

al.

Fig.

15.

Predicted

2023

SOC

(left

of

each

pair)

and

calibrated

90%

prediction-interval

width

(right).

4.6.

Limitations

and

future

directions

Because

the

recommended

model

is

compact

(

≈

87k

parameters),

inference

cost

is

not

a

major

barrier

to

adoption

relative

to

simpler

methods;

the

more

pressing

needs

are

explainability

and

epistemic

uncertainty

quantification,

beyond

the

conformal

prediction

intervals

reported

here

,

A

central

limitation

is

the

modest

achievable

accuracy

itself.

Under

spatial

cross-validation

the

best

architecture

reaches

a

fold-mean

𝑅

2

of

only

≈ 0

.

40

.

With

16,514

samples

spread

over

∼

70,550

km

2

and

covariates

at

250–1000

m

resolution,

this

appears

to

be

close

to

the

upper

bound

of

what

is

recoverable

for

out-of-region

prediction

at

this

scale.

A

further

limitation

concerns

the

scope

of

the

uncertainty

we

report.

The

90%

prediction

intervals

mapped

earlier

(

15

)

are

conformal

bands

derived

from

each

model’s

out-of-fold

residual

quan-

tiles:

they

calibrate

the

empirical

spread

of

held-out

errors

conditioned

on

the

predicted

level,

but

they

do

not

propagate

model

(parameter

and

epistemic)

uncertainty.

Monte

Carlo

dropout

and

deep

ensembles

would

add

that

epistemic

component

on

top

of

the

conformal

bands,

and

we

identify

them

as

priority

future

work.

We

also

suggest

testing

transferability

across

diverse

ecoregions

with

differing

soil–climate

interactions.

By

validating

the

model’s

abil-

ity

to

capture

responses

to

climate

change

and

land

management,

the

field

can

shift

from

static

mapping

to

dynamic

system

monitoring.

Technically,

two

constraints

warrant

attention.

First,

this

analysis

was

confined

to

topsoil

(0–20

cm);

extending

the

framework

to

predict

vertical

profiles

is

critical

for

total

stock

assessment

,

).

A

further

constraint

concerns

the

temporal

resolution

of

the

covariates.

Annual

aggregation

was

chosen

to

match

the

multi-year

timescale

of

SOC

response

and

to

keep

sequence

length

tractable,

but

it

smooths

out

intra-annual

signals

such

as

vegetation

phenology

and

seasonally-timed

climate

extremes.

Future

work

should

Geoderma

472

(2026)

117933

15

V.

Fourel

et

al.

Table

A.5

Comparison

of

soil

organic

carbon

mapping

performance

across

different

studies

in

Bavaria.

RMSE

and

MAE

are

in

g kg

−

1

.

All

five

prior

studies

are

cropland-

only,

a

scope

imposed

by

bare-soil

reflectance

compositing,

which

requires

periodically

bare

soil.

This

study

spans

all

land-use

classes;

on

a

matched

cropland

subset

under

the

same

blocked

cross-validation,

tree

baselines

reproduce

the

prior

performance

(

𝑅

2

≈ 0

.

66

),

the

basis

for

the

land-use

stratification

discussed

in

Section

4.2

∗

Prior

studies

report

metrics

on

cropland-only

datasets

of

475–1723

samples,

mostly

under

random

hold-out

or

internal

𝑘

-fold

cross-validation;

two

and

)

use

a

spatial

or

geographic

split.

Their

𝑅

2

values

are

not

directly

comparable

to

the

all-land-use,

10-fold

spatially-blocked

cross-validation

used

here,

which

evaluates

out-of-region

generalization

on

a

far

larger

sample.

‡

Our

XGBoost

on

the

matched

cropland

subset

under

the

same

blocked

cross-validation;

the

recommended

compact

model’s

fold-mean

𝑅

2

is

0.375

on

the

full

domain,

and

the

single

highest-scoring

configuration

overall

(a

≈

45.1M

pure

Transformer)

reached

0.401.

Paper

Samples

𝑹

𝟐

RPIQ

RMSE

MAE

Spatiotemporal

Monitoring

of

Cropland

Soil

Organic

Carbon

Changes

From

Space

(

,

1723

(LfL/LUCAS)

0.61

–

5.58

–

Estimation

of

Soil

Organic

Carbon

Contents

in

Croplands

of

Bavaria

from

SCMaP

Soil

Reflectance

Composites

)

1523

(LfL,

LfU,

LUCAS)

0.67

–

12.4

–

Transferability

of

Covariates

to

Predict

Soil

Organic

Carbon

in

Cropland

Soils

,

475

(LUCAS,

LGRB,

LfU)

0.68

–

14.2

7.4

Soil

organic

carbon

estimation

using

spaceborne

hyperspectral

composites

on

a

large

scale

(

,

828

(LfU,

LfL,

LUCAS)

0.695

1.919

17.52

–

Soil

organic

carbon

mapping

utilizing

convolutional

neural

networks

and

Earth

observation

data

)

1723

(LfU,

LfL,

LUCAS)

0.67

0.92

11.60

–

This

study

-

XGBoost

model

9,385

(only

cropland)

0.66

‡

2.17

3.69

2.45

test

whether

monthly

or

seasonal

aggregation

improves

performance,

especially

in

cropland-dominated

regions,

potentially

via

a

hierarchical

temporal

encoding

that

combines

within-year

and

multi-year

structure.

Ultimately,

scaling

this

framework

to

larger

areas

(

,

)

offers

a

robust

pathway

for

climate

mitigation.

By

quantifying

how

temporal

environmental

factors

drive

SOC,

gated

CNN-Transformer

provide

the

essential

evidence

base

for

sustainable

land

management.

5.

Conclusion

This

study

evaluated

a

family

of

architectures

for

regional

SOC

mapping

under

strict

spatial

cross-validation,

using

16,514

soil

samples

across

Bavaria

(2007–2023).

Rather

than

establishing

the

superiority

of

a

single

network,

the

analysis

isolates

which

design

choices

transfer

to

spatially

held-out

regions.

Three

findings

stand

out.

First,

scale

provides

no

practical

advantage

at

this

sample

size:

every

attention-based

model

clusters

within

one

fold

standard

deviation

(0.375–0.401),

so

the

compact

gated

CNN-

Transformer

(

≈

87k

parameters,

𝑅

2

= 0

.

375 ± 0

.

100

)

trails

the

≈

45.1M

pure

Transformer

(0.401)

by

only

a

marginal

𝛥𝑅

2

= 0

.

026

that

its

parameter

cost

cannot

justify.

Second,

architectural

elaboration

is

not

decisive:

neither

the

convolutional

front-end

nor

the

gated

residual

network

separates

the

attention

models

beyond

fold-to-fold

noise,

and

the

pure

Transformers

without

a

CNN

encoder

are

in

fact

marginally

ahead,

while

strong

tree

baselines

(RF

0.342,

XGBoost

0.317)

trail

only

modestly.

We

therefore

recommend

the

most

parameter-efficient

model

rather

than

the

largest

or

the

most

elaborate,

which

lowers

the

computational

barrier

to

operational

adoption

without

sacrificing

mea-

surable

accuracy.

Third,

predictive

skill

is

land-use

stratified:

on

the

full

multi-land-use

domain

the

attention

family

out-generalizes

strong

tree

ensembles

under

all

three

spatial-CV

geometries

(by

0.05–0.07

in

fold-

mean

𝑅

2

),

whereas

on

cropland

alone

the

ordering

inverts

decisively

(trees

≈ 0

.

66

versus

attention

≈ 0

.

21

),

reproducing

the

cropland-

only

Bavarian

literature

and

implying

a

land-use-stratified

map,

tree

ensembles

on

arable

land

and

attention

models

on

the

high-variance

organic

remainder,

rather

than

a

single

model

(Section

4.2

).

We

deliberately

report

a

modest,

honest

ceiling:

a

fold-mean

𝑅

2

of

about

0.40

is,

on

current

evidence,

near

the

limit

of

out-of-region

predictability

for

250

m

regional

SOC

mapping

at

this

sample

size,

and

it

should

be

read

as

a

realistic

benchmark

rather

than

a

shortcoming

of

any

one

model.

The

recommended

model

nonetheless

produces

a

spatially

coherent

wall-to-wall

2023

SOC

map

of

Bavaria

13

).

The

broader

contribution

is

methodological:

under

spatially-rigorous

validation,

parameter

efficiency

and

the

right

inductive

bias,

a

compact

CNN-Transformer

rather

than

a

large

model

yields

generalization

esti-

mates

that

are

honest

about

out-of-region

performance,

a

prerequisite

for

trustworthy

operational

soil

mapping

and

for

the

carbon-accounting

applications

that

depend

on

it.

CRediT

authorship

contribution

statement

Valerian

Fourel:

Writing

–

review

&

editing,

Writing

–

original

draft,

Methodology,

Investigation,

Formal

analysis,

Data

curation,

Con-

ceptualization.

Martin

Wiesmeier:

Resources,

Project

administration,

Investigation,

Data

curation.

Nafiseh

Kakhani:

Validation,

Methodol-

ogy,

Investigation,

Formal

analysis,

Data

curation,

Conceptualization.

Thomas

Scholten:

Validation,

Supervision,

Methodology,

Investiga-

tion,

Formal

analysis.

Declaration

of

competing

interest

The

authors

declare

that

they

have

no

known

competing

finan-

cial

interests

or

personal

relationships

that

could

have

appeared

to

influence

the

work

reported

in

this

paper.

Acknowledgements

We

gratefully

acknowledge

the

Bavarian

Environment

Agency

(LfU)

and

the

Bavarian

State

Research

Center

for

Agriculture

(LfL)

for

pro-

viding

the

extensive

soil

databases

that

form

the

foundation

of

this

study;

without

their

long-term

commitment

to

systematic

soil

moni-

toring

across

Bavaria,

this

research

would

not

have

been

possible.

We

Geoderma

472

(2026)

117933

16

V.

Fourel

et

al.

Fig.

A.16.

Per-model

2023

SOC

maps

of

Bavaria

on

the

shared

0–150

g

kg

−

1

colour

scale

(PowerNorm

𝛾

= 0

.

7

),

part

1

of

2

(attention

baselines):

(a)

un-gated

CNN-Transformer,

(b)

pure

(no-CNN)

Transformer

(

≈

45.1M),

(c)

lightweight

Transformer

(

≈

313k),

and

(d)

CNN–LSTM.

Built-up

areas

(black)

and

water

(deep

blue)

are

masked.

The

recommended

gated

CNN-Transformer

is

the

flagship

map

and

is

not

repeated

here;

the

tree

ensembles

and

the

3D-CNN

are

shown

in

A.17

All

four

models

here

produce

broadly

comparable,

spatially

coherent

patterns

separating

the

carbon-rich

alpine

south

from

the

carbon-depleted

northern

lowlands.

further

thank

Eurostat

for

the

LUCAS

dataset.

We

acknowledge

the

Max

Planck

Institute

for

Intelligent

Systems

in

Tübingen

for

compu-

tational

resources,

the

Department

of

Soil

Science

and

Geomorphology

at

the

University

of

Tübingen

for

their

support,

and

the

University

of

Hamburg’s

Institute

for

Statistics

with

Applications

in

Business

Admin-

istration

for

their

collaboration.

Financial

support

from

the

German

Research

Foundation

(DFG)

is

gratefully

acknowledged

for

the

projects

’MLTRANS-Transferability

of

Machine

Learning

Models

in

Digital

Soil

Mapping’

(project

number

448762063),

’Mathematical

methods

and

algorithms

for

learning

effective

embeddings

of

semi-structured

infor-

mation

for

anomaly

detection

problems’

(project

number

448795504)

and

Germany’s

Excellence

Strategy

Cluster

EXC

2064

Machine

Learn-

ing:

New

Perspectives

for

Science

(project

number

390727645).

Open

Access

funding

was

enabled

and

organized

by

Projekt

DEAL.

The

au-

thors

gratefully

acknowledge

the

Jülich

Supercomputing

Centre

(JSC)

at

Forschungszentrum

Jülich

for

computing

time

on

the

JUPITER

sys-

tem,

and

the

Karlsruhe

Institute

of

Technology

(KIT)

for

access

to

the

HoreKa

supercomputer.

Appendix

A.

Comparison

of

mapping

performance

See

A.18

https://doi.org/10.1016/j.geoderma.2026.117933

Appendix

B.

Supplementary

data

Supplementary

material

this

article

can

be

found

online

at

.

Data

availability

The

LfL

and

LfU

soil

databases

are

not

publicly

available

due

to

institutional

restrictions

but

may

be

obtained

upon

reasonable

request

from

the

Bavarian

State

Research

Center

for

Agriculture

(LfL)

and

the

Bavarian

Environment

Agency

(LfU).

The

LUCAS-derived

subset

used

in

this

study

is

based

on

the

publicly

available

Eurostat

Land

Use/Cover

Area

Frame

Survey

(LUCAS)

topsoil

data

and

can

be

shared.

All

preprocessing,

training,

and

mapping

scripts

are

openly

avail-

able

at

https://github.com/ValerianFourel/SOCmapping

.

The

complete

covariate–SOC

dataset

used

for

training

and

evaluation

is

released

on

Hugging

Face

at

https://huggingface.co/datasets/ValerianFourel/

sgt-bavaria-soc-2002-2023-large

https://huggingface.co/datasets/

and

the

trained

model

checkpoints

together

with

the

full

parameter-sweep

and

ablation

results

and

the

predicted

SOC

maps

are

available

at

ValerianFourel/SOCrebuttal

.

Geoderma

472

(2026)

117933

17

V.

Fourel

et

al.

Fig.

A.17.

Per-model

2023

SOC

maps

of

Bavaria

on

the

shared

0–150

g

kg

−

1

colour

scale

(PowerNorm

𝛾

= 0

.

7

),

part

2

of

2

(tree

ensembles

and

3D-CNN):

(e)

Random

Forest,

(f)

XGBoost,

and

(g)

3D-CNN.

Built-up

areas

(black)

and

water

(deep

blue)

are

masked.

The

tree

ensembles

reproduce

the

same

broad

spatial

gradient

as

the

attention

models

in

A.16

;

only

the

3D-CNN

(g)

collapses

towards

uniformly

low

SOC,

consistent

with

its

negative

spatial-CV

𝑅

2

.

Geoderma

472

(2026)

117933

18

V.

Fourel

et

al.

Fig.

A.18.

Out-of-fold

residuals

(predicted

−

actual)

of

the

large

≈

45.1M

pure

(no-CNN)

Transformer,

pooled

across

the

ten

longitude-blocked

hold-out

folds

(colour

scale

±

18

g

kg

−

1

).

Its

residual

structure

is

visually

comparable

to

that

of

the

compact

recommended

model

8

).

Geoderma

472

(2026)

117933

19

V.

Fourel

et

al.

References

Azamat,

S.,

Ilgiz,

A.,

Ruslan,

S.,

Mirsayapov,

R.,

Ilyusya,

G.,

Tuktarova,

I.,

Belan,

L.,

2024.

Assessing

and

mapping

of

soil

organic

carbon

at

multiple

depths

in

the

semi-arid

trans-ural

steppe

zone.

Geoderma

Reg.

38,

e00855.

1016/j.geodrs.2024.e00855

,

URL:

https://www.sciencedirect.com/science/article/

pii/S2352009424001020

.

Bayerisches

Landesamt

für

Umwelt,

2023.

Bodendauerbeobachtung

bayern:

soil

moni-

toring

network

of

the

bavarian

environment

agency

(lfu).

bavarian

Environment

Agency

(LfU);

long-term

soil

monitoring

data,

URL:

https://www.lfu.bayern.de/

boden/bodendauerbeobachtung/index.htm

.

Bellon-Maurel,

V.,

Fernandez-Ahumada,

E.,

Palagos,

B.,

Roger,

J.-M.,

McBratney,

A.,

2010.

Critical

review

of

chemometric

indicators

commonly

used

for

assessing

the

quality

of

the

prediction

of

soil

attributes

by

NIR

spectroscopy.

TRAC

Trends

Anal.

Chem.

29,

1073–1081.

http://dx.doi.org/10.1016/j.trac.2010.05.006

.

Bojko,

O.,

Kabala,

C.,

2017.

Organic

carbon

pools

in

mountain

soils

—

sources

of

variability

and

predicted

changes

in

relation

to

climate

and

land

use

changes.

Catena

149,

209–220.

http://dx.doi.org/10.1016/j.catena.2016.09.022

URL:

//www.sciencedirect.com/science/article/pii/S0341816216303940

http://dx.doi.org/10.1023/

Breiman,

L.,

2001.

Random

forests.

Mach.

Learn.

45,

5–32.

A:1010933404324

http://dx.doi.org/10.3390/rs15040876

Broeg,

T.,

Blaschek,

M.,

Seitz,

S.,

Taghizadeh-Mehrjardi,

R.,

Zepp,

S.,

Scholten,

T.,

2023.

Transferability

of

covariates

to

predict

soil

organic

carbon

in

cropland

soils.

Remote.

Sens.

15,

,

URL:

https://www.mdpi.

com/2072-4292/15/4/876

http://dx.doi.org/10.1111/gcb.17608

Broeg,

T.,

Don,

A.,

Wiesmeier,

M.,

Scholten,

T.,

Erasmi,

S.,

2024.

Spatiotemporal

monitoring

of

cropland

soil

organic

carbon

changes

from

space.

Global

Change

Biol.

30,

17608.

.

Candido,

C.,

Blanco,

A.,

Medina,

J.,

Gubatanga,

E.,

Santos,

A.,

Ana,

R.S.,

Reyes,

R.,

2021.

Improving

the

consistency

of

multi-temporal

land

cover

mapping

of

la-

guna

lake

watershed

using

light

gradient

boosting

machine

(lightgbm)

approach,

change

detection

analysis,

and

markov

chain.

Remote.

Sens.

Appl.:

Soc.

Environ.

23,

100565.

http://dx.doi.org/10.1016/j.rsase.2021.100565

URL:

sciencedirect.com/science/article/pii/S2352938521001014

.

Castaldi,

F.,

Chabrillat,

S.,

Don,

A.,

van

Wesemael,

B.,

2019.

Soil

organic

carbon

mapping

using

lucas

topsoil

database

and

sentinel-2

data:

An

approach

to

reduce

soil

moisture

and

crop

residue

effects.

Remote.

Sens.

11,

http://dx.doi.org/10.3390/

rs11182121

,

URL:

https://www.mdpi.com/2072-4292/11/18/2121

.

Chen,

S.,

Arrouays,

D.,

Leatitia

Mulder,

V.,

Poggio,

L.,

Minasny,

B.,

Roudier,

P.,

Libohova,

Z.,

Lagacherie,

P.,

Shi,

Z.,

Hannam,

J.,

Meersmans,

J.,

de

Forges,

A.C.R.,

Walter,

C.,

2022.

Digital

mapping

of

globalsoilmap

soil

properties

at

a

broad

scale:

A

review.

Geoderma

409,

115567.

http://dx.doi.org/10.1016/j.

geoderma.2021.115567

,

URL:

S0016706121006479

http://dx.doi.org/10.1145/2939672.

Chen,

T.,

Guestrin,

C.,

2016.

Xgboost:

A

scalable

tree

boosting

system.

In:

Proceedings

of

the

22nd

ACM

SIGKDD

International

Conference

on

Knowledge

Discovery

and

Data

Mining.

KDD

’16,

ACM,

pp.

785–794.

2939785

.

Chen,

Q.,

Wang,

Y.,

Zhu,

X.,

2024.

Soil

organic

carbon

estimation

using

remote

sensing

data-driven

machine

learning.

PeerJ

12,

e17836.

http://dx.doi.org/10.7717/peerj.

17836

.

Coleman,

K.,

Müller,

J.,

Kuenzer,

C.,

2024.

Remote

sensing

of

forests

in

bavaria:

A

review.

Remote.

Sens.

16,

http://dx.doi.org/10.3390/rs16101805

URL:

//www.mdpi.com/2072-4292/16/10/1805

Davidson,

E.A.,

Janssens,

I.A.,

2006.

Temperature

sensitivity

of

soil

carbon

decomposi-

tion

and

feedbacks

to

climate

change.

Nature

440,

165–173.

doi.org/10.1016/j.rse.2018.04.047

1038/nature04514

.

Demattê,

J.A.M.,

Fongaro,

C.T.,

Rizzo,

R.,

Safanelli,

J.L.,

2018.

Geospatial

soil

sensing

system

(GEOS3):

A

powerful

data

mining

procedure

to

retrieve

soil

spectral

reflectance

from

satellite

images.

Remote

Sens.

Environ.

212,

161–175.

http://dx.

//dx.doi.org/10.3390/rs9121245

Diek,

S.,

Fornallaz,

F.,

Schaepman,

M.E.,

de

Jong,

R.,

2017.

Barest

pixel

composite

for

agricultural

areas

using

Landsat

time

series.

Remote.

Sens.

9,

1245.

http:

.

Dong,

Z.,

Yao,

L.,

Bao,

Y.,

Zhang,

J.,

Yao,

F.,

Bai,

L.,

Zheng,

P.,

2024.

Prediction

of

soil

organic

carbon

content

in

complex

vegetation

areas

based

on

cnn-lstm

model.

Land

13,

http://dx.doi.org/10.3390/land13070915

https://www.mdpi.com/2073-

URL:

445X/13/7/915

.

Farr,

T.G.,

Rosen,

P.A.,

Caro,

E.,

Crippen,

R.,

Duren,

R.,

Hensley,

S.,

Kobrick,

M.,

Paller,

M.,

Rodriguez,

E.,

Roth,

L.,

Seal,

D.,

Shaffer,

S.,

Shimada,

J.,

Umland,

J.,

Werner,

M.,

Oskin,

M.,

Burbank,

D.,

Alsdorf,

D.,

2007.

The

shuttle

radar

topography

mission.

Rev.

Geophys.

45,

RG2004.

http://dx.doi.org/10.1029/2005RG000183

http://dx.doi.org/10.3969/j.issn.1002-0829.2014.02.009

Feng,

C.,

Wang,

H.,

Lu,

N.,

Chen,

T.,

He,

H.,

Lu,

Y.,

Tu,

X.M.,

2014.

Log-transformation

and

its

implications

for

data

analysis.

Shanghai

Arch.

Psychiatry

26,

105–109.

http://dx.doi.org/10.1016/

Finke,

P.,

Opolot,

E.,

Balesdent,

J.,

Berhe,

A.A.,

Boeckx,

P.,

Cornu,

S.,

Harden,

J.,

Hatté,

C.,

Williams,

E.,

Doetterl,

S.,

2019.

Can

soc

modelling

be

improved

by

accounting

for

pedogenesis?

Geoderma

338,

513–524.

j.geoderma.2018.10.018

,

URL:

S0016706118307432

http://dx.doi.org/10.1016/j.rse.2017.06.031

Gorelick,

N.,

Hancher,

M.,

Dixon,

M.,

Ilyushchenko,

S.,

Thau,

D.,

Moore,

R.,

2017.

Google

Earth

Engine:

Planetary-scale

geospatial

analysis

for

everyone.

Remote

Sens.

Environ.

202,

18–27.

.

Grunwald,

S.,

2021.

Grand

challenges

in

pedometrics-ai

research.

Front.

Soil

Sci.

Volume

1

-

2021,

http://dx.doi.org/10.3389/fsoil.2021.714323

,

URL:

frontiersin.org/journals/soil-science/articles/10.3389/fsoil.2021.714323

http://dx.doi.org/10.1111/ejss.13300

Han,

S.Y.,

Filippi,

P.,

Singh,

K.,

Whelan,

B.M.,

Bishop,

T.F.A.,

2022.

Assessment

of

global,

national

and

regional-level

digital

soil

mapping

products

at

different

spatial

supports.

Eur.

J.

Soil

Sci.

73,

e13300.

,

URL:

https://bsssjournals.onlinelibrary.wiley.com/doi/abs/10.1111/ejss.13300

http://dx.doi.org/10.1023/A:

Hassink,

J.,

1997.

The

capacity

of

soils

to

preserve

organic

C

and

N

by

their

association

with

clay

and

silt

particles.

Plant

Soil

191,

77–87.

1004213929699

org/10.1371/journal.pone.0169748

Hengl,

T.,

de

Jesus,

J.

Mendes,

Heuvelink,

G.B.M.,

Gonzalez,

M.

Ruiperez,

Kilibarda,

M.,

Blagotić,

A.,

Shangguan,

W.,

Wright,

M.N.,

Geng,

X.,

Bauer-Marschallinger,

B.,

Gue-

vara,

M.A.,

Vargas,

R.,

MacMillan,

R.A.,

Batjes,

N.H.,

Leenaars,

J.G.B.,

Ribeiro,

E.,

Wheeler,

I.,

Mantel,

S.,

Kempen,

B.,

2017.

SoilGrids250m:

Global

gridded

soil

information

based

on

machine

learning.

PLoS

One

12,

e0169748.

http://dx.doi.

.

Hong,

Y.,

Chen,

S.,

Chen,

Y.,

Linderman,

M.,

Mouazen,

A.M.,

Liu,

Y.,

Guo,

L.,

Yu,

L.,

Liu,

Y.,

Cheng,

H.,

Liu,

Y.,

2020.

Comparing

laboratory

and

airborne

hyperspectral

data

for

the

estimation

and

mapping

of

topsoil

organic

carbon:

Feature

selection

coupled

with

random

forest.

Soil

Tillage

Res.

199,

104589.

1016/j.still.2020.104589

URL:

http://dx.doi.org/10.5194/soil-

S0167198719307536

.

Hounkpatin,

K.O.L.,

Stendahl,

J.,

Lundblad,

M.,

Karltun,

E.,

2021.

Predicting

the

spatial

distribution

of

soil

organic

carbon

stock

in

swedish

forests

using

a

group

of

covariates

and

site-specific

data.

Soil

7,

377–398.

7-377-2021

,

URL:

https://soil.copernicus.org/articles/7/377/2021/

.

Kakhani,

N.,

Rangzan,

M.,

Jamali,

A.,

Attarchi,

S.,

Alavipanah,

S.

Kazem,

Mommert,

M.,

Tziolas,

N.,

Scholten,

T.,

2024.

Ssl-soilnet:

A

hybrid

transformer-based

frame-

work

with

self-supervised

learning

for

large-scale

soil

organic

carbon

prediction.

IEEE

Trans.

Geosci.

Remote

Sens.

62,

1–15.

http://dx.doi.org/10.1109/TGRS.2024.

3446042

https://arxiv.org/abs/2308.03586

URL:

,

arXiv:2308.03586

http://dx.doi.org/10.1111/ejss.70071

Kakhani,

N.,

Taghizadeh-Mehrjardi,

R.,

Omarzadeh,

D.,

Ryo,

M.,

Heiden,

U.,

Scholten,

T.,

2025.

Towards

explainable

ai:

Interpreting

soil

organic

carbon

prediction

models

using

a

learning-based

explanation

method.

Eur.

J.

Soil

Sci.

76,

e70071.

https://bsssjournals.onlinelibrary.wiley.com/doi/abs/10.1111/ejss.70071

e70071

EJSS-499-24.R1,

URL:

Kingma,

D.P.,

Ba,

J.,

2017.

Adam:

A

method

for

stochastic

optimization.

URL:

//arxiv.org/abs/1412.6980

,

arXiv:1412.6980

.

Le,

T.-D.,

2024.

Transformer

meets

gated

residual

networks

to

enhance

photoplethys-

mogram

artifact

detection

informed

by

mutual

information

neural

estimation.

http://dx.doi.org/10.48550/arXiv.2405.16177

Lim,

B.,

Arik,

S.O.,

Loeff,

N.,

Pfister,

T.,

2020.

Temporal

fusion

transformers

for

interpretable

multi-horizon

time

series

forecasting.

URL:

https://arxiv.org/abs/

1912.09363

arXiv:1912.09363

.

Lima,

A.A.J.,

Lopes,

J.C.,

Lopes,

R.P.,

de

Figueiredo,

T.,

Vidal-Vázquez,

E.,

Hernán-

dez,

Z.,

2025.

Soil

organic

carbon

assessment

using

remote-sensing

data

and

machine

learning:

A

systematic

literature

review.

Remote.

Sens.

17,

http://dx.doi.

org/10.3390/rs17050882

https://www.mdpi.com/2072-4292/17/5/882

URL:

http://dx.doi.org/10.1111/ele.13363

Liu,

Y.,

Schwalm,

C.R.,

Samuels-Crow,

K.E.,

Ogle,

K.,

2019.

Ecological

memory

of

daily

carbon

exchange

across

the

globe

and

its

importance

in

drylands.

Ecol.

Lett.

22,

1806–1816.

,

URL:

https://onlinelibrary.wiley.

com/doi/abs/10.1111/ele.13363

http://dx.doi.org/10.2136/sssaj2018.11.0413

Ludwig,

B.,

Murugan,

R.,

Parama,

V.R.R.,

Vohland,

M.,

2019.

Accuracy

of

estimating

soil

properties

with

mid-infrared

spectroscopy:

Implications

of

different

chemo-

metric

approaches

and

software

packages

calibration

sample

size.

Soil

Sci.

Am.

J.

83,

1542–1552.

,

URL:

https://acsess.onlinelibrary.wiley.com/doi/abs/10.2136/sssaj2018.11.0413

.

Mcbratney,

A.,

Santos,

M.

Mendonça,

Minasny,

B.,

2003.

On

digital

soil

mapping.

Geoderma

117,

3–52.

http://dx.doi.org/10.1016/S0016-7061(03)00223-4

.

McNally,

S.,

Pronger,

J.,

Goodrich,

J.,

Allen,

K.,

Graham,

S.,

McNeill,

S.,

Roudier,

P.,

Norris,

T.,

Barnett,

A.,

Schipper,

L.,

Mudge,

P.,

2025.

Reconciling

historic

and

contemporary

sampling

of

soil

organic

carbon

stocks:

Does

sampling

approach

create

systematic

bias?

Geoderma

458,

http://dx.doi.org/10.1016/j.geoderma.2025.

117338

.

Muñoz-Sabater,

J.,

Dutra,

E.,

Agustí-Panareda,

A.,

Albergel,

C.,

Arduini,

G.,

Balsamo,

G.,

Boussetta,

S.,

Choulga,

M.,

Harrigan,

S.,

Hersbach,

H.,

Marténs,

B.,

Miralles,

D.G.,

Piles,

M.,

Rodríguez-Fernández,

N.J.,

Zsoter,

E.,

Buontempo,

C.,

Thépaut,

J.-N.,

2021.

ERA5-Land:

a

state-of-the-art

global

reanalysis

dataset

for

land

applications.

Earth

Syst.

Sci.

Data

13,

4349–4383.

http://dx.doi.org/10.5194/essd-13-4349-2021

http://dx.doi.org/10.5067/MODIS/MCD15A2H.061

Myneni,

R.,

Knyazikhin,

Y.,

Park,

T.,

2021.

Modis/terra+aqua

leaf

area

index/fpar

8-day

l4

global

500m

sin

grid

v061.

(Accessed

30

May

2025).

Padarian,

J.,

McBratney,

A.B.,

Minasny,

B.,

2020.

Game

theory

interpretation

of

digital

soil

mapping

convolutional

neural

networks.

Soil

6,

389–397.

5194/soil-6-389-2020

https://soil.copernicus.org/articles/6/389/2020/

URL:

Geoderma

472

(2026)

117933

20

V.

Fourel

et

al.

Ploton,

P.,

Mortier,

F.,

Réjou-Méchain,

M.,

Barbier,

N.,

Picard,

N.,

Rossi,

V.,

Dor-

mann,

C.,

Cornu,

G.,

Viennois,

G.,

Bayol,

N.,

Lyapustin,

A.,

Gourlet-Fleury,

S.,

Pélissier,

R.,

2020.

Spatial

validation

reveals

poor

predictive

performance

of

large-

scale

ecological

mapping

models.

Nat.

Commun.

11,

4540.

10.1038/s41467-020-18321-y

,

URL:

https://www.nature.com/articles/s41467-020-

18321-y

.

Poggio,

L.,

de

Sousa,

L.M.,

Batjes,

N.H.,

Heuvelink,

G.B.M.,

Kempen,

B.,

Ribeiro,

E.,

Rossiter,

D.,

2021.

SoilGrids

2.0:

producing

soil

information

for

the

globe

with

quantified

spatial

uncertainty.

Soil

7,

217–240.

http://dx.doi.org/10.5194/soil-7-

217-2021

http://dx.doi.org/10.1016/j.catena.2023.107409

Pouladi,

N.,

Gholizadeh,

A.,

Khosravi,

V.,

Borůvka,

L.,

2023.

Digital

mapping

of

soil

organic

carbon

using

remote

sensing

data:

A

systematic

review.

Catena

232,

107409.

URL:

sciencedirect.com/science/article/pii/S0341816223005003

.

Rakotonindrina,

H.,

Moritsuka,

N.,

Kawamura,

K.,

Tsujimoto,

Y.,

Nishigaki,

T.,

An-

drianary,

H.B.,

Razafimbelo,

T.,

Razakamanarivo,

H.,

Andriamananjara,

A.,

2023.

Prediction

of

the

soil

properties

of

malagasy

rice

soils

based

on

the

soil

color

and

magnetic

susceptibility.

Soil

Sci.

Plant

Nutr.

69,

24–35.

http://dx.doi.org/10.1080/

00380768.2022.2136929

http://dx.doi.org/10.3390/rs11020185

Ramezan,

C.A.,

Warner,

T.A.,

Maxwell,

A.E.,

2019.

Evaluation

of

sampling

and

cross-validation

tuning

strategies

for

regional-scale

machine

learning

classification.

Remote.

Sens.

11,

,

URL:

https://www.mdpi.

com/2072-4292/11/2/185

Rasse,

D.P.,

Rumpel,

C.,

Dignac,

M.-F.,

2005.

Is

soil

carbon

mostly

root

carbon?

Mechanisms

for

a

specific

stabilisation.

Plant

Soil

269,

341–356.

10.1007/s11104-004-0907-y

dx.doi.org/10.1111/ejss.70172

Rentschler,

T.,

Scholten,

T.,

2025.

A

note

on

spurious

correlations

and

explainable

machine

learning

in

digital

soil

mapping.

Eur.

J.

Soil

Sci.

76,

e70172.

http://

,

e70172

EJSS-263-25.R2.

URL:

https://bsssjournals.

onlinelibrary.wiley.com/doi/abs/10.1111/ejss.70172

.

Roberts,

D.R.,

Bahn,

V.,

Ciuti,

S.,

Boyce,

M.S.,

Elith,

J.,

Guillera-Arroita,

G.,

Hauen-

stein,

S.,

Lahoz-Monfort,

J.J.,

Schröder,

B.,

Thuiller,

W.,

Warton,

D.I.,

Wintle,

B.A.,

Hartig,

F.,

Dormann,

C.F.,

2017.

Cross-validation

strategies

for

data

with

tem-

poral,

spatial,

hierarchical,

or

phylogenetic

structure.

Ecography

40,

913–929.

http://dx.doi.org/10.1111/ecog.02881

,

URL:

https://onlinelibrary.wiley.com/doi/

10.1111/ecog.02881

http://dx.doi.org/10.1002/rse2.74

Robinson,

N.P.,

Allred,

B.W.,

Smith,

W.K.,

Jones,

M.O.,

Moreno,

A.,

Erickson,

T.A.,

Naugle,

D.E.,

Running,

S.W.,

2018.

Terrestrial

primary

production

for

the

con-

terminous

united

states

derived

from

landsat

30

m

and

modis

250

m.

Remote.

Sens.

Ecol.

Conserv.

4,

264–280.

URL:

//zslpublications.onlinelibrary.wiley.com/doi/abs/10.1002/rse2.74

.

Rogge,

D.,

Bauer,

A.,

Zeidler,

J.,

Müller,

A.,

Esch,

T.,

Heiden,

U.,

2018.

Building

an

exposed

soil

composite

processor

(scmap)

for

mapping

spatial

and

temporal

characteristics

of

soils

with

landsat

imagery

(1984–2014).

Remote

Sens.

Environ.

205,

1–17.

http://dx.doi.org/10.1016/j.rse.2017.11.004

.

Rossel,

R.A.

Viscarra,

Minasny,

B.,

Roudier,

P.,

McBratney,

A.B.,

2006.

Colour

space

models

for

soil

science.

Geoderma

133,

320–337.

http://dx.doi.org/10.1016/j.

geoderma.2005.07.017

http://dx.doi.org/10.5067/MODIS/MOD16A2.

Running,

S.,

Mu,

Q.,

Zhao,

M.,

2017.

Mod16a2

modis/terra

net

evapotranspiration

8-day

l4

global

500m

sin

grid

v006.

006

,

(Accessed

30

May

2025).

Sakhaee,

A.,

Gebauer,

A.,

Ließ,

M.,

Don,

A.,

2022.

Spatial

prediction

of

organic

carbon

in

german

agricultural

topsoil

using

machine

learning

algorithms.

Soil

8,

587–604.

http://dx.doi.org/10.5194/soil-8-587-2022

http://dx.doi.org/10.1016/j.geoderma.2021.115402

URL:

https://soil.copernicus.

org/articles/8/587/2022/

.

Sothe,

C.,

Gonsamo,

A.,

Arabian,

J.,

Snider,

J.,

2022.

Large

scale

mapping

of

soil

organic

carbon

concentration

with

3d

machine

learning

and

satellite

observations.

Geoderma

405,

.

Stenberg,

B.,

Rossel,

R.A.

Viscarra,

Mouazen,

A.M.,

Wetterlind,

J.,

2010.

Visible

and

near

infrared

spectroscopy

in

soil

science.

Adv.

Agron.

107,

163–215.

http://dx.

doi.org/10.1016/S0065-2113(10)07005-7

.

Taghizadeh-Mehrjardi,

R.,

Khademi,

H.,

Khayamim,

F.,

Zeraatpisheh,

M.,

Heung,

B.,

Scholten,

T.,

2022.

A

comparison

of

model

averaging

techniques

to

predict

the

spatial

distribution

of

soil

properties.

Remote.

Sens.

14,

http://dx.doi.org/10.3390/

rs14030472

,

URL:

https://www.mdpi.com/2072-4292/14/3/472

.

Thom,

D.,

Rammer,

W.,

Garstenauer,

R.,

Seidl,

R.,

2018.

Legacies

of

past

land

use

have

a

stronger

effect

on

forest

carbon

exchange

than

future

climate

change

in

a

temperate

forest

landscape.

Biogeosciences

15,

5699–5713.

5194/bg-15-5699-2018

https://bg.copernicus.org/articles/15/5699/2018/

URL:

.

Tian,

X.,

de

Bruin,

S.,

Simoes,

R.,

Isik,

M.S.,

Minarik,

R.,

Ho,

Y.-F.,

Şahin,

M.,

Herold,

M.,

Consoli,

D.,

Hengl,

T.,

2025.

Spatiotemporal

prediction

of

soil

organic

carbon

density

in

europe

(2000–2022)

using

earth

observation

and

machine

learning.

PeerJ

13,

e19605.

http://dx.doi.org/10.7717/peerj.19605

URL:

//doi.org/10.7717/peerj.19605

.

Tóth,

G.,

Antofie,

T.,

Jones,

A.,

Apostol,

B.,

2016.

The

lucas

2012

topsoil

survey

and

derived

cropland

and

grassland

soil

properties

of

bulgaria

and

romania.

Environ.

Eng.

Manag.

J.

15,

2651–2662.

http://dx.doi.org/10.30638/eemj.2016.291

.

Tóth,

G.,

Jones,

A.,

Montanarella,

L.,

2013.

The

lucas

topsoil

database

and

derived

information

on

the

regional

variability

of

cropland

topsoil

properties

in

the

european

union.

Environ.

Monit.

Assess.

185,

7409–7425.

http://dx.doi.org/10.3390/w15122278

1007/s10661-013-3109-3

.

Tziachris,

P.,

Nikou,

M.,

Aschonitis,

V.,

Kallioras,

A.,

Sachsamanoglou,

K.,

Fi-

delibus,

M.D.,

Tziritis,

E.,

2023.

Spatial

or

random

cross-validation?

the

effect

of

resampling

methods

in

predicting

groundwater

salinity

with

machine

learning

in

mediterranean

region.

Water

15,

https://www.mdpi.com/2073-4441/15/12/2278

URL:

http://dx.doi.org/10.1016/

Tziolas,

N.,

Tsakiridis,

N.,

Heiden,

U.,

van

Wesemael,

B.,

2024.

Soil

organic

carbon

mapping

utilizing

convolutional

neural

networks

and

earth

observation

data,

a

case

study

in

bavaria

state

germany.

Geoderma

444,

116867.

j.geoderma.2024.116867

URL:

S001670612400096X

http://dx.doi.org/10.1016/j.ecolmodel.2021.109692

Wadoux,

A.M.J.-C.,

Heuvelink,

G.B.M.,

de

Bruin,

S.,

Brus,

D.J.,

2021.

Spatial

cross-

validation

is

not

the

right

way

to

evaluate

map

accuracy.

Ecol.

Model.

457,

109692.

http://dx.doi.org/10.5067/MODIS/MOD11A2.061

Wan,

Z.,

Hook,

S.,

Hulley,

G.,

2021.

Modis/terra

land

surface

temperature/emissivity

8-

day

l3

global

1km

sin

grid

v061.

(Accessed

30

May

2025).

Wiesmeier,

M.,

Burmeister,

J.,

Garcia-Franco,

N.,

Sümmerer,

M.,

2025.

Long-

term

changes

(1986–2016)

in

soil

organic

carbon

and

nitrogen

in

agricul-

tural

soils

of

bavaria.

Agric.

Ecosyst.

Environ.

394,

109874.

10.1016/j.agee.2025.109874

,

URL:

https://www.sciencedirect.com/science/article/

pii/S0167880925004062

.

Wiesmeier,

M.,

von

Lützow,

M.,

Spörlein,

P.,

Geuß,

U.,

Hangen,

E.,

Reischl,

A.,

Schilling,

B.,

Kögel-Knabner,

I.,

2015.

Land

use

effects

on

organic

carbon

storage

in

soils

of

bavaria:

The

importance

of

soil

types.

Soil

Tillage

Res.

146,

296–302.

http://dx.doi.org/10.1016/j.still.2014.10.003

,

URL:

sciencedirect.com/science/article/pii/S0167198714002049

.

Wiesmeier,

M.,

Spörlein,

P.,

Geuß,

U.,

Hangen,

E.,

Haug,

S.,

Reischl,

A.,

Schilling,

B.,

von

Lützow,

M.,

Kögel-Knabner,

I.,

2012.

Soil

organic

carbon

stocks

in

southeast

germany

(bavaria)

as

affected

by

land

use,

soil

type

and

sampling

depth.

Global

Change

Biol.

18,

2233–2245.

http://dx.doi.org/10.1111/j.1365-2486.2012.02699.x

https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1365-2486.2012.02699.x

URL:

http://dx.doi.org/10.1038/

Yang,

C.,

Shen,

F.,

Li,

X.,

Cui,

W.,

Zhang,

L.,

Yang,

L.,

Zhou,

C.,

2025.

Spatio-temporal

mapping

reveals

changes

in

soil

organic

carbon

stocks

across

the

contiguous

United

States

since

1955.

Commun.

Earth

Environ.

6,

615.

s43247-025-02605-6

Zanaga,

D.,

Van

De

Kerchove,

R.,

De

Keersmaecker,

W.,

Souverijns,

N.,

Brockmann,

C.,

Quast,

R.,

Wevers,

J.,

Grosu,

A.,

Paccini,

A.,

Vergnaud,

S.,

Cartus,

O.,

Santoro,

M.,

Fritz,

S.,

Georgieva,

I.,

Lesiv,

M.,

Carter,

S.,

Herold,

M.,

Li,

L.,

Tsendbazar,

N.-E.,

Ramoino,

F.,

Arino,

O.,

2021.

Esa

worldcover

10

m

2020

v100.

http://dx.doi.org/10.1016/j.isprsjprs.2023.06.003

10.5281/zenodo.5571936

.

Zepp,

S.,

Heiden,

U.,

Bachmann,

M.,

Möller,

M.,

Wiesmeier,

M.,

van

Wesemael,

B.,

2023.

Optimized

bare

soil

compositing

for

soil

organic

carbon

prediction

of

topsoil

croplands

in

bavaria

using

landsat.

ISPRS

J.

Photogramm.

Remote

Sens.

202,

287–302.

www.sciencedirect.com/science/article/pii/S0924271623001685

URL:

https://

.

Zepp,

S.,

Heiden,

U.,

Bachmann,

M.,

Wiesmeier,

M.,

Steininger,

M.,

van

Wesemael,

B.,

2021.

Estimation

of

soil

organic

carbon

contents

in

croplands

of

bavaria

from

scmap

soil

reflectance

composites.

Remote.

Sens.

13,

http://dx.doi.org/10.3390/

rs13163141

,

URL:

https://www.mdpi.com/2072-4292/13/16/3141

.

Zhang,

L.,

Cai,

Y.,

Huang,

H.,

Li,

A.,

Yang,

L.,

Zhou,

C.,

2022.

A

cnn-lstm

model

for

soil

organic

carbon

content

prediction

with

long

time

series

of

modis-based

phenological

variables.

Remote.

Sens.

14,

http://dx.doi.org/10.3390/rs14184441

https://www.mdpi.com/2072-4292/14/18/4441

URL:

Zhao,

X.,

Xiong,

Z.,

Karlshöfer,

P.,

Tziolas,

N.,

Wiesmeier,

M.,

Heiden,

U.,

Zhu,

X.X.,

2025.

Soil

organic

carbon

estimation

using

spaceborne

hyperspectral

composites

on

a

large

scale.

Int.

J.

Appl.

Earth

Obs.

Geoinf.

140,

104504.

1016/j.jag.2025.104504

URL: