Diagnosing Linearity Along the Carbon Cascade in Terrestrial Biosphere Models and Observations

Huanyuan Zhang-Zheng; Vivek K. Arora; Peter Anthoni; Thomas A.M. Pugh; Atul K. Jain; Wenping Yuan; Yadvinder Malhi; Julia Nabel; Daniel S. Goll; Julia Pongratz; Benjamin Poulter; Anthony P. Walker; Sönke Zaehle; Jürgen Knauer; Etsushi Kato; Ruijie Ding; Minxue Tang; Stephen Sitch; Michael O'Sullivan; César Terrer; Hanqin Tian; Naiqing Pan; Pierre Friedlingstein; Akihiko Ito; Qing Sun; Jeanne Decayeux; Benjamin D. Stocker

doi:10.1111/gcb.70982

Diagnosing Linearity Along the Carbon Cascade in Terrestrial Biosphere Models and Observations

Huanyuan Zhang-Zheng
, Vivek K. Arora
, Peter Anthoni
, Thomas A.M. Pugh
, Atul K. Jain
, Wenping Yuan
, Yadvinder Malhi
, Julia Nabel
, Daniel S. Goll
, Julia Pongratz
, Benjamin Poulter
, Anthony P. Walker
, Sönke Zaehle
, Jürgen Knauer
, Etsushi Kato
, Ruijie Ding
, Minxue Tang
, Stephen Sitch
, Michael O'Sullivan
, César Terrer

Hanqin Tian, Naiqing Pan, Pierre Friedlingstein, Akihiko Ito, Qing Sun, Jeanne Decayeux, Benjamin D. Stocker

École Polytechnique

University of Oxford
Umeå University
Meteorological Research Branch
Institute of Meteorology and Climate Research
Lund University
University of Birmingham
University of Illinois at Urbana-Champaign
Tsinghua University
Max Planck Institute for Biogeochemistry
Max Planck Institute for Meteorology
Université Paris-Saclay
Universität München
Spark Climate Solutions
University of Maryland, College Park
Oak Ridge National Laboratory
University of Technology Sydney
Hawkesbury Institute for the Environment
Institute of Applied Energy (IAE)
Imperial College London
University of Exeter
Massachusetts Institute of Technology
Boston College
Graduate School of Agricultural and Life Sciences The University of Tokyo
University of Bern, Institute of Applied Physics
University of Bern
Université Paul Sabatier

Research output: Contribution to journal › Article › peer-review

Abstract

Elevated carbon dioxide (eCO₂) acts as a fertiliser for photosynthesis, driving an increase in gross primary production (GPP). However, it is unclear how effectively increased GPP propagates along the ‘carbon (C) cascade’ to increase net primary production (NPP) and vegetation C stocks (C_veg) in different plant compartments. Vegetation models were criticised for being overly sensitive to photosynthesis (source-driven), neglecting sink-driven processes which may attenuate (or amplify) changes in NPP and vegetation C stocks. Here, we introduce an analytical framework to diagnose linearity (L) as ratios of relative changes in linked fluxes and pools. We then apply this framework to 16 models of the TRENDY v11 ensemble and to observation-based estimates of CO₂ sensitivities. We found widely varying global patterns in L across models. Six models showed a majority of grid cells with larger relative changes in NPP than in GPP (L_NPP:GPP > 1 for > 60% of gridcells), indicating increased vegetation carbon use efficiency under eCO₂. Only three models had L_NPP:GPP < 1 for > 60% of gridcells. Four models showed a majority of gridcells with larger relative changes in estimated steady-state C_veg than in NPP, while five models showed the opposite—in both cases with a large spread of L_Cveg*:NPP across grid cells within models. Observations-based analysis reveals median L_Cveg*:NPP < 1 overall but evidence is insufficient for a conclusion. Three models showed a larger relative increase in root C than in C_veg, (L_Croot:Cveg > 1) while five models showed the opposite. Most field evidence shows L_Croot:Cveg > 1. Widely differing distributions of L among models and links in the C cascade reveal a strong influence of nonlinear behaviour in individual models. However, due to the spread in L, across the whole models ensemble, L deviations from 1 were roughly balanced, leading to an overall linear behaviour of terrestrial C cycle representations in the multi-model-mean.

Original language	English
Article number	e70982
Journal	Global Change Biology
Volume	32
Issue number	7
DOIs	https://doi.org/10.1111/gcb.70982
Publication status	Published - 1 Jul 2026

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 2 Zero Hunger

Keywords

carbon allocation
carbon cycle
elevated CO
gross primary production
net primary production
vegetation models

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10.1111/gcb.70982

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Zhang-Zheng, H., Arora, V. K., Anthoni, P., Pugh, T. A. M., Jain, A. K., Yuan, W., Malhi, Y., Nabel, J., Goll, D. S., Pongratz, J., Poulter, B., Walker, A. P., Zaehle, S., Knauer, J., Kato, E., Ding, R., Tang, M., Sitch, S., O'Sullivan, M., ... Stocker, B. D. (2026). Diagnosing Linearity Along the Carbon Cascade in Terrestrial Biosphere Models and Observations. Global Change Biology, 32(7), Article e70982. https://doi.org/10.1111/gcb.70982

@article{669eeb78a8d046c6b6741c0cfcf94e2e,

title = "Diagnosing Linearity Along the Carbon Cascade in Terrestrial Biosphere Models and Observations",

abstract = "Elevated carbon dioxide (eCO2) acts as a fertiliser for photosynthesis, driving an increase in gross primary production (GPP). However, it is unclear how effectively increased GPP propagates along the {\textquoteleft}carbon (C) cascade{\textquoteright} to increase net primary production (NPP) and vegetation C stocks (Cveg) in different plant compartments. Vegetation models were criticised for being overly sensitive to photosynthesis (source-driven), neglecting sink-driven processes which may attenuate (or amplify) changes in NPP and vegetation C stocks. Here, we introduce an analytical framework to diagnose linearity (L) as ratios of relative changes in linked fluxes and pools. We then apply this framework to 16 models of the TRENDY v11 ensemble and to observation-based estimates of CO2 sensitivities. We found widely varying global patterns in L across models. Six models showed a majority of grid cells with larger relative changes in NPP than in GPP (LNPP:GPP > 1 for > 60\% of gridcells), indicating increased vegetation carbon use efficiency under eCO2. Only three models had LNPP:GPP < 1 for > 60\% of gridcells. Four models showed a majority of gridcells with larger relative changes in estimated steady-state Cveg than in NPP, while five models showed the opposite{\textemdash}in both cases with a large spread of LCveg*:NPP across grid cells within models. Observations-based analysis reveals median LCveg*:NPP < 1 overall but evidence is insufficient for a conclusion. Three models showed a larger relative increase in root C than in Cveg, (LCroot:Cveg > 1) while five models showed the opposite. Most field evidence shows LCroot:Cveg > 1. Widely differing distributions of L among models and links in the C cascade reveal a strong influence of nonlinear behaviour in individual models. However, due to the spread in L, across the whole models ensemble, L deviations from 1 were roughly balanced, leading to an overall linear behaviour of terrestrial C cycle representations in the multi-model-mean.",

keywords = "carbon allocation, carbon cycle, elevated CO, gross primary production, net primary production, vegetation models",

author = "Huanyuan Zhang-Zheng and Arora, \{Vivek K.\} and Peter Anthoni and Pugh, \{Thomas A.M.\} and Jain, \{Atul K.\} and Wenping Yuan and Yadvinder Malhi and Julia Nabel and Goll, \{Daniel S.\} and Julia Pongratz and Benjamin Poulter and Walker, \{Anthony P.\} and S{\"o}nke Zaehle and J{\"u}rgen Knauer and Etsushi Kato and Ruijie Ding and Minxue Tang and Stephen Sitch and Michael O'Sullivan and C{\'e}sar Terrer and Hanqin Tian and Naiqing Pan and Pierre Friedlingstein and Akihiko Ito and Qing Sun and Jeanne Decayeux and Stocker, \{Benjamin D.\}",

note = "Publisher Copyright: {\textcopyright} 2026 The Author(s). Global Change Biology published by John Wiley \& Sons Ltd.",

year = "2026",

month = jul,

day = "1",

doi = "10.1111/gcb.70982",

language = "English",

volume = "32",

journal = "Global Change Biology",

issn = "1354-1013",

publisher = "Wiley-Blackwell Publishing Ltd",

number = "7",

}

Zhang-Zheng, H, Arora, VK, Anthoni, P, Pugh, TAM, Jain, AK, Yuan, W, Malhi, Y, Nabel, J, Goll, DS, Pongratz, J, Poulter, B, Walker, AP, Zaehle, S, Knauer, J, Kato, E, Ding, R, Tang, M, Sitch, S, O'Sullivan, M, Terrer, C, Tian, H, Pan, N, Friedlingstein, P, Ito, A, Sun, Q, Decayeux, J & Stocker, BD 2026, 'Diagnosing Linearity Along the Carbon Cascade in Terrestrial Biosphere Models and Observations', Global Change Biology, vol. 32, no. 7, e70982. https://doi.org/10.1111/gcb.70982

TY - JOUR

T1 - Diagnosing Linearity Along the Carbon Cascade in Terrestrial Biosphere Models and Observations

AU - Zhang-Zheng, Huanyuan

AU - Arora, Vivek K.

AU - Anthoni, Peter

AU - Pugh, Thomas A.M.

AU - Jain, Atul K.

AU - Yuan, Wenping

AU - Malhi, Yadvinder

AU - Nabel, Julia

AU - Goll, Daniel S.

AU - Pongratz, Julia

AU - Poulter, Benjamin

AU - Walker, Anthony P.

AU - Zaehle, Sönke

AU - Knauer, Jürgen

AU - Kato, Etsushi

AU - Ding, Ruijie

AU - Tang, Minxue

AU - Sitch, Stephen

AU - O'Sullivan, Michael

AU - Terrer, César

AU - Tian, Hanqin

AU - Pan, Naiqing

AU - Friedlingstein, Pierre

AU - Ito, Akihiko

AU - Sun, Qing

AU - Decayeux, Jeanne

AU - Stocker, Benjamin D.

PY - 2026/7/1

Y1 - 2026/7/1

N2 - Elevated carbon dioxide (eCO2) acts as a fertiliser for photosynthesis, driving an increase in gross primary production (GPP). However, it is unclear how effectively increased GPP propagates along the ‘carbon (C) cascade’ to increase net primary production (NPP) and vegetation C stocks (Cveg) in different plant compartments. Vegetation models were criticised for being overly sensitive to photosynthesis (source-driven), neglecting sink-driven processes which may attenuate (or amplify) changes in NPP and vegetation C stocks. Here, we introduce an analytical framework to diagnose linearity (L) as ratios of relative changes in linked fluxes and pools. We then apply this framework to 16 models of the TRENDY v11 ensemble and to observation-based estimates of CO2 sensitivities. We found widely varying global patterns in L across models. Six models showed a majority of grid cells with larger relative changes in NPP than in GPP (LNPP:GPP > 1 for > 60% of gridcells), indicating increased vegetation carbon use efficiency under eCO2. Only three models had LNPP:GPP < 1 for > 60% of gridcells. Four models showed a majority of gridcells with larger relative changes in estimated steady-state Cveg than in NPP, while five models showed the opposite—in both cases with a large spread of LCveg*:NPP across grid cells within models. Observations-based analysis reveals median LCveg*:NPP < 1 overall but evidence is insufficient for a conclusion. Three models showed a larger relative increase in root C than in Cveg, (LCroot:Cveg > 1) while five models showed the opposite. Most field evidence shows LCroot:Cveg > 1. Widely differing distributions of L among models and links in the C cascade reveal a strong influence of nonlinear behaviour in individual models. However, due to the spread in L, across the whole models ensemble, L deviations from 1 were roughly balanced, leading to an overall linear behaviour of terrestrial C cycle representations in the multi-model-mean.

AB - Elevated carbon dioxide (eCO2) acts as a fertiliser for photosynthesis, driving an increase in gross primary production (GPP). However, it is unclear how effectively increased GPP propagates along the ‘carbon (C) cascade’ to increase net primary production (NPP) and vegetation C stocks (Cveg) in different plant compartments. Vegetation models were criticised for being overly sensitive to photosynthesis (source-driven), neglecting sink-driven processes which may attenuate (or amplify) changes in NPP and vegetation C stocks. Here, we introduce an analytical framework to diagnose linearity (L) as ratios of relative changes in linked fluxes and pools. We then apply this framework to 16 models of the TRENDY v11 ensemble and to observation-based estimates of CO2 sensitivities. We found widely varying global patterns in L across models. Six models showed a majority of grid cells with larger relative changes in NPP than in GPP (LNPP:GPP > 1 for > 60% of gridcells), indicating increased vegetation carbon use efficiency under eCO2. Only three models had LNPP:GPP < 1 for > 60% of gridcells. Four models showed a majority of gridcells with larger relative changes in estimated steady-state Cveg than in NPP, while five models showed the opposite—in both cases with a large spread of LCveg*:NPP across grid cells within models. Observations-based analysis reveals median LCveg*:NPP < 1 overall but evidence is insufficient for a conclusion. Three models showed a larger relative increase in root C than in Cveg, (LCroot:Cveg > 1) while five models showed the opposite. Most field evidence shows LCroot:Cveg > 1. Widely differing distributions of L among models and links in the C cascade reveal a strong influence of nonlinear behaviour in individual models. However, due to the spread in L, across the whole models ensemble, L deviations from 1 were roughly balanced, leading to an overall linear behaviour of terrestrial C cycle representations in the multi-model-mean.

KW - carbon allocation

KW - carbon cycle

KW - elevated CO

KW - gross primary production

KW - net primary production

KW - vegetation models

UR - https://www.scopus.com/pages/publications/105045899208

U2 - 10.1111/gcb.70982

DO - 10.1111/gcb.70982

M3 - Article

AN - SCOPUS:105045899208

SN - 1354-1013

VL - 32

JO - Global Change Biology

JF - Global Change Biology

IS - 7

M1 - e70982

ER -

Diagnosing Linearity Along the Carbon Cascade in Terrestrial Biosphere Models and Observations

Abstract

UN SDGs

Keywords

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