Diagnosing linearity along the carbon cascade in terrestrial biosphere models

Elevated carbon dioxide (eCO ₂ ) fertilises photosynthesis, driving an increase in terrestrial 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 simulate divergent C cycle projections and have been criticised for being overly photosynthesis-driven (source-driven), neglecting processes that lead to non-linear behaviour in response to the GPP increase, which may attenuate (or amplify) changes in NPP and vegetation C stocks. Here, we introduce an analytical framework to diagnose linearity ( L ) of the land C cycle as the ratio of relative changes in linked fluxes and pools and apply it to outputs from 16 models of the TRENDY v11 ensemble. We found widely varying patterns in L across models and for the different links. Six models showed a clear dominance of larger relative changes in NPP than in GPP in global simulations ( L _NPP:GPP >1 for >60% of gridcells), indicating increased carbon use efficiency under eCO ₂ . Only three models had L _NPP:GPP < 1 for >60% of gridcells. Four models showed a clear dominance of larger relative changes in steady-state C _veg than in NPP, while five models showed an opposite pattern - in both cases with a large spread of L _Cveg*:NPP across gridcells within models. Three models showed a larger relative increase in root C than in C _veg , while two models showed a clear dominance of the opposite pattern. Widely differing distributions of L across models and links reveal a strong influence of alternative process representations (nonlinear behaviour) in individual models. However, for all links, L deviations from 1 were roughly balanced across the model ensemble, leading to an overall linear behaviour of terrestrial C cycle representations.