Overestimated natural biological nitrogen fixation translates to an exaggerated CO ₂ fertilization effect in Earth system models

CO₂ fertilization of the terrestrial biosphere is limited by nitrogen. Biological nitrogen fixation (BNF) is the dominant natural nitrogen source to the terrestrial biosphere and can alleviate nitrogen limitation but is poorly constrained in Earth system models (ESMs). Here, we compare terrestrial BNF from an ensemble of ESMs of the 6th Coupled Model Intercomparison Project to a new global synthesis of observations across natural and agricultural biomes. We find that compared to observations, ESMs underestimate agricultural BNF but overestimate natural BNF in the present day by over 50%. Natural BNF is overestimated in the most productive ecosystems that contribute most to the terrestrial carbon sink (forests and grasslands). ESMs with different BNF representations yield a range of BNF responses to CO₂ enrichment. Some ESMs with phenomenological representations of BNF predict a natural BNF increase in response to a doubling of CO₂ that aligns with a meta-analysis of CO₂ enrichment experiments (31% increase) but fail to account for the substantial carbon cost of BNF. In contrast, ESMs with mechanistic representations of BNF account for its carbon cost as well as its regulation by nitrogen limitation but overestimate the BNF response to a doubling of CO₂ (135% increase). Overall, all current BNF representations in ESMs fall short of fully capturing its response to rising atmospheric CO₂. Finally, we find a positive correlation between modeled present-day natural BNF and the CO₂ fertilization effect across ESMs, suggesting that overestimated natural BNF translates to an exaggerated CO₂ fertilization effect of approximately 11% in ESMs.