Estimated remaining carbon budgets under terrestrial nutrient limitation

Nutrient limitation is a core regulation on the amount of carbon fixed by terrestrial vegetation. Hence, the addition of nutrients such as nitrogen and phosphorus in land model structures in Earth system models is essential for an accurate representation of the carbon cycle feedback in future climate projections. Thereby, the estimation of the remaining carbon budget is impacted by the regulation of nutrient limitation in terrestrial ecosystems, and yet it is rarely accounted for. Here, we estimate the carbon budget and remaining carbon budget of a nutrient limited Earth system model, using nitrogen and phosphorus cycles to limit vegetation productivity and biomass. We use eight Shared Socioeconomic Pathways scenarios on three distinct model structures: 1) carbon cycle without nutrient limitation, 2) carbon cycle with terrestrial nitrogen limitation and 3) carbon cycle with terrestrial nitrogen and phosphorus limitation. The three model structures were calibrated to historical temperature data, and to capture the uncertainty of the remaining carbon budget, three different climate sensitives were tuned for each model version. Our results show that overall the nutrient limitation reduced the remaining carbon budget for all simulations in comparison with the carbon cycle without nutrient limitation. Between the nitrogen and nitrogen-phosphorus limitation, the latter had the lowest remaining carbon budget. The mean remaining carbon budget from the Shared Socioeconomic Pathways scenarios simulations for the 1.5 °C target in the no nutrient limitation, nitrogen limited and nitrogen-phosphorus limited models obtained were 303±31, 280±40 and 241±28 Pg C respectively. As for the  2 °C target the mean remaining carbon budget were 517±193, 468±175 and 436±163 Pg C for the no nutrient limitation, nitrogen limited and nitrogen-phosphorus limited models respectively. This represents a reduction of 7.5 and 20.1% for the 1.5 °C target and 9.4 and 15.6% for the 2 °C target in the nitrogen and nitrogen-phosphorus limited simulations compared to the no nutrient limitation model. These results show that terrestrial nutrient limitations constitute an important factor to be considered when estimating or interpreting remaining carbon budgets and are an essential uncertainty of carbon budgets in Earth system models.